Week 6 - CHT Analysis on a Graphics card

Aim: To understand the concept of Conjugate Heat Transfer (CHT) Analysis.

Objective: To perform a CHT analysis in Graphics Card and to monitor the effect of velocity (Reynolds Number) on the heat transfer.

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Heat Transfer Coefficient:

Empiricle Coorelation:

• Reynolds Number:

`Re = (U_(infty)*rho*L_c)/(mu)`

• Prandtl Number:

`Pr = (c_p*mu)/k`

• Nusselt Number:

`Nu = f(Re,Pr)`

also,

`Nu = (hL_c)/k`

Here k is thermal conductivity of fluid.

Therefore, h (heat transfer coefficient) is a function of Re and Pr too.

If the velocity (`U_(infty)`) increases, the surface heat transfer coefficient is also going to increase.Therefore, the heat transfer is also going to increase.

Idea in a nutshell, for our case, we must have higher heat transfer coefficient (h) in order to keep the processor cool.

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Simulation Procedure:

Three cases were run for this setup.

Case 1 : Velocity = 1m/s

Case 2 : Velocity = 3 m/s

Case 3 : Velocity = 5 m/s

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Case 1 : Velocity of 1 m/s

Geometry:

• Import the given geometry into the spaceclaim.
• Unable share topology in order to get conformal mesh.

Meshing:

• For this particular case mesh must be refined for the processor and the sink for better Temperature field values.
• Before, meshing, one must make sure the geometry assigned solid and fluid to appropriate bodies.
• Select geometry --> new graphics card, select the component and assign as solid against 'fluid/solid'. Do this for all the components except the enclosure. Asign fluid for enclosure.

• Then create named selection for the components.

• Assign the top, bottom and the side walls as 'wall'.
• And the domain as 'flow_domain'.
• Now selec the porcessor and assign body sizing. Elemnt size = 0.4 mm
• Similarly do it for capacitor, heat sink and the PCB board. Element Size = 1 mm, 0.5 mm, 1 mm respectively.
• Then finally for domain, assign a global mesh size of 3 mm.

• Mesh Statistics:

Setting up the physics:

• Make sure steady state is selected.
• Hover over to 'Physics tab' and check the energy check box, conduct a k-epsilon model.
• Select 'Material Edit/Create' tab.
• Select solid from dropdown menu. Select 'Fluent Database' then select aluminium and copy and give name as silicon.

• Similarly create a new material for PCB board.

PROPERTIES OF MATERIAL CREATED:

• FR-4: for PCB board

• Silicon: for Processor

• Aluminium (already in fluent): for Capacitor and Heat Sink

• Go to cell zone and select processor. Check the 'source term' check box.
• For Energy assign one and a window will popup and give a value of 7,81,25,000 `W/m^3`. 5W divided by (8*10^-3*8*10^-3*10^-3) = 7,81,25,000.
• Select boundaries, select inlet and assign velocity value of 1 m/s.
• Go to 'soluitons' tab, select report definition and then select Surface Report --> Area Weighted Average --> Wall fluxs --> Surface Heat Transfer and then select the processor. Similarly instead of selecting Wall Fluxs, slect Temperature.

• Initialize the soluiton using Hybrid Initialization.
• Carry the simulation for 350 iterations. Finner the mesh faster will be the convergence.

NOTE: The above procedure is same for all the cases the only thing that changes is the velocity value. For Case 2 velocity value is 3 m/s and for Case 3 it is 5 m/s.

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Results:

Case 1:

• Residuals Plot:

• Surface Heat Transfer Coefficient Plot (Processor):

• Temperature Plot (Processor):

Here negative sign represents the heat is leaving the system. Heat is leaving the body.

• Contours:

- It is evident that heat is conducted better from the heat sink rather than PCB as heat sink is made up of Aluminium which sits exactly above the processor and has higher thermal conductivity.

- The hot spot is visible clearly above the processor and that is what is expected.

- The max temperature reached is 147.5161 C, which is very high for a processor.

- This must be taken care of by increasing the inlet velocity.

Animation:

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Case 2:

• Residuals Plot:

• Surface Heat Transfer Coefficient Plot (Processor):

• Temperature Plot (Processor):

• Contours:

• Animation:

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Case 3:

• Residuals Plot:

• Surface Heat Transfer Coefficient Plot (Processor):

• Temperature Plot (Processor):

• Contours:

• Animation:

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Convergence:

• Looking at the temperature plot, the temperature reaches steady-state after 150 iterations. This is the indication of solution being converged.
• But looking at the residual plot, the error is still big for a converged solution (k, epsilon and continuity). This could be furthur refined by refining the mesh.

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Potential Hotspots:

• All the three cases have hotspot near the processor and that is what we expect as it is the only component that is generating heat (in this case).

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Conclusion:

• The heat generation (5W) considered is too large for (8*8*1)mm processor. It can be assumed to be less.
• The high temperatures are near the processor and the heat sink.
• Further mesh refinement is necessary for better results.
• It is quite evident that the temperature decreases with increase in veocity due to Reynolds-Nusselt-Prandtl Number relation.

	CASE 1 (1 m/s)	CASE 2 (3 m/s)	CASE 3 (5 m/s)
Surface Heat Transfer Coeff. `W/(m^2*k)`	-7.1611	-12.2092	-16.9939
Max Temperature C	147.5161	90.6804	75.4007

Therefore, Case 3 with velocity of 5 m/s maintaines the temperature of the processor at 75 C.

Drive link for animation: Link