Conjugate Heat Transfer Analysis on a graphics card.

Aim- To perform steady-state conjugate heat transfer analysis on a model of graphics card and find out the maximum temperature and heat transfer coefficient attained by the processor with potential hotspots on the model.

Introduction- This project deals with the CHT analysis of graphics card with three different inlet velocities i.e. 5m/s, 3m/s and 1m/s. The results of the simulation for different velocities are computed and conclusion is made based on the comparison of same output result for different velocities.

Theory-

CHT stands for Conjugate Heat Transfer. It corresponds with the combination of heat transfer in solids and heat transfer in fluids. Transfer of heat in solids takes place mainly by conduction and in liquids by convection. Hence, it is obvious to observe CHT in our day to day scenarios like coolers, heaters, heat exchangers, heat sinks, engine ports, exhaust manifolds, etc.

CHT Analysis is a simulation of heat transfer between solid and fluid domains by exchanging thermal energy at the interface between them. It predicts heat transfer by simultaneous solving all the relevant solid and flow field heat transfer process because of which effective heat transfer and energy savings can be analyzed easily. Generally, the segregate fluid temperature model is used to solve the total energy equation with temperature as the solvable variable.

The energy equation written in integral form is,

where,

E = Total Energy

H = Total Enthalpy

q̇ = Heat flux vector

T = Viscous Stress Tensor

V = Velocity Vector

V_g= grid velocity vector

f = body force vector

Standard K-ɛ Model :

Geometry- A small enclosure was prepared on imported geometry to refine the mesh. Also, the interference between the enclosures was removed so that there is no interference of different types of mesh, and share topology option was enabled to have a proper node to node connection between the different types of mesh. The Cut-section of prepared geometry can be observed in Figure 1.

Figure 1. Cut-section of prepared geometry

Meshing- Meshing is an integral part of the engineering simulation process where complex geometries are divided into simple elements that can be used as discrete local approximations of the larger domain. The mesh influences the accuracy, convergence and speed of the simulation. It is very important to define an appropriate mesh for the higher accuracy of results. Hence, multizone mesh option was selected while meshing the prepared geometry. Hexahedron elements were generated with mesh size of 3 mm for outer enclosure. Tetra mesh was given to inner enclosure and graphic card with sizing of 2mm and 1 mm respectively. For the generated mesh, number of nodes and elements are 81262 and 370140 respectively. Generated mesh for the geometry can be observed in Figure 2.

Figure 2. Meshing of prepared geometry

Other than setting up meshing method and giving fine mesh size there is also need to have a sufficiently fine mesh to adequately capture regions where the flow will experience rapid change in key variables such as pressure, velocity or temperature. This leads to providing inflation mesh to the wall. By providing inflation the boundary layer profile is resolved all the way to the wall. For certain simulations such as flows with strong wall-bounded effects, this resolution is absolutely necessary. For the prepared geometry, total thickness inflation option was selected with 5 layers, maximum thickness of 12.5 mm and growth rate of 1.2. Generated inflation layers around the geometry of graphic card can be observed in Figure 3.

Figure 3. Inflation Layers

Boundary Conditions- The front plane was given the “velocity-inlet” boundary condition. The bottom, top, and sides of the domain are set as “Symmetry” so that these surfaces would not bring any effects on the simulation. The outlet boundary condition is set to “Pressure-outlet” with a gauge pressure of 0 Pascal. All the boundaries can be observed in Figure 4.

Copper and Aluminium were added in materials and FR-4 was defined as new material. Properties of these materials assigned to different components are tabulated in Table 1. In cell zone condition Aluminum was assigned to Fins, Copper was assigned to Processor, and FR-4 was assigned to the base. Also, source terms option was enabled for the processor with heat generation rate of 3*10⁸ watt/m³ which can be observed from Figure 5. Calculation for heat generation is given below,

Let, the power generated by the processor, P = 19.2 watt

volume of the processor, V = 8*8*1 = 64 mm³ = 6.4*10^-8 m³

Heat Generation Rate = P/V

= 19.2/6.4*10^-8

= 3*10⁸ watt/m³

Table 1. Properties of Materials

Components	Materials	Density (ρ)	Specific Heat(Cp)	Thermal Conductivity (k)
Fins	Aluminum	2719 kg/m3	871 j/kg-k	202.4 w/m-k
Processor	Copper	8978 kg/m3	381 j/kg-k	387.6 w/m-k
Base	FR-4	1850 kg/m3	1200 j/kg-k	0.29 w/m-k
Fluid	Air	1.225 kg/m3	1006.43 j/kg-k	0.0242 w/m-k

Figure 4. Boundary Conditions

Figure 5. Assigning processor as a power source

Simulation Results- After the input of boundary conditions, simulations were performed for 3 different velocities. The residual plot plays very important role in determining the convergence of a solution. This criterion requires scaled residuals decrease to 10^-3 or less for all equations except energy equation, for which the criterion is 10^-6. For all the cases convergence was obtained in less than 60 iterations whose residual plot can be observed as follows:

Velocity=1m/sec

Figure 6. Residuals plot for the velocity of 1m/sec.

Figure 7. Convergence for 1 m/sec velocity

Velocity=3 m/sec

Figure 8. Residuals plot for the velocity of 3 m/sec.

Figure 9. Convergence for 3 m/sec velocity

Velocity=5 m/sec

Figure 10. Residuals plot for the velocity of 5 m/sec.

Figure 11. Convergence for 5 m/sec velocity

Post-processing- After the simulation, to examine and analyze the results, post-processing is very important as visuals of variation in every parameter over the analyzed body can be observed. Following are the results of post-processing for different velocities:

Velocity=1m/sec

Figure 12. Temperature contours of Base

Figure 13. Temperature contours of processor

Figure 14. Temperature contours of fins

Figure 15. Heat Transfer Coefficient

Velocity=3m/sec

Figure 16. Temperature contours of Base

Figure 17. Temperature contours of processor

Figure 18. Temperature contours of fins

Figure 19. Heat Transfer Coefficient

Velocity=5m/sec

Figure 20. Temperature contours of Base

Figure 21. Temperature contours of processor

Figure 22. Temperature contours of fins

Figure 23. Heat Transfer Coefficient

Results- The maximum value of temperature and Heat transfer coefficient for different velocities are tabulated below in Table 2.

Table 2. Values for different velocities

Velocity of Air	Temperature of processor	Heat Transfer Coefficient
1 m/s	797.37 K	101.76 W/m2K
3 m/s	598.03 K	142.29 W/m2K
5 m/s	544.38 K	183.35 W/m2K

From the above results, we can conclude that, with an increase in velocity of air the rate of heat transfer increases. As the heat transfer coefficient is directly proportional to the heat transfer rate, with an increase in velocity of air heat transfer coefficient increases. Also due to the increase in heat transfer rate, temperature of the processor decreases.

Hence, we can say that to increase the efficiency of Graphics Card, velocity of air should be increased (as less the temperature difference, more efficient the Graphics Card).

References-

1. https://en.wikipedia.org/wiki/FR-4 (FR-4 Properties)