Conjugate heat transfer analysis on a graphics card using Ansys fluent

Abstract: Processors in the electronic devices such as graphics card,CPUs etc tends to get heat up which results in decrease in preformance or damage of the electronic devices. Proper cooling system of these electronic devices is essential.Therefore in our present case, numerical conjugate heat transfer analysis of a graphics card has been simulated. To ensure proper cooling of the processor, a fin plate(of aluminium material) has been attached to processor(of silicon material). The base material of the processor(card) is made of Thermoplastic. Air is let pass through the graphics card, thereby carrying away heat from fin plate.For present case, steady state approach is adopted since the end result is our main interest. Standard `k-epsilon` turbulence model is implemented.

Objective:

1. To perform numerical conjugate heat transfer analysis of a graphics card.

2. To determine maximum temperature attained by the processor

3. To determine heat transfer coefficient between the graphics card and fluid passing over it.

I. Conjugate heat transfer(CHT):

The term conjugate heat transfer is used to describe processes which involve variations of temperature within solids and fluids, due to thermal interaction between the solids and fluids. A typical example is the heating or cooling of a solid object by the flow of air in which it is immersed.

Conjugate heat transfer corresponds with the combination of heat transfer in solids and heat transfer in fluids. In solids, conduction often dominates whereas in fluids, convection usually dominates. Efficiently combining heat transfer in fluids and solids is the key to designing effective coolers, heaters, or heat exchangers. Forced convection is the most common way to achieve high heat transfer rate. In some applications, the performances are further improved by combining convection with phase change (for example liquid water to vapor phase change).

Heat transfer in solids and heat transfer in fluids are combined in the majority of applications. This is because fluids flow around solids or between solid walls, and because solids are usually immersed in a fluid.

The fluid flow and heat transfer problems can be tightly coupled through the convection term in the energy equation and when physical properties are temperature dependent. While analytical solutions exist for some simple problems, we must rely on computational methods to solve most industrially relevant applications.

Practical applications:

1. CHT can be performed to improve cooling performance of the water jacket and increase engine life.

2. Advancements in cooling for applications such as gas turbines components.

3. Conjugate Heat Transfer analysis provides the temperature distribution in solid and coolant of the engine and clear insight on velocity distribution and mechanism of heat transfer of coolant.

II. Graphics card:

III. Computational fluid domain:

Since for present case, air flows over the graphics card, An enclosure is created in order to define the region of flow of air with appropriate dimensions.

Since in present case we are going to perform CHT analysis,the solid-fluid interaction surface has to be well defined in order to accurately analyse the heat transfer between solid and fluid and also to obtain conformal mesh in the intersection layer.This is done by using share topology option under workbench in spaceclaim.

IV. Mesh:

Case 1: Baseline mesh

Element size: 0.003 m

Number of elements: 148012

Face sizing : Processor( Since heat is being generated at processor, mesh is refined)

Face sizing element size: 0.001 m

Case 2: Refined mesh

Element size: 0.0025 m

Number of elements: 469485

Face sizing : Both processor and fins plate is being refined. Since heat is being generated at the processor,the processor is refined. And since heat tranfer between the fluid and solid(fins plate) is our area of interest,refined mesh at fins plate is expected to provide more accurate solution.

Face sizing element size: 0.0005 m

V . Governing Equations:

Continuity equation:

`frac{delrho}{delt}+ nabla.(rhoV)=0`

Momentum equation:

x component: `frac{del(rhou)}{delt}+grad.(rhouV)=-frac{delp}{delx}+frac{del(tau_(x x ))}{delx}+frac{del(tau_(yx))}{dely}+frac{del(tau_(zx))}{delz}+rhof_x`

Y component: `frac{del(rhov)}{delt}+grad.(rhovV)=-frac{delp}{dely}+frac{del(tau_(x y ))}{delx}+frac{del(tau_(yy))}{dely}+frac{del(tau_(zy))}{delz}+rhof_y`

z component: `frac{del(rhow)}{delt}+grad.(rhowV)=-frac{delp}{delz}+frac{del(tau_(x z ))}{delx}+frac{del(tau_(yz))}{dely}+frac{del(tau_(zz))}{delz}+rhof_z`

Energy equation:

`frac{del}{delt}[rho(e+frac{V^2}{2})]+grad.[rho(e+frac{V^2}{2})V]= rhodotq+frac{del}{delx}(kfrac{delT}{delx})+frac{del}{dely}(kfrac{delT}{dely})+frac{del}{delz}(kfrac{delT}{delz})-frac{del(up)}{delx}-frac{del(vp)}{dely}-frac{del(wp)}{delz}+frac{del(utau_(x x))}{delx}+frac{del(utau_(yx))}{dely}+frac{del(utau_(zx))}{delz}+frac{del(vtau_(xy))}{delx}+frac{del(vtau_(yy))}{dely}+frac{del(vtau_(zy))}{delz}+frac{del(wtau_(xz))}{delx}+frac{del(wtau_(yz))}{dely}+frac{del(wtau_(zz))}{delz}+rhof.V`

For current case, we have considered steady, in-compressible flow.

VI. Turbulence Modeling:

The Reynolds-averaged Navier-Stokes (RANS) equations govern the transport of the averaged flow quantities, with the whole range of the scales of turbulence being modeled. The RANS-based modeling approach therefore greatly reduces the required computational effort and resources, and is widely adopted for practical engineering applications.

Standard `k-epsilon` Turbulence Model:

The standard k-ε model is a model based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate (ε). The model transport equation for k is derived from the exact equation, while the model transport equation for ε was obtained using physical reasoning and bears little resemblance to its mathematically exact counterpart.

Transport Equations for Standard `k-epsilon` Turbulence Model:

The modelled transport equations for k and `epsilon` in the Standard `k-epsilon` model are

`frac{del(rhok)}{delt}+frac{del(rhoku_j)}{delx_j}=frac{del}{delx_j}[(mu+frac{mu_t}{sigma_k})frac{delk}{delx_j}]+G_k+G_b-rhoepsilon-Y_M+S_k`

Physical Meaning of k equation:

Time derivative of k+ Convective transport = diffusive transport + Rate of production-Rate of destruction

`frac{del(rhoepsilon)}{delt}+frac{del(rhoepsilonu_j)}{delx_j}=frac{del}{delx_j}[(mu+frac{mu_t}{sigma_(epsilon)})frac{del(epsilon)}{delx_j}]+C_(1epsilon)frac{epsilon}{k}(G_k+C_(3epsilon)G_b)-C_(2epsilon)rhofrac{epsilon^2}{k}+S_epsilon`

Physical Meaning of `epsilon` equation:

Time derivative of ε+ Convective transport = Diffusive transport + Rate of production-Rate of destruction.

where,

k= Turbulent kinetic energy

`epsilon`= Turbulent dissipation rate

`G_k`= generation of turbulence kinetic energy due to the mean velocity gradients

`G_b`= generation of turbulence kinetic energy due to buoyancy

`Y_M`= represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate

`sigma_k`,`sigma_epsilon`= turbulent Prandtl numbers for k and `epsilon` respectively

`C_(1epsilon),C_(2epsilon),C_(3epsilon)`= Constants

Model Constants:

Cmu= 0.09

C1-epsilon= 1.44

C2-epsilon=1.92

TKE prandtl number= 1

TDR prandtl number= 1.3

Energy prandtl number= 0.85

wall prandtl number= 0.85

VII. Fluid properties:

Fluid: Air

Density(kg/m^3) : 1.225

Dynamic viscosity(kg/m-s) : 1.7894e-05

Cp(j/kg-K) : 1006.43

Thermal conductivity(w/m-k) : 0.0242

VIII. Solid properties:

Solid 1: Aluminium(assigned as the material of fins because of higher thermal conductivity hence heat tranfer rate will be higher)

Density(kg/m3) : 2719

Cp (j/kg-K): 871

Thermal conductivity(w/m-k): 202.4

Solid 2: Silicon(assigned as the material of processor)

Density(kg/m3) : 2330

Cp (j/kg-K): 710

Thermal conductivity(w/m-k): 130

Why silicon is used as a material for processors?

Answer: Silicon is an essential component of modern electronics because silicon in the pure form is a semiconductor, which means it possess properties of both a metal (which conducts electricity) and an insulator (which blocks electricity). By controlling semiconducting silicon, we can manipulate electrical signals.Silicon is also a relative abundant element on Earth

Solid 3: Thermoplastic(assigned as the material of base plate,because of lower thermal conductivity base plate will not transfer much heat to other components of a graphics card)

Density(kg/m3) : 1060

Cp (j/kg-K): 2000

Thermal conductivity(w/m-k): 0.1

IX. Boundary Conditions:

Suitable boundary conditions have been applied according to the physics of the flow.

1. Processor acts as a heat source,

Heat generation rate(w/m3) = 1e+07.(this value is input as source terms in the coresponding cell zones)

2. At Inlet : (the inlet of the enclosure is named as inlet BC)

Velocity inlet of magnitude 20 m/s normal to boundary,

Temperature(K)= 300,

Turbulent intensity(%)= 5 and turbulent viscosity ratio= 10.

3. At outlet: (The outlet of the enclosure is named as outlet BC)

Pressure outlet at zero gauge pressure(atmospheric pressure),

Turbulent intensity(%)= 5 and turbulent viscosity ratio= 10.

4. At symmetry: (the other four sides of the enclosure is given as symmetry boundary condition)

Symmetry Boundary condition:The symmetry boundary condition defines a mirror face/surface. The symmetry condition should only be used if the physical object or geometry and the expected flow field pattern of the developed solution is mirrored along that surface. This boundary condition helps to reduces the computational domain in size and enables the modeling of a sub-domain of the complete setup.

In general, the symmetry condition applies the following constraints on the flow variables:

• The fluxes across a symmetry are zero.

• The normal components of velocity are set to zero.

• The normal components of all other variables are set to zero.

X. Numerical schemes:

Solver: Pressure-based solver

Pressure-based solver: The pressure-based solver employs an algorithm which belongs to a general class of methods called the projection method . In the projection method, wherein the constraint of mass conservation (continuity) of the velocity field is achieved by solving a pressure (or pressure correction) equation. The pressure equation is derived from the continuity and the momentum equations in such a way that the velocity field, corrected by the pressure, satisfies the continuity. Since the governing equations are nonlinear and coupled to one another, the solution process involves iterations wherein the entire set of governing equations is solved repeatedly until the solution converges.

1. Pressure velocity coupling: COUPLED

Coupled: The pressure-based solver allows you to solve your flow problem in either a segregated or coupled manner. Using the coupled approach offers some advantages over the non-coupled or segregated approach. The coupled scheme obtains a robust and efficient single phase implementation for steady-state flows, with superior performance compared to the segregated solution schemes.

The coupled algorithm solves the momentum and pressure-based continuity equations together. The full implicit coupling is achieved through an implicit discretization of pressure gradient terms in the momentum equations, and an implicit discretization of the face mass flux, including the Rhie-Chow pressure dissipation terms.

2. Spatial discretization:

Gradient: Least squares cell based

Pressure: Second order

Momemtum: Second order upwind

Turbulent kinectic energy: First order upwind

Turbulent dissipation energy : Second order upwind

Energy: Second order upwind

First-order upwind scheme- When first-order accuracy is desired, quantities at cell faces are determined by assuming that the cell-center values of any field variable represent a cell-average value and hold throughout the entire cell; the face quantities are identical to the cell quantities.

Second-order upwind scheme- When second-order accuracy is desired, quantities at cell faces are computed using a multidimensional linear reconstruction approach . In this approach, higher-order accuracy is achieved at cell faces through a Taylor series expansion of the cell-centered solution about the cell centroid.

XI. Initialization:

Hybrid Initialization: Hybrid Initialization is a collection of recipes and boundary interpolation methods. It solves the Laplace equation to produce a velocity field that conforms to complex domain geometries, and a pressure field which smoothly connects high and low pressure values in the computational domain. All other variables (that is temperature, turbulence, VOF, species, and so on) will be patched based on domain averaged values or a predetermined recipe.

XII. Residual plots:

Case 1: baseline mesh

Case 2: Refined mesh

XIII. Results:

Case 1:

1. Velocity contour at cut plane:

cut-plane: cut plane is a plane taken at the centre of the enclosure ,and normal to the plane is perpendicular to the fluid flow direction.

2. Temperature contour at cut plane:

3. Temperature contour at fins plate:

4. Temperature contour at processor and base plate:

5. Wall heat transfer coefficient plot at cut plane:

6. Temperature distribution of air at outlet cross section:

Case 2:

1. Velocity contour at cut plane:

cut-plane: cut plane is a plane taken at the centre of the enclosure ,and normal to the plane is perpendicular to the fluid flow direction.

2. Temperature contour at cut plane:

3. Temperature contour at fins plate:

4. Temperature contour at processor and base plate:

5. Wall heat transfer coefficient plot at cut plane:

6. Temperature distribution of air at outlet cross section:

Discussions:

1. From velocity contour at cut plane, we can observe that air enters the enclosure with a velocity 20 m/s as per specified boundary condition.No slip condition applied on the walls of graphics card can be observed.Formation of boundary layer and hence decrease in velocity can be observed in the region of interaction between the fluid(air) and the solid(graphics card).Flow separation can be observed in the wake of graphics card.Maximum fluid velocity is 24.160m/s(for case 1) and 24.581 m/s(for case 2).

2. From temperature contour at cut plane, we can observe that the air is inlet with temperature of 300K. And heat dissipation from the heat source(processor) to fin plate and base plate can be observed.Since fins plate is made material of higher thermal conductivity,more heat is being dissipated to fin plate than base plate( in other words temperature of fin plate is higher than base plate).At the region of interaction between fins plate and air, air can be observed at a higher temperature,therefore heat dissipation from solid(fin plate) to flowing fluid(air) by means of forced convection can be observed. Due to course mesh, contour of case 1 can be observed as poor quality.

3. From temperature contour at fins plate, we can observe that temperature is maximum at the centre of fin plate. Heat dissipation from the centre of fin plate to its corners by means of conduction can be observed.The maximum temperature of the fin plate is 303.636 K(for case 1) and 303.344 K(for case 2) both located at the centre of the fin plate.

4. From temperature contour at processor and base plate, we can observe that the maximum temperature of processor is 303.636 K (for case 1) and 303.344 K(for case 2). Heat dissipation from processor to the base plate can be observed but it is comparatively less as compared to heat disspation from processor to fins plate, this is due to the lower thermal conductivity of base plate compared to that of fins plate. Base plate material of lower thermal conductivity is essential in order to prevent other electrical components of the graphics card from damage.

5. From wall heat transfer coefficient contour at cut plane, heat tranfer coefficients can be observed of high value at the walls of processor and fins plate. The maximum value of heat tranfer coefficient is 1002.420(w/m2K) (for case 1) and 703.697 (w/m2K)(for case 2). By observing the contour of case 1 and case 2, case 2 values can be considered more accurate.

6. From temperature distribution plot at outlet cross section, comparatively higher temperature of air is observed at the lower side of the cross section this is due to graphics card being placed at lower portion of the enclosure.