 NATURAL CONVECTIVE HEAT TRANSFER FROMINCLINED NARROW PLATES
ABSTRACT
Natural Convection flow in a vertical channel with internal objects is encountered in several technological applications of particular interest of heat dissipation from electronic circuits, refrigerators, heat exchangers, nuclear reactors fuel elements, dry cooling towers, and home ventilation etc.

In this thesis the air flow through vertical narrow plates is modeled using PRO-E design software. The thesis will focus on thermal and CFD analysis with different Reynolds number (2×106 & 4×106) and different angles (00,300,450&600) of the vertical narrow plates. Thermal analysis done for the vertical narrow plates by steel, aluminum & copper at different heat transfer coefficient values. These values are taken from CFD analysis at different Reynolds numbers.

In this thesis the CFD analysis to determine the heat transfer coefficient, heat transfer rate, mass flow rate, pressure drop and thermal analysis to determine the temperature distribution, heat flux with different materials.

3D modeled in parametric software Pro-Engineer and analysis done in ANSYS.

Chapter- 1
Natural Convection
In natural convection, the fluid motion occurs by natural means such as buoyancy. Since the fluid velocity associated with natural convection is relatively low, the heat transfer coefficient encountered in natural convection is also low.
Mechanisms of Natural Convection
Consider a hot object exposed to cold air. The temperature of the outside of the object will drop  (as a result of heat transfer with cold air), and the temperature of adjacent air to the object will rise. Consequently, the object is surrounded with a thin layer of warmer air and heat will be transferred from this layer to the outer layers of air.

Natural convection heat transfer from a hot body
The temperature of the air adjacent to the hot object is higher, thus its density is lower. As a resut, the heated air rises. This movement is called the natural convection current. Note that in the absence of this movement, heat transfer would be by conduction only and its rate would be much lower.

In a gravitational field, there is a net force that pushes a light fluid placed in a heavier fluid upwards. This force is called the buoyancy force.

Natural convection is a mechanism, or type of heat transport, in which the fluid motion is not generated by any external source (like a pump, fan, suction device, etc.) but only by density differences in the fluid occurring due to temperature gradients. In natural convection, fluid surrounding a heat source receives heat, becomes less dense and rises. The surrounding, cooler fluid then moves to replace it. This cooler fluid is then heated and the process continues, forming convection current; this process transfers heat energy from the bottom of the convection cell to top. The driving force for natural convection is buoyancy, a result of differences in fluid density. Because of this, the presence of a proper acceleration such as arises from resistance to gravity, or an equivalent force (arising from acceleration, centrifugal force or Coriolis effect), is essential for natural convection. For example, natural convection essentially does not operate in free-fall (inertial) environments, such as that of the orbiting International Space Station, where other heat transfer mechanisms are required to prevent electronic components from overheating.

Natural convection has attracted a great deal of attention from researchers because of its presence both in nature and engineering applications. In nature, convection cells formed from air raising above sunlight-warmed land or water are a major feature of all weather systems. Convection is also seen in the rising plume of hot air from fire, oceanic currents, and sea-wind formation (where upward convection is also modified by Coriolis forces). In engineering applications, convection is commonly visualized in the formation of microstructures during the cooling of molten metals, and fluid flows around shrouded heat-dissipation fins, and solar ponds. A very common industrial application of natural convection is free air cooling without the aid of fans: this can happen on small scales (computer chips) to large scale process equipment.

No bulk flow- no power consumption.

No noise- quiet operation.

Hardly any vibration.

Heat transfer coefficients are low.

Larger area requirement.
Orientation dependence.
Difficult to control.

First, there is no bulk flow in natural convection so we don’t have to consume any power to drive a pump or rotate a compressor or blower. Perhaps, because there is no power consumption required the natural convection may perhaps be called as free convection. Because there is no fluid flow equipment involved, associated with natural convection, there is no noise process of natural convection – almost invariably proceeds in a quiet fashion. Because there is no bulk flow, there is hardly any vibration associated with flow phenomenon or with equipment nearby.

The disadvantages compared to forced convection are – heat transfer coefficients in natural convection are low typically by an order of magnitude. If you look up the problems we have solved with the forced convectio0,n forced convection with air gave us heat transfer coefficient of the order of maybe 7500 Watt per meter squared Kelvin. With natural convection, the order of heat transfer coefficients with air would typically be10-12 Watt per meter squared Kelvin.With water, forced convection would easily provide heat transfer coefficients of the order of a 1000 Watt per meter squared Kelvin or even higher. Water during the process of natural convection will lead to heat transfer coefficient of the order of a few tens of Watts per meter squared Kelvin – maybe 20,30, 40 of that order perhaps 10000 and 50 that is about it.

Because the heat transfer coefficients are low, the area required for a given amount of transfer of heat is large. Because natural convection depends on density differences and gravity, the direction of gravity and the orientation of the surface plays a role and because there is no fluid flow, no blower to switch on or off, no velocity to adjust, natural convection is difficult to control.

Now let us look at some dimensionless numbers associated with the phenomenon of natural convection.

Natural Convection from a Vertical Plate
In this system heat is transferred from a vertical plate to a fluid moving parallel to it by natural convection. This will occur in any system wherein the density of the moving fluid varies with position. These phenomena will only be of significance when the moving fluid is minimally affected by forced convection.
When considering the flow of fluid is a result of heating, the following correlations can be used, assuming the fluid is an ideal diatomic, has adjacent to a vertical plate at constant temperature and the flow of the fluid is completely laminar.
Num = 0.478(Gr0.25)
Mean Nusselt Number = Num = hmL/k
Where
hm = mean coefficient applicable between the lower edge of the plate and any point in a distance L (W/m2. K)
L = height of the vertical surface (m)
k = thermal conductivity (W/m. K)
Grashof Number = Gr = gL3(ts?t?)/v2T{displaystyle gL^{3}(t_{s}-t_{infty })/v^{2}T} gL3(ts?t?)/v2T{displaystyle gL^{3}(t_{s}-t_{infty })/v^{2}T}
Where
g = gravitational acceleration (m/s2)
L = distance above the lower edge (m)
ts = temperature of the wall (K)
t? = fluid temperature outside the thermal boundary layer (K)
v = kinematic viscosity of the fluid (m²/s)
T = absolute temperature (K)
When the flow is turbulent different correlations involving the Rayleigh Number (a function of both the Grashof Number and the Prandtl Number) must be used.
Note that the above equation differs from the usual expression for Grashoff number because the value ?{displaystyle eta }has been replaced by its approximation1/T{displaystyle 1/T}, which applies for ideal gases only (a reasonable approximation for air at ambient pressure).

Natural or “Buoyant” or “Free” convection is a very important mechanism that is operative in a variety of environments from cooling electronic circuit boards in computers to causing large scale circulation in the atmosphere as well as in lakes and oceans that influences the weather. It is caused by the action of density gradients in conjunction with a gravitational field. This is a brief introduction that will help you understand the qualitative features of a variety of situations you might encounter.

There are two basic scenarios in the context of natural convection. In one, a density gradient exists in a fluid in a direction that is parallel to the gravity vector or opposite to it. Such situations can lead to “stable” or “unstable” density stratification of the fluid. In a stable stratification, less dense fluid is at the top and more dense fluid at the bottom. In the absence of other effects, convection will be absent, and we can treat the heat transfer problem as one of conduction. In an unstable stratification, in which less dense fluid is at the bottom, and more dense fluid at the top, provided the density gradient is sufficiently large, convection will start spontaneously and significant mixing of the fluid will occur.

Hot
Cold
Fluid
Fluid
?T?T
Cold
Hot
StableUnstable
You should note that density gradients can arise not only from temperature gradients, but also from composition gradients even in an isothermal system. Here, we restrict our discussion to the case when temperature gradients are the source of the density gradients.

The more common situation that we encounter in heat transfer is one in which there is a density gradient perpendicular to the gravity vector. Consider a burning candle. The air next to the hot candle flame is hot, whereas the air laterally farther from it is relatively cooler. This will set up a natural convection flow around the candle, in which the cool surrounding air approaches the surface of the candle, rises, and flows in a hot plume above the flame. It is this flow that causes
the visible flame to take the shape it does. In the absence of gravity, a candle flame would be spherical.

Another example is the flow of air at the tip of a lit cigarette; in this case, the smoke from the cigarette actually traces that flow for us. In a common technique used for home heating, the baseboard heater consists of a tube through which hot water flows, and the heater is placed close to the floor. The tube is outfitted with fins to provide additional heat transfer surface. The neighboring air is heated, and the hot air rises, with cooler air moving in toward the baseboard at floor level. This natural convection circulation set up by the hot baseboard provides a simple mixing mechanism for the air in the room and helps us maintain a relatively uniform temperature everywhere. Clearly, the convection helps the heat transfer process here.

Natural Convection adjacent to a heated vertical surface
Consider a hot vertical surface present in a fluid. The surface is maintained at a temperature Ts , which is larger than the ambient temperature in the fluid Te . Here is a sketch of the momentum boundary layer along the plate.

?m
TsTe
As shown in the sketch, the cold fluid rises along the plate surface, becoming heated in the process, and the momentum boundary layer grows in thickness with distance along the plate. A sample velocity profile in the momentum boundary layer is shown. Note that in this type of boundary layer, the velocity must be zero not only at the solid surface, but also at the edge of the boundary layer. Because the profile was sketched free-hand in PowerPoint, I am unable to show the smooth approach to zero velocity with a zero slope at the edge of the boundary layer properly, but that is how the correct velocity profile would appear. Compare this velocity profile with that in a momentum boundary layer that forms on a flat plate when fluid approaches it with a uniform velocity U??. You should try to make a sketch of the thermal boundary layer on the same plate when the fluid is air, for example, and also when it is a viscous liquid with a Prandtl number that is large compared with unity.

Now, let us consider a typical window in a home on a winter day when the outside air is at . What will the momentum boundary and the inside of the room is at a balmy 68 F10 F layers on either side of the window look like? Try to sketch them yourself before looking at the sketch. The arrows in the sketch show the direction of air flow at the location where the air enters the boundary layer on the inside as well as on the outside, and the direction of air flow within the boundary layer. There is a slight transverse flow in each boundary layer, but on the scale of the picture, it is difficult to use the arrows to show it; therefore, I have drawn the flow in the boundary layers as being vertically downward or upward as appropriate.

Other natural convection flows Mills recommends suitable correlations for natural convection flow over a horizontal heated cylinder and a heated sphere. For other objects of arbitrary shape, he recommends a correlation due to Lienhard. 6 1/4 0.52 Nu Ra average = Here the length L to be used in both the Nusselt and Rayleigh numbers is the length of the boundary layer; for example, L R = ? for a cylinder or sphere of radius R . But for those two geometries it is better to use the specific correlations given in the textbook by Mills. Mills also provides some useful correlations for natural convection in enclosures. Windows used in homes are termed “single-pane” or “thermopane.” A single pane window is a glass plate that separates the inside of a room from the outside.
Heat transfer between the indoor air and the air outside occurs by conduction through the glass, and the heat transfer rate can be large. Therefore, the “thermopane” window was designed to reduce the heat loss by using two glass plates with a small gap between them. Let us assume the gap is filled with air, and for the sake of simplicity, that the plates are wide and long, and are each maintained at a uniform temperature. The sketch given below is taken from a textbook by Bird et al. (2); it depicts the temperature distribution between the two plates and the resulting natural convection velocity distribution.

Note that even though there is convection in the air, it does not influence the heat flux through the air gap, because the temperature distribution still remains linear at this order of approximation. The air gap significantly increases the thermal resistance of the window and reduces the heat flux between the outside air and that inside the room. In modern thermopane windows, the gap between the two plates is evacuated, so that the heat transfer rate is further reduced, at least initially when the window is new. Over time, air leaks through the seals into the gap, increasing heat loss in the winter and heat gain in the summer. It is worth noting that as the gap width is increased, the velocity in the gap increases proportionally to the cube of the gap width. At larger gap widths, the temperature profile is no longer linear, and the convection actually increases the heat flux through the gap over that occurring due to pure conduction. This is the reason for the choice of a small width of the order of 1-2 mm for the air gap in thermo pane windows.

Chapter -2
LITERATURE REVIEW
In 1972, Aung et al. 12 presented a coupled numerical experimental study. Under isothermal conditions at high Rayleigh numbers their experimental results were 10% lower than the numerical ones. This difference has also been observed between Bodoia’s and Osterle’s numerical results 8 and Elenbaas’ experimental ones 7. They ascribed the discrepancies to the assumption of a flat velocity profile at the channel inlet.

However, the difference could also be attributed to the 2D hypothesis for the numerical simulations. In their 2D simulations in 1981, Dalbert et al. 13 introduced a pressure loss at the channel inlet in order to satisfy the Bernoulli equation between the hydrostatic conditions far from the channel and the channel inlet. Their results agreed better with the vertical flat plate regime than those of previous studies.

In 2004, Olsson 17 presented a similar study. He worked on the different existing correlations, including those of Bar-Cohen and Rohsenow, and compared them with experimental results. Finaly he proposed some corrected correlations that are valid for a wide range of Rayleigh numbers. In 1989,Webb and Hill 18 studied the laminar convective flow in an experimental asymmetrically heated vertical channel. They worked on isoflux heating with a modified Rayleigh number (see eq. 13) changing from 500 to 107. Their temperature measurements performed in horizontal direction on the heated wall showed variations of ± 1.5%, and the flow was assumed to be 2D. They studied correlations for local, average and higher channel Nusselt numbers and compared them to previous works (9, 10and 11). Their correlations were calculated for pure convective
flow and the radiation losses were estimated and subtracted from the heat input. They found that constants C1and C2 were strongly dependent on modified Rayleigh numbers
below Ra_b _ 105 but that they were independent for higher Rayleigh numbers. Good agreement was seen between their resultsfor high Rayleigh numbers and the flat plate solution of Sparrow and Gregg 10. However, in the log-log diagram theslope of their correlation was found to be 11% higher than theanalytical one. They explained this difference by the uncertaintyon correction for radiation and conduction losses and the
variation of the thermophysical properties with temperature.

The papers listed above dealt with laminar free convection, but in BIPV applications flows are mainly turbulent. The firstauthors to study turbulent free convective flow in a vertical channel were Borgers and Akbari in 1984 19. They simulated an isothermally heated 2D channel and used former studies on turbulent vertical flat plate flows to develop a code capable of modeling the transition from laminar to turbulent flow. They gave correlations to predict flow rate and heat transfer in turbulent was developed by Miyamoto et al. in 1986 20. They work done a 5 m high and 50 – 200 mm wide channel asymmetrically heated under iso flux conditions. They focused on the transition from laminar to turbulent regime via velocity and temperature profiles. The flow was seen to be fully turbulent up to 4 min all the experiments. In 1997, Fedorov et Viskanta 21 present eda numerical simulation based on Miyamoto’s results. In their simulations radiative heat transfers between surfaces were

Chapter -3
Problem description ; methodology
Air flow through vertical narrow plates is modeled using PRO-E design software. The thesis will focus on thermal and CFD analysis with different Reynolds number (2×106 ; 4×106) and different angles (00,300,450;600) of the vertical narrow plates. Thermal analysis done for the vertical narrow plates by steel, aluminum ; copper at different heat transfer coefficient values.

Reynolds numbers Angle of plate material
2×106 00,300,450;600 Copper
4×106 aluminum
steel
Chapter-4
Throughout the history of our industrial society, many inventions have been patented and
whole new technologies have evolved. Perhaps the single development that has impacted
manufacturing more quickly and significantly than any previous technology is the digital computer. Computers are being used increasingly for both design and detailing of engineering components in the drawing office. Computer-aided design (CAD) is defined as the application of computers and graphics software to aid or enhance the product design from conceptualization to documentation. CAD is most commonly associated with the use of an interactive computer graphics system, referred to as a CAD system. Computer-aided design systems are powerful tools and in the mechanical design and geometric modeling of products and components.

There are several good reasons for using a CAD system to support the engineering design
Function:
To increase the productivity
To improve the quality of the design
To uniform design standards
To create a manufacturing data base
To eliminate inaccuracies caused by hand-copying of drawings and inconsistency between
Drawings
Software allows the human user to turn a hardware configuration into a powerful design and manufacturing system. CAD/CAM software falls into two broad categories,2-D and 3-D, based on the number of dimensions are called 2-D representations of 3-D objects is inherently confusing. Equally problem has been the inability of manufacturing personnel to properly read and interpret complicated 2-D representations of objects. 3-D software permits the parts to be viewed with the 3-D planes-height, width, and depth-visible. The trend in CAD/CAM is toward 3-D representation of graphic images. Such representation approximates the actual shape and appearance of the object to be produced; therefore, they are easier to read and understand.

The emergence of CAD/CAM has had a major impact on manufacturing, by standardizing product development and by reducing design effort, tryout, and prototype work; it has made possible significantly reduced costs and improved productivity.

Some typical applications of CAD/CAM are as follows:
Programming for NC, CNC, and industrial robots;
Design of dies and molds for casting, in which, for example, shrinkage
allowances are preprogrammed;
Design of tools and fixtures and EDM electrodes;
Quality control and inspection—-for instance, coordinate-measuring
machines programmed on a CAD/CAM workstation;
Process planning and scheduling.

INTRODUCTION TO PRO/ENGINEER
Pro/ENGINEER, PTC’s parametric, integrated 3D CAD/CAM/CAE solution, is used by discrete manufacturers for mechanical engineering, design and manufacturing.

Created by Dr. Samuel P. Geisberg in the mid-1980s, Pro/ENGINEER was the industry’s first successful parametric, 3D CAD modeling system. The parametric modeling approach uses parameters, dimensions, features, and relationships to capture intended product behavior and create a recipe which enables design automation and the optimization of design and product development processes.

This powerful and rich design approach is used by companies whose product strategy is family-based or platform-driven, where a prescriptive design strategy is critical to the success of the design process by embedding engineering constraints and relationships to quickly optimize the design, or where the resulting geometry may be complex or based upon equations. Pro/ENGINEER provides a complete set of design, analysis and manufacturing capabilities on one, integral, scalable platform. These capabilities, include Solid Modeling, Surfacing, Rendering, Data Interoperability, Routed Systems Design, Simulation, Tolerance Analysis, and    NC and Tooling Design.

Companies use Pro/ENGINEER to create a complete 3D digital model of their products. The models consist of 2D and 3D solid model data which can also be used downstream in finite element analysis, rapid prototyping, tooling design, and CNC manufacturing. All data is associative and interchangeable between the CAD, CAE and CAM modules without conversion. A product and its entire bill of materials(BOM) can be modeled accurately with fully associative engineering drawings, and revision control information. The associativity in Pro/ENGINEER enables users to make changes in the design at any time during the product development process and automatically update downstream deliverables. This capability enables concurrent engineering — design, analysis and manufacturing engineers working in parallel — and streamlines product development processes.

Pro/ENGINEER is an integral part of a broader product development system developed by PTC. It seamlessly connects to PTC’s other solutions including Wind-chill, Product View, MathCAD and Arbor text.

DIFFERENT MODULES IN PRO/ENGINEER
PART DESIGN
ASSEMBLY
DRAWING
SHEETMETAL
MANUFACTURING
INTRODUCTION TO FINITE ELEMENT METHOD
Finite Element Method (FEM) is also called as Finite Element Analysis (FEA). Finite Element Method is a basic analysis technique for resolving and substituting complicated problems by simpler ones, obtaining approximate solutions Finite element method being a flexible tool is used in various industries to solve several practical engineering problems. In finite element method it is feasible to generate the relative results.

In the present day, finite element method is one of the most effective and widely used tools. By doing more computational analysis the approximate solution can be improved or refined in Finite element method. In Finite element method, matrices play an important role in handling large number of equations. The procedure for FEM is a Variation approach where this concept has contributed substantially in formulating the method.

FEM/FEA helps in evaluating complicated structures in a system during the planning stage. The strength and design of the model can be improved with the help of computers and FEA which justifies the cost of the analysis. FEA has prominently increased the design of the structures that were built many years ago.

General Description of FEM:
To acquire a solution for a continuum problem by FEM, the procedure follows an orderly step by step process. The step- by step procedure is as follows:
1. Discretization of the Structure: The first step involves dividing the structure into elements. Therefore suitable finite element should be used to model the structure.

2. Selection of a proper interpolation or displacement model: Since the displacement solution is not known exactly for a complex structure under any given load, we assume an approximate solution. The assumed solution must be simple and should satisfy the convergence requirements. In general, interpolation or displacement model should be in polynomial form.

3. Derivation of element stiffness matrices and load vector: From the second step, stiffness matrix k^ (e) and load vector P^ (e) of element e is solved from either equilibrium conditions or variation principle.

4. Assemblage of element equations to obtain the overall equilibrium equation: Since the structure is divided into several finite elements, load vector and individual element stiffness matrices are arranged in a suitable manner. From this, the overall equilibrium equation is formulated as
K? = P
Where k = assembled stiffness matrix.

? = vector of nodal displacement.

P = vector of nodal forces for the complete structure.

Computation of element strains and stresses:
Since ? is known, element strain and stress are computed using necessary equations.

Engineering Applications of Finite Element Method:
Initially FEM method was used for only structural mechanics problems but over the years researchers have successfully applied it to various engineering problems. It has been validated that this method can be used for other numerical solution of ordinary and partial differential equations.

The finite element method is applicable to three categories of boundary value problems:
Equilibrium or Steady State or Time-Independent problems
Eigen value problems
Propagation or transient problems
Various applications of FEM:
Civil Engineering Structures
Aircraft Structures
Heat Conduction
Geo-mechanics
Hydraulic and Water Resource Engineering
Nuclear engineering
Bio-Medical Engineering
Mechanical Engineering
Electrical Machines and Electromagnetic
Non-linear problems are easily solved.

Several types of problems can be solved with easy formulation.

Reduces the costs in the development of new products.

Improves the quality of the end product.

Life of the product is increased.

Rapid development of new products
High product reliability.

Product fabrication process is enhanced.

Extreme aspect ratios can cause problems.

Not well suited for open region problems.

ANSYS Software:
ANSYS is an Engineering Simulation Software (computer aided Engineering). Its tools cover Thermal, Static, Dynamic, and Fatigue finite element analysis along with other tools all designed to help with the development of the product. The company was founded in 1970 by Dr. John A. Swanson as Swanson Analysis Systems, Inc. SASI. Its primary purpose was to develop and market finite element analysis software for structural physics that could simulate static (stationary), dynamic (moving) and heat transfer (thermal) problems. SASI developed its business in parallel with the growth in computer technology and engineering needs. The company grew by 10 percent to 20 percent each year, and in 1994 it was sold. The new owners took SASI’s leading software, called ANSYS®, as their flagship product and designated ANSYS, Inc. as the new company name.

Benefits of ANSYS:
The ANSYS advantage and benefits of using a modular simulation system in the design process are well documented. According to studies performed by the Aberdeen Group, best-in-class companies perform more simulations earlier. As a leader in virtual prototyping, ANSYS is unmatched in terms of functionality and power necessary to optimize components and systems.

ANSYS is a virtual prototyping and modular simulation system that is easy to use and extends to meet customer needs; making it a low-risk investment that can expand as value is demonstrated within a company. It is scalable to all levels of the organization, degrees of analysis complexity, and stages of product development.

Structural Analysis:
Structural analysis is probably the most common application of the finite element method. The term structural (or structure) implies not only civil engineering structures such as ship hulls, aircraft bodies, and machine housings, as well as mechanical components such as pistons, machine parts, and tools.

Types of Structural Analysis:
Different types of structural analysis are:
Static analysis
Modal analysis
Harmonic analysis
Transient dynamic analysis
Spectrum analysis
Bucking analysis
Explicit dynamic analysis
Static Analysis:
Static analysis calculates the effects of steady loading conditions on a structure, while ignoring inertia and damping effects, such as those caused by time varying loads. A static analysis can, however, include steady inertia loads (such as gravity and rotational velocity), and time-varying loads that can be approximated as static equivalent loads (such as the static equivalent wind arid seismic loads commonly defined in many building codes).

Static analysis is used to determine the displacements, stresses, strains, and forces in structural components caused by loads that do not induce significant inertia and damping effects. Steady loading and response are assumed to vary slowly with respect to time.

The kinds of loading that can be applied in a static analysis include:
Externally applied forces and pressures
Steady-state inertial forces (such as gravity or rotational velocity)
Imposed (non-zero) displacements
Temperatures (for thermal stain)
A static analysis can be either linear or non-linear. All types of non-linearities are allowed-large deformations, plasticity, creep, stress, stiffening, contact (gap) elements, hyper elastic elements, and so on.

Over-view of steps in a static analysis:
The procedure for a modal analysis consists of three main steps:
Build the model.

Apply loads and obtain the solution.
Review the results.

Basic Steps in ANSYS:

Pre-Processing (Defining the Problem): The major steps in pre-processing are given below
Define key points/lines/ areas/volumes.

Define element type and material/geometric properties
Mesh lines/ areas/volumes as required.

The amount of detail required will depend on the dimensionality of the analysis (i.e., 1D, 2D, axi-symmetric, 3D).

Solution (Assigning Loads, Constraints, And Solving): Here the loads (point or pressure), constraints (translational and rotational) are specified and finally solve the resulting set of equations.

Post Processing: In this stage, further processing and viewing of the results can be done such as:
Lists of nodal displacements
Element forces and moments
Deflection plots
Stress contour diagrams
ANSYS provides a comprehensive set of post-processing tools to display results on the models as contours or vector plots, provide summaries of the results (like min/max values and locations). Powerful and intuitive slicing techniques allow getting more detailed results over given parts of your geometries. All the results can also be exported as text data or to a spreadsheet for further calculations. Animations are provided for static cases as well as for nonlinear or transient histories. Any result or boundary condition can be used to create customized charts.

INTRODUCTION TO CFD
Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial experimental validation of such software is performed using a wind tunnel with the final validation coming in full-scale testing, e.g. flight tests.

BACKGROUND AND HISTORY

A computer simulation of high velocity air flow around the Space Shuttle during re-entry.

A simulation of the Hyper-X scramjet vehicle in operation at Mach-7
The fundamental basis of almost all CFD problems are the Navier–Stokes equations, which define any single-phase (gas or liquid, but not both) fluid flow. These equations can be simplified by removing terms describing viscous actions to yield the Euler equations. Further simplification, by removing terms describing vorticity yields the full potential equations. Finally, for small perturbations in subsonic and supersonic flows (not transonic or hypersonic) these equations can be linearized to yield the linearized potential equations.

Historically, methods were first developed to solve the linearized potential equations. Two-dimensional (2D) methods, using conformal transformations of the flow about a cylinder to the flow about an airfoil were developed in the 1930s.

One of the earliest type of calculations resembling modern CFD are those by Lewis Fry Richardson, in the sense that these calculations used finite differences and divided the physical space in cells. Although they failed dramatically, these calculations, together with Richardson’s book “Weather prediction by numerical process”, set the basis for modern CFD and numerical meteorology. In fact, early CFD calculations during the 1940s using ENIAC used methods close to those in Richardson’s 1922 book.

The computer power available paced development of three-dimensional methods. Probably the first work using computers to model fluid flow, as governed by the Navier-Stokes equations, was performed at Los Alamos National Labs, in the T3 group. This group was led by Francis H. Harlow, who is widely considered as one of the pioneers of CFD. From 1957 to late 1960s, this group developed a variety of numerical methods to simulate transient two-dimensional fluid flows, such as Particle-in-cell method (Harlow, 1957), Fluid-in-cell method (Gentry, Martin and Daly, 1966), Vorticity stream function method (Jake Fromm, 1963),8 and Marker-and-cell method (Harlow and Welch, 1965). Fromm’s vorticity-stream-function method for 2D, transient, incompressible flow was the first treatment of strongly contorting incompressible flows in the world.

The first paper with three-dimensional model was published by John Hess and A.M.O. Smith of Douglas Aircraft in 1967. This method discretized the surface of the geometry with panels, giving rise to this class of programs being called Panel Methods. Their method itself was simplified, in that it did not include lifting flows and hence was mainly applied to ship hulls and aircraft fuselages. The first lifting Panel Code (A230) was described in a paper written by Paul Rubbert and Gary Saaris of Boeing Aircraft in 1968. In time, more advanced three-dimensional Panel Codes were developed at Boeing (PANAIR, A502), Lockheed (Quadpan), Douglas (HESS), McDonnell Aircraft (MACAERO), NASA (PMARC) and Analytical Methods (WBAERO, USAERO and VSAERO. Some (PANAIR, HESS and MACAERO) were higher order codes, using higher order distributions of surface singularities, while others (Quadpan, PMARC, USAERO and VSAERO) used single singularities on each surface panel. The advantage of the lower order codes was that they ran much faster on the computers of the time. Today, VSAERO has grown to be a multi-order code and is the most widely used program of this class. It has been used in the development of many submarines, surface ships, automobiles, helicopters, aircraft, and more recently wind turbines. Its sister code, USAERO is an unsteady panel method that has also been used for modeling such things as high speed trains and racing yachts. The NASA PMARC code from an early version of VSAERO and a derivative of PMARC, named CMARC, is also commercially available.

In the two-dimensional realm, a number of Panel Codes have been developed for airfoil analysis and design. The codes typically have a boundary layer analysis included, so that viscous effects can be modeled. Professor Richard Eppler of the University of Stuttgart developed the PROFILE code, partly with NASA funding, which became available in the early 1980s. This was soon followed by MIT Professor Mark Drela’s XFOIL code. Both PROFILE and XFOIL incorporate two-dimensional panel codes, with coupled boundary layer codes for airfoil analysis work. PROFILE uses a conformal transformation method for inverse airfoil design, while XFOIL has both a conformal transformation and an inverse panel method for airfoil design.

An intermediate step between Panel Codes and Full Potential codes were codes that used the Transonic Small Disturbance equations. In particular, the three-dimensional WIBCO code, developed by Charlie Boppe of Grumman Aircraft in the early 1980s has seen heavy use.

Developers turned to Full Potential codes, as panel methods could not calculate the non-linear flow present at transonic speeds. The first description of a means of using the Full Potential equations was published by Earll Murman and Julian Cole of Boeing in 1970. Frances Bauer, Paul Garabedian and David Korn of the Courant Institute at New York University (NYU) wrote a series of two-dimensional Full Potential airfoil codes that were widely used, the most important being named Program H. A further growth of Program H was developed by Bob Melnik and his group at Grumman Aerospace as Grumfoil. Antony Jameson, originally at Grumman Aircraft and the Courant Institute of NYU, worked with David Caughey to develop the important three-dimensional Full Potential
code FLO22 in 1975. Many Full Potential codes emerged after this, culminating in Boeing’s Tranair (A633) code, which still sees heavy use.

The next step was the Euler equations, which promised to provide more accurate solutions of transonic flows. The methodology used by Jameson in his three-dimensional FLO57 code (1981) was used by others to produce such programs as Lockheed’s TEAM program and IAI/Analytical Methods’ MGAERO program. MGAERO is unique in being a structured cartesian mesh code, while most other such codes use structured body-fitted grids (with the exception of NASA’s highly successful CART3D code, Lockheed’s SPLITFLOW code34 and Georgia Tech’s NASCART-GT). Antony Jameson also developed the three-dimensional AIRPLANE code which made use of unstructured tetrahedral grids.

In the two-dimensional realm, Mark Drela and Michael Giles, then graduate students at MIT, developed the ISES Euler program (actually a suite of programs) for airfoil design and analysis. This code first became available in 1986 and has been further developed to design, analyze and optimize single or multi-element airfoils, as the MSES program. MSES sees wide use throughout the world. A derivative of MSES, for the design and analysis of airfoils in a cascade, is MISES,developed by Harold “Guppy” Youngren while he was a graduate student at MIT. The Navier–Stokes equations were the ultimate target of developers. Two-dimensional codes, such as NASA Ames’ ARC2D code first emerged. A number of three-dimensional codes were developed (ARC3D, OVERFLOW, CFL3D are three successful NASA contributions), leading to numerous commercial packages.

Methodology
In all of these approaches the same basic procedure is followed.

During preprocessingThe geometry (physical bounds) of the problem is defined.

The volume occupied by the fluid is divided into discrete cells (the mesh). The mesh may be uniform or non-uniform.

The physical modeling is defined – for example, the equations of motion + enthalpy + radiation + species conservation
Boundary conditions are defined. This involves specifying the fluid behaviour and properties at the boundaries of the problem. For transient problems, the initial conditions are also defined.

The simulation is started and the equations are solved iteratively as a steady-state or transient.

Chapter-5
MODELLING AND ANALYSIS
Models of narrow plate using pro-e wildfire 5.0
The vertical narrow plate is modeled using the given specifications and design formula from data book. The isometric view of vertical narrow plate is shown in below figure. The vertical narrow plate profile is sketched in sketcher and then it is extruded vertical narrow plate using extrude option.

Vertical narrow plate at 00 3D model vertical narrow plates at 00 2D models

Vertical narrow plate at 300 3D model vertical narrow plates at 300 2D models

Vertical narrow plate at 450 3D model vertical narrow plates at 450 2D models

Vertical narrow plate at 600 3D model vertical narrow plates at 600 2D models

VERTICAL NARROW PLATE SURFACE MODELS
Vertical narrow plate at 00 3D modelsVertical narrow plate at 300 3D models

Vertical narrow plate at 450 3D modelsVertical narrow plate at 600 3D models

CFD ANALYSIS OF VERTICAL NARROW PLATES
REYNOLDS NUMBER 2×106, 4×106
FLUID –AIR
MATERIAL PROPERTIES OF AIR
Thermal conductivity = 0.024w/m-k
Density=1.225kg/m3
Viscosity =1.98×10-5 kg/m-s
??Ansys ? workbench? select analysis system ? fluid flow fluent ? double click
??Select geometry ? right click ? import geometry ? select browse ?open part ? ok

?? select mesh on work bench ? right click ?edit ? select mesh on left side part tree ? right click ? generate mesh ?

The model is designed with the help of pro-e and then import on ANSYS for Meshing and analysis. The analysis by CFD is used in order to calculating pressure profile and temperature distribution. For meshing, the fluid ring is divided into two connected volumes. Then all thickness edges are meshed with 360 intervals. A tetrahedral structure mesh is used. So the total number of nodes and elements is 6576 and 3344.

Select faces ? right click ? create named section ? enter name ? water inlet
Select faces ? right click ? create named section ? enter name ? water outlet

Model ? energy equation ? on.

Viscous ? edit ? k- epsilon
Enhanced Wall Treatment ? ok
Materials ? new ? create or edit ? specify fluid material or specify properties ? ok
Select air and water
Boundary conditions ? select water inlet ? Edit ? Enter Water Flow Rate ? 2Kg/s and Inlet Temperature – 353K
Solution ? Solution Initialization ? Hybrid Initialization ?done
Run calculations ? no of iterations = 50 ? calculate ? calculation complete
?? Results ? graphics and animations ? contours ? setup

VERTICAL NARROW PLATE AT 00
REYNOLDS NUMBER – 2×106
STATIC PRESSURE

According to the above contour plot, the maximum static pressure at inlet of the narrow plate because the applying the boundary conditions at inlet of the boundary and minimum static pressure at the adjacent sides of the narrow plate. According to the above contour plot, the maximum pressure is 2.50e+04Pa and minimum static pressure is -2.14e+04Pa.

VELOCITY

According to the above contour plot, the maximum velocity magnitude of the air at corners of narrow plate, because the applying the boundary conditions at inlet of the boundary of the narrow plate and minimum velocity magnitude at around edges of the narrow plate. According to the above contour plot, the maximum velocity is 2.22e+02m/s and minimum velocity is 1.11e+01m/s.

HEAT TRANSFER COEFFICIENT

According to the above contour plot, the maximum heat transfer coefficient of the air at edges of the narrow plate and minimum heat transfer coefficient between around the boundary edges and narrow plate edges. According to the above contour plot, the maximum heat transfer coefficient is 3.14e+02w/m2-k and minimum heat transfer coefficient is 1.57e+01w/m2-k.

MASS FLOW RATE

HEAT TRANSFER RATE

REYNOLDS NUMBER – 4×106
STATIC PRESSURE

According to the above contour plot, the maximum static pressure at inlet of the narrow plate because the applying the boundary conditions at inlet of the boundary and minimum static pressure at the adjacent sides of the narrow plate. According to the above contour plot, the maximum pressure is 1.03e+05Pa and minimum static pressure is -8.57e+04Pa.

VELOCITY

According to the above contour plot, the maximum velocity magnitude of the air at corners of narrow plate, because the applying the boundary conditions at inlet of the boundary of the narrow plate and minimum velocity magnitude at around edges of the narrow plate. According to the above contour plot, the maximum velocity is 4.44e+02m/s and minimum velocity is 2.22e+01m/s.

HEAT TRANSFER COEFFICIENT

According to the above contour plot, the maximum heat transfer coefficient of the air at edges of the narrow plate and minimum heat transfer coefficient between around the boundary edges and narrow plate edges. According to the above contour plot, the maximum heat transfer coefficient is 5.52e+02w/m2-k and minimum heat transfer coefficient is 2.76e+01w/m2-k.

MASS FLOW RATE

HEAT TRANSFER RATE

VERTICAL NARROW PLATE AT 300
REYNOLDS NUMBER – 2×106
STATIC PRESSURE

According to the above contour plot, the maximum static pressure at inlet of the narrow plate because the applying the boundary conditions at inlet of the boundary and minimum static pressure at the adjacent sides of the narrow plate. According to the above contour plot, the maximum pressure is 3.25e+04Pa and minimum static pressure is -5.05e+04Pa.

VELOCITY

According to the above contour plot, the maximum velocity magnitude of the air at corners of narrow plate, because the applying the boundary conditions at inlet of the boundary of the narrow plate and minimum velocity magnitude at around edges of the narrow plate. According to the above contour plot, the maximum velocity is 2.80e+02m/s and minimum velocity is 1.40e+01m/s.

HEAT TRANSFER COEFFICIENT

According to the above contour plot, the maximum heat transfer coefficient of the air at edges of the narrow plate and minimum heat transfer coefficient between around the boundary edges and narrow plate edges. According to the above contour plot, the maximum heat transfer coefficient is 3.39e+02w/m2-k and minimum heat transfer coefficient is 1.70e+01w/m2-k.

MASS FLOW RATE

HEAT TRANSFER RATE

REYNOLDS NUMBER – 4×106
STATIC PRESSURE

According to the above contour plot, the maximum static pressure at inlet of the narrow plate because the applying the boundary conditions at inlet of the boundary and minimum static pressure at the adjacent sides of the narrow plate. According to the above contour plot, the maximum pressure is 1.31e+05Pa and minimum static pressure is -2.03e+05Pa.

VELOCITY

According to the above contour plot, the maximum velocity magnitude of the air at corners of narrow plate, because the applying the boundary conditions at inlet of the boundary of the narrow plate and minimum velocity magnitude at around edges of the narrow plate. According to the above contour plot, the maximum velocity is 5.60e+02m/s and minimum velocity is 2.80e+01m/s.

HEAT TRANSFER COEFFICIENT

According to the above contour plot, the maximum heat transfer coefficient of the air at edges of the narrow plate and minimum heat transfer coefficient between around the boundary edges and narrow plate edges. According to the above contour plot, the maximum heat transfer coefficient is 5.95e+02w/m2-k and minimum heat transfer coefficient is 2.97 e+01w/m2-k.

MASS FLOW RATE

HEAT TRANSFER RATE

VERTICAL NARROW PLATE AT 450
REYNOLDS NUMBER – 2×106
STATIC PRESSURE

According to the above contour plot, the maximum static pressure at inlet of the narrow plate because the applying the boundary conditions at inlet of the boundary and minimum static pressure at the adjacent sides of the narrow plate. According to the above contour plot, the maximum pressure is 6.49e+04Pa and minimum static pressure is -6.45e+04Pa.

VELOCITY

According to the above contour plot, the maximum velocity magnitude of the air at corners of narrow plate, because the applying the boundary conditions at inlet of the boundary of the narrow plate and minimum velocity magnitude at around edges of the narrow plate. According to the above contour plot, the maximum velocity is 3.40 e+02m/s and minimum velocity is 1.70e+01m/s.

HEAT TRANSFER COEFFICIENT

According to the above contour plot, the maximum heat transfer coefficient of the air at edges of the narrow plate and minimum heat transfer coefficient between around the boundary edges and narrow plate edges. According to the above contour plot, the maximum heat transfer coefficient is 4.06e+02w/m2-k and minimum heat transfer coefficient is 2.03e+01w/m2-k.

MASS FLOW RATE

HEAT TRANSFER RATE

REYNOLDS NUMBER – 4×106
STATIC PRESSURE

According to the above contour plot, the maximum static pressure at inlet of the narrow plate because the applying the boundary conditions at inlet of the boundary and minimum static pressure at the adjacent sides of the narrow plate. According to the above contour plot, the maximum pressure is 2.57e+05Pa and minimum static pressure is -2.61e+05Pa.

VELOCITY

According to the above contour plot, the maximum velocity magnitude of the air at corners of narrow plate, because the applying the boundary conditions at inlet of the boundary of the narrow plate and minimum velocity magnitude at around edges of the narrow plate. According to the above contour plot, the maximum velocity is 6.80e+02m/s and minimum velocity is 3.40e+01m/s.

HEAT TRANSFER COEFFICIENT

According to the above contour plot, the maximum heat transfer coefficient of the air at edges of the narrow plate and minimum heat transfer coefficient between around the boundary edges and narrow plate edges.

According to the above contour plot, the maximum heat transfer coefficient is 7.09e+02w/m2-k and minimum heat transfer coefficient is 3.55e+01w/m2-k.

MASS FLOW RATE

HEAT TRANSFER RATE

VERTICAL NARROW PLATE AT 600
REYNOLDS NUMBER – 2×106
STATIC PRESSURE

According to the above contour plot, the maximum static pressure at inlet of the narrow plate because the applying the boundary conditions at inlet of the boundary and minimum static pressure at the adjacent side of the narrow plate. According to the above contour plot, the maximum pressure is 1.35e+05Pa and minimum static pressure is -8.68e+04Pa.

VELOCITY

According to the above contour plot, the maximum velocity magnitude of the air at corners of narrow plate, because the applying the boundary conditions at inlet of the boundary of the narrow plate and minimum velocity magnitude at around edges of the narrow plate. According to the above contour plot, the maximum velocity is 5.01e+02m/s and minimum velocity is 2.50e+01m/s.

HEAT TRANSFER COEFFICIENT

According to the above contour plot, the maximum heat transfer coefficient of the air at edges of the narrow plate and minimum heat transfer coefficient between around the boundary edges and narrow plate edges.

According to the above contour plot, the maximum heat transfer coefficient is 4.93e+02w/m2-k and minimum heat transfer coefficient is 2.47e+01w/m2-k.

MASS FLOW RATE

HEAT TRANSFER RATE

REYNOLDS NUMBER – 4×106
STATIC PRESSURE

According to the above contour plot, the maximum static pressure at inlet of the narrow plate because the applying the boundary conditions at inlet of the boundary and minimum static pressure at the adjacent sides of the narrow plate. According to the above contour plot, the maximum pressure is 4.65e+05Pa and minimum static pressure is -3.47e+05Pa.

VELOCITY

According to the above contour plot, the maximum velocity magnitude of the air at corners of narrow plate, because the applying the boundary conditions at inlet of the boundary of the narrow plate and minimum velocity magnitude at around edges of the narrow plate. According to the above contour plot, the maximum velocity is 1.00e+03m/s and minimum velocity is 5.01e+01m/s.

HEAT TRANSFER COEFFICIENT

According to the above contour plot, the maximum heat transfer coefficient of the air at edges of the narrow plate and minimum heat transfer coefficient between around the boundary edges and narrow plate edges. According to the above contour plot, the maximum heat transfer coefficient is 8.55e+02w/m2-k and minimum heat transfer coefficient is 4.28e+01w/m2-k.

MASS FLOW RATE

HEAT TRANSFER RATE

THERMAL ANALYSIS OF VERTICAL NARROW FLAT PLATE
Open work bench 14.5>select steady state thermal in analysis systems>select geometry>right click on the geometry>import geometry>select IGES file>open
Copper, Aluminum alloy 6061 & aluminum alloy 7075
Copper material properties
Thermal conductivity = 385w/m-k
Aluminum alloy material properties
Thermal conductivity = 30.0w/m-k
Steel material properties
Thermal conductivity = 50.2 w/m-k

IMPORTED MODEL

MESHED MODEL

Finite element analysis or FEA representing a real project as a “mesh” a series of small, regularly shaped tetrahedron connected elements, as shown in the above fig. And then setting up and solving huge arrays of simultaneous equations. The finer the mesh, the more accurate the results but more computing power is required.

BOUNDARY CONDITIONS

T =343K
Select steady state thermal >right click>insert>select convection> enter film coefficient value Select steady state thermal >right click>insert>select heat flux
Select steady state thermal >right click>solve
Solution>right click on solution>insert>select temperature
Heat transfer co-efficient values are taken from CFD analysis at different velocities

VERTICAL NARROW PLATE AT 00
MATERIAL – COPPER
TEMPERATURE

According to the contour plot, the temperature distribution maximum temperature at bottom of the narrow plate because the temperature passing from the bottom of the plate. So we are applying the temperature bottom of the plate and applying the convection except bottom of the plate.
HEAT FLUX

According to the contour plot, the maximum heat flux at corner portion of the narrow plates. Minimum heat flux except corners of the narrow plates.

According to the above contour plot, the maximum heat flux is 0.15657w/mm2 and minimum heat flux is 0.039277w/mm2.

MATERIAL – ALUMINUM ALLOY
TEMPERATURE

According to the contour plot, the temperature distribution maximum temperature at bottom of the narrow plate because the temperature passing from the bottom of the plate. So we are applying the temperature bottom of the plate and applying the convection except bottom of the plate.
HEAT FLUX

According to the contour plot, the maximum heat flux at corner portion of the narrow plates. Minimum heat flux except corners of the narrow plates.

According to the above contour plot, the maximum heat flux is 0.15159w/mm2 and minimum heat flux is 0.038387w/mm2.

MATERIAL – STEEL
TEMPERATURE

According to the contour plot, the temperature distribution maximum temperature at bottom of the narrow plate because the temperature passing from the bottom of the plate. So we are applying the temperature bottom of the plate and applying the convection except bottom of the plate.
HEAT FLUX

According to the contour plot, the maximum heat flux at corner portion of the narrow plates. Minimum heat flux except corners of the narrow plates.

According to the above contour plot, the maximum heat flux is 0.14103w/mm2 and minimum heat flux is 0.036432w/mm2.

VERTICAL NARROW PLATE AT 300
MATERIAL – COPPER
TEMPERATURE

According to the contour plot, the temperature distribution maximum temperature at bottom of the narrow plate because the temperature passing from the bottom of the plate. So we are applying the temperature bottom of the plate and applying the convection except bottom of the plate.
HEAT FLUX

According to the contour plot, the maximum heat flux at corner portion of the narrow plates. Minimum heat flux except corners of the narrow plates.

According to the above contour plot, the maximum heat flux is 0.1951w/mm2 and minimum heat flux is 0.039119w/mm2.

MATERIAL – ALUMINUM ALLOY
TEMPERATURE

According to the contour plot, the temperature distribution maximum temperature at bottom of the narrow plate because the temperature passing from the bottom of the plate. So we are applying the temperature bottom of the plate and applying the convection except bottom of the plate.
HEAT FLUX

According to the contour plot, the maximum heat flux at corner portion of the narrow plates. Minimum heat flux except corners of the narrow plates.

According to the above contour plot, the maximum heat flux is 0.18744w/mm2 and minimum heat flux is 0.03824w/mm2.

MATERIAL – STEEL
TEMPERATURE

According to the contour plot, the temperature distribution maximum temperature at bottom of the narrow plate because the temperature passing from the bottom of the plate. So we are applying the temperature bottom of the plate and applying the convection except bottom of the plate.
HEAT FLUX

According to the contour plot, the maximum heat flux at corner portion of the narrow plates. Minimum heat flux except corners of the narrow plates.

According to the above contour plot, the maximum heat flux is 0.17153w/mm2 and minimum heat flux is 0.036307w/mm2.

VERTICAL NARROW PLATE AT 450
MATERIAL – COPPER
TEMPERATURE

According to the contour plot, the temperature distribution maximum temperature at bottom of the narrow plate because the temperature passing from the bottom of the plate. So we are applying the temperature bottom of the plate and applying the convection except bottom of the plate.
HEAT FLUX

According to the contour plot, the maximum heat flux at corner portion of the narrow plates. Minimum heat flux except corners of the narrow plates.

According to the above contour plot, the maximum heat flux is 0.23701w/mm2 and minimum heat flux is 0.039416w/mm2.

MATERIAL – ALUMINUM ALLOY
TEMPERATURE

According to the contour plot, the temperature distribution maximum temperature at bottom of the narrow plate because the temperature passing from the bottom of the plate. So we are applying the temperature bottom of the plate and applying the convection except bottom of the plate.
HEAT FLUX

According to the contour plot, the maximum heat flux at corner portion of the narrow plates. Minimum heat flux except corners of the narrow plates.

According to the above contour plot, the maximum heat flux is 0.22608w/mm2 and minimum heat flux is 0.038521w/mm2.

MATERIAL – STEEL
TEMPERATURE

According to the contour plot, the temperature distribution maximum temperature at bottom of the narrow plate because the temperature passing from the bottom of the plate. So we are applying the temperature bottom of the plate and applying the convection except bottom of the plate.
HEAT FLUX

According to the contour plot, the maximum heat flux at corner portion of the narrow plates. Minimum heat flux except corners of the narrow plates.

According to the above contour plot, the maximum heat flux is 0.20385w/mm2 and minimum heat flux is 0.03655w/mm2.

VERTICAL NARROW PLATE AT 600
MATERIAL – COPPER
TEMPERATURE

According to the contour plot, the temperature distribution maximum temperature at bottom of the narrow plate because the temperature passing from the bottom of the plate. So we are applying the temperature bottom of the plate and applying the convection except bottom of the plate.
HEAT FLUX

According to the contour plot, the maximum heat flux at corner portion of the narrow plates. Minimum heat flux except corners of the narrow plates.

According to the above contour plot, the maximum heat flux is 0.38359w/mm2 and minimum heat flux is 0.04045w/mm2.

MATERIAL – ALUMINUM ALLOY
TEMPERATURE

According to the contour plot, the temperature distribution maximum temperature at bottom of the narrow plate because the temperature passing from the bottom of the plate. So we are applying the temperature bottom of the plate and applying the convection except bottom of the plate.
HEAT FLUX

According to the contour plot, the maximum heat flux at corner portion of the narrow plates. Minimum heat flux except corners of the narrow plates. According to the above contour plot, the maximum heat flux is 0.35993w/mm2 and minimum heat flux is 0.039493w/mm2.

MATERIAL – STEEL
TEMPERATURE

According to the contour plot, the temperature distribution maximum temperature at bottom of the narrow plate because the temperature passing from the bottom of the plate. So we are applying the temperature bottom of the plate and applying the convection except bottom of the plate.
HEAT FLUX

According to the contour plot, the maximum heat flux at corner portion of the narrow plates. Minimum heat flux except corners of the narrow plates.

According to the above contour plot, the maximum heat flux is 0.3144w/mm2 and minimum heat flux is 0.037395w/mm2.

CFD ANALYSIS RESULT TABLE
Reynolds number Models Pressure
(Pa) Velocity (m/s) Heat transfer co-efficient
(w/m2-k) Mass flow rate (kg/s)
Heat transfer rate (W)
2×106 00 2.59e+04 2.22e+02 3.14e+02 0.0141983 57075.5
300 3.25e+04 2.80e+02 3.39e+02 0.13510132 2022.375
450 6.49e+04 3.40e+02 4.06e+02 0.246078 3677.875
600 1.16e+05 5.01e+02 4.93e+02 0.50804138 9873.625
4×106 00 1.03e+05 4.44e+02 5.52e+02 0.02565 120081
300 1.31e+05 5.60e+02 5.96e+02 0.86120605 12874.25
450 2.57e+05 6.80e+02 7.09e+02 0.611465 9129
600 4.65e+05 1.00e+03 8.55e+02 1.05348 20294.25

THERMAL ANALYSIS RESULT TABLE
Models Materials Temperature (0C) Heat flux (w/mm2)
Max. Min. 00 Steel 343 333.99 0.14103
Aluminum 343 339.2 0.15159
Copper 343 341.76 0.15657
300 Steel 343 331.7 0.17153
Aluminum 343 338.22 0.18744
Copper 343 341.41 1.1951
450 Steel 343 329.74 0.20385
Aluminum 343 341.08 0.23701
Copper 343 337.26 0.22608
600 Steel 343 325.73 0.3144
Aluminum 343 335.2 0.35993
Copper 343 340.34 0.38359

GRAPHS
CFD ANALYSIS GRAPHS
PRESSURE PLOT

VELOCITY PLOT

HEAT TRANSFER COEFFICIENT PLOT

MASS FLOW RATE PLOT

HEAT TRANSFER RATE PLOT

THERMAL ANALYSIS
HEAT FLUX PLOT

CONCLUSION
In this thesis the air flow through vertical narrow plates is modeled using PRO-E design software. The thesis will focus on thermal and CFD analysis with different Reynolds number (2×106 & 4×106) and different angles (00,300,450&600) of the vertical narrow plates. Thermal analysis done for the vertical narrow plates by steel, aluminum & copper at different heat transfer coefficient values. These values are taken from CFD analysis at different Reynolds numbers.

By observing the CFD analysis the pressure drop & velocity increases by increasing the inlet Reynolds numbers and increasing the plate angles. The heat transfer rate increasing the inlet Reynolds numbers, more heat transfer rate at 00 angles.

By observing the thermal analysis, the taken different heat transfer coefficient values are from CFD analysis. Heat flux value is more for copper material than steel& aluminum.

So we can conclude the copper material is better for vertical narrow plates.

REFERENCES
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3.Cheung, F. B., i980a, “HeatSource-Driven Thermal Convection at Arbirrary Prandtl Numbers,” J. Fluid Mech., YoL 97, pp. 743-758.

4. Cheung, F. B., 1980b, “The Boundry Layer Behavior in Transient Turbulent Thermal Convection Flow,” ASME JoURNAL oF HEAr TRANSFERV, ol. 102, pp.373-375.

5.Cheung, F. B., 1978, “Turbulent Thermal Convection in a Horizontal FluidLayer With Time Dependent Volumetric Energy Sources.” AIAA/ASME Thermo physics and Heat Transfer Conf.,78-HT-6, Palo Alto.

6. Cheung, F.8., 1977, “Natural Convection in a Volumerrically Heared FluidLayer at High Rayleigh Numbers,” Int. J. Heat Mass Transfer, Vol. 20, pp.499-
506.

7.Cheung, F. B., Shiah, S. W., Cho, D. H., and Tan, M. J., 1992, “Modeling ofHeat Transfer in a Horizontal HearGenerating Layer by an Effective DiffusivityApproach,” ASME/HTD, Vol. 192, pp.55-62.

8.Dinh, T. N., and Nourgalier, R. R., 1997, “On Turbulence Modeling in LargeVolumetrically Heated Liquid Pools,” Nncl. Engng. Design, in press.Fan, T. H., 1996, “Heat Transport Phenomena ofTurbulent Natural Convectionin a Melt Layer With Solidification,” M.S. thesis, The Pennsylvania State University, University Park, PA.

9.Fielder, H. E., and Wille, R., 1970, “Turbulante Freie Konvektion in EinerHorizontalea Flussigkeitss chicht mit Volumen-Warmequelle,” Paper NC 4.5,Proc. Fourth Int. Heat Transfer Conf., Vol. IV, pp. l-12.