Week 6 - CHT Analysis on a Graphics card

Aim: Steady-state conjugate heat transfer analysis on a model of a graphics card

Objectives:

1. Run the simulation by varying the velocity from 1m/sec to 5m/sec for at least 3 velocities and discuss the results.
2. Find out the maximum temperature and heat transfer coefficient attained by the processor.
3. Prove that the simulation has achieved convergence with appropriate images and plots.
4. Identify potential hotspots on the model.

Introduction: Conjugate heat transfer analysis is based on a mathematically structured problem, which describes the heat transfer between a body and a fluid flowing over or inside it as a result of interaction between two objects. At the matching interface, the details are provided for temperature distribution and heat flux along the interface eliminating the need of calculating the heat transfer coefficient. Moreover, the heat transfer coefficient can be calculated later.

One of the simplest ways to realize conjugation is through numerical methods. The boundary condition for the fluid and solid interface is set and solved through iteration methods. There are no right guesses for the values of the initial boundary condition for the convergence except through the hit and trial method.

Application: The conjugate heat transfer methods have become a more powerful tool for modeling and investigating nature phenomena and engineering systems in different areas ranging from aerospace and nuclear reactors to thermal goods treatment and food processing from the complex medicines' complex procedures ocean thermal interaction in metrology.

CHT in recent years has significantly improved the cooling performance of electronic equipment such as the design of heat sinks and the design of heat exchangers for the waste treatment plant. One such application of CHT is the exhaust port system.

Solving & Modelling approach

• The geometry is loaded into Spaceclaim.
• The graphics card consists of a processor, PCB base, aluminum fin base, memory cards, and capacitors.
• CHT analysis requires both the solid and the liquid volume under consideration, Spaceclaim gives an option of volume extract for selecting edges for fluid volume, here the solid volume under consideration is graphics card components and the liquid volume under consideration is air. 
• The general principle underlying the fact that the heat generated by the processor is carried away by air. The aluminum fin is used for increasing the surface area of heat transfer.
• The share topology is set to reduce the interpolation error and to make the mesh conformal.
• It is then loaded into the meshing window for creating the named selection, and setting the baseline mesh and refined mesh.
• The fluid material and the solid material are separated and the construction of the material is selected for the same.
• The necessary contour images and graphs are studied to understand the behavior of temperature, velocity, and surface heat transfer coefficient at the interface.

Preprocessing and solver setting

Baseline mesh

The geometry is loaded into Spaceclaim

The share topology is created to reduce the interpolation error and to make the mesh conformal.

The geometry is loaded into the meshing interface, and the baseline mesh of `0.01mm` is created.

The named selection is created for the graphics card interface.

Inlet (Type velocity inlet) `1frac{m}{sec}, 2.5frac{m}[sec}``, 5frac{m}{sec}`

Outlet (Pressure outlet) Gauge pressure 0 Pa

Fluid domain wall (type wall)

Graphics card base wall (type wall)

Aluminium fins base wall (type wall)

Processor wall (type wall)

Setting up of physics and boundary condition

Reference values

The energy equation is turned on.

Viscous model

Material properties

Fluid

Solid 

Processor

Aluminum fin base

Base

Cell zone condition

Under the zone section of the tab the processor wall is selected, the edit option is clicked, the source term is enabled by selecting one source, and the value of volumetric heat source corresponding to 5e7 `frac{W}{m^3}`is entered as a constant which equates to 150 W which is enough for the most graphics cards, cards like Nvidia RTX requires more than 320 W and a system power of 750 W. Since 150 W will be enough for the most mid-range cards these usually come up with the 6 pin power connector. Source https://www.gpumag.com/gpu-power-connectors-explained/

The maximum temperature plot is created by selecting the processor wall.

The temperature contour is created by selecting the entire graphics card zones.

 

Meshing: It is the process of discretization of the entire volume using the finite volume method. The steady-state solution is carried by selecting "SIMPLE", "SIMPLEC", "COUPLED". For the coupled scheme the momentum for the baseline mesh is first order upwind (since the mesh is coarse), for the refined mesh pressure, momentum, energy are of second order. The gradient is selected as the "Least square cell-based scheme". As far as the refined mesh is concerned body sizing and edge sizing method are employed to improve the numerical accuracy and to bring the solution closer to convergence.

 Case-1

Element size: `0.01m`

Inlet velocity: `1frac{m}{sec}`

Number of element: `84494`

Number of nodes: `15849`

Pressure-velocity coupling scheme: SIMPLE

Enclosure mesh

Graphics card meshing

 

Residual plot

 

Max of temperature plot

 

Pressure-velocity coupling scheme: SIMPLEC

Residual plot

Max of temperature plot

Pressure-velocity coupling scheme: COUPLED

Momentum: First order upwind scheme

Residual plot

Max of temperature plot

Mesh statistics and maximum temperature

Element size	Number of elements	Number of nodes	Maximum temperature (K) (SIMPLE)	Maximum temperature (K) (SIMPLEC)	Maximum temperature (K) (COUPLED)	Average temperature (K) (SIMPLE)	Average temperature (K) (SIMPLEC)	Average temperature (K) (COUPLED)
`0.01m`	`84494`	`15849`	`374.961`	`375.1435`	`378.7989`	`320.0105`	`320.0264`	`312.1207`

 

It can be inferred that the most stable graph is given by the "COUPLED" scheme. Moreover, the "COUPLED" scheme takes less time for convergence because the pressure and velocity equation are solved instantaneously but require more computer space, on the other hand, "SIMPLE" and "SIMPLEC" scheme are segregated schemes where the pressure and velocity equations are solved sequentially, takes more time for convergence and requires less computer space.

Case-2 First refinement

Enclosure mesh

Graphic card component

 

 

Body mesh sizing statistics

Mesh Refinement	Element size	Body size(support bracket)	Body size(fins base and graphics card base)	Body size(processor, memory card, and capacitors)	Percentage decrease in element size
First refinement	`9.9mm`	`8.91mm`	`8.019mm`	`7.2171mm`	`10%`

 

Edge sizing statistics

Mesh Refinement	Edge sizing processor Number of divisions	Edge sizing memory card Number of divisions	Edge sizing capacitors Number of divisions along the diameter	Number of elements	Number of nodes
First refinement	`10`	`2`	`9`	`176936`	`35312`

 

Residual plot for `1` `frac{m}{sec}`

The convergence is achieved after 100 iterations.

Max of temperature plot for `1` `frac{m}{sec}`

 

Residual plot for `2.5` `frac{m}{sec}`

The convergence is achieved after 100 iterations.

 

Max of temperature plot for `2.5` `frac{m}{sec}`

 

Residual plot for `5` `frac{m}{sec}`

The convergence is achieved after 100 iterations.

Max of temperature plot for `5` `frac{m}{sec}`

 

 

Case-3 Second refinement

Body mesh sizing statistics

Mesh Refinement	Element size	Body size(support bracket)	Body size(fins base and graphics card base)	Body size(processor, memory card, and capacitors)	Percentage decrease in element size
Second refinement	`9mm`	`8.1mm`	`7.29mm`	`6.561mm`	`10%`

 

Edge sizing statistics

Mesh Refinement	Edge sizing processor Number of divisions	Edge sizing memory card Number of divisions	Edge sizing capacitors Number of divisions along the diameter	Number of elements	Number of nodes
Second refinement	`12`	`4`	`10`	`260034`	`51694`

 

Residual plot for `1` `frac{m}{sec}`

The convergence is achieved after 100 iterations.

Max of temperature plot `1` `frac{m}{sec}`

Residual plot for `2.5` `frac{m}{sec}`

The convergence is achieved after 100 iterations.

Max of temperature plot `2.5` `frac{m}{sec}`

Residual plot for `5` `frac{m}{sec}`

The convergence is achieved after 100 iterations.

Max of temperature plot `5` `frac{m}{sec}`

Case-4 Third refinement

Body mesh sizing statistics

Mesh Refinement	Element size	Body size(support bracket)	Body size(fins base and graphics card base)	Body size(processor, memory card, and capacitors)	Percentage decrease in element size
Third  refinement	`8mm`	`7.2mm`	`6.48mm`	`5.832mm`	`10%`

 

Edge sizing statistics

Mesh Refinement	Edge sizing processor Number of divisions	Edge sizing memory card Number of divisions	Edge sizing capacitors Number of divisions along the diameter	Number of elements	Number of nodes
Third refinement	`14`	`6`	`12`	`316756`	`64056`

 

Residual plot for `1` `frac{m}{sec}`

The convergence is achieved after 100 iterations.

Max of temperature plot `1` `frac{m}{sec}`

Residual plot for `2.5` `frac{m}{sec}`

The convergence is achieved after 100 iterations.

Max of temperature plot `2.5` `frac{m}{sec}`

Residual plot for `5` `frac{m}{sec}`

The convergence is achieved after 100 iterations.

 

Max of temperature plot `5` `frac{m}{sec}`

 

Result

First refinement

Velocity `1` `frac{m}{sec}`

Temperature contour

Potential hotspot region

Temperature profile

Velocity profile

Velocity `2.5` `frac{m}{sec}`

Temperature contour

Potential hotspot region

 

Temperature profiles

Velocity profiles

 

Velocity `5` `frac{m}{sec}`

Temperature contour

Potential hotspot region

Temperature profiles

 

Velocity profiles

Second refinement

Velocity `1` `frac{m}{sec}`

Temperature contour

Potential hotspot region

Temperature profiles

Velocity profiles 

Velocity `2.5` `frac{m}{sec}`

Temperature contour

Potential hotspot region

Temperature profiles

Velocity profiles 

Velocity `5` `frac{m}{sec}`

Temperature contour

Potential hotspot region

Temperature profiles

Velocity profiles 

 

 

 

Third  refinement

Velocity `1` `frac{m}{sec}`

Temperature contour

Potential hotspot region

Temperature profiles

Velocity profiles 

Velocity `2.5` `frac{m}{sec}`

Temperature contour

Potential hotspot region

Temperature profiles

Velocity profiles

Velocity `5` `frac{m}{sec}`

Temperature contour

Potential hotspot region

Temperature profiles

Velocity profiles

Vector analysis for the refined mesh

Calculation of heat transfer coefficient

Length of processor=`0.008m`

Width of processor=`0.008m`

Height of processor=`0.001m`

Aspect ratio=`frac{H}{L}``=` `frac{1}{8}`

Characteristic length`=` `L**(2*(AR+1))^0.5``=0.008**(2**(frac{1}{8}+1))^0.5``=``0.012`

Reynolds number`=``frac{rho**v**L_(char)}{mu}``=frac{1.225**v**0.012}{1.7894e-05}`

Reynolds number for inlet velocity `1` `frac{m}{sec}``=``821.50`

Reynolds number for inlet velocity `2.5` `frac{m}{sec}``=``2053.76`

Reynolds number for inlet velocity `5` `frac{m}{sec}``=``4107.52`

Prandtl number for the air `=` `frac{mu**c_p}{K}``=``frac{1.7894e-05**1006.43}{0.0242}``=` `0.744`

Nusselt number for characteristics length `L_(char)``=frac{2}{(pi)^0.5}**frac{1}{(frac{(AR+1)**C}{(2**(AR+1))^0.5})^0.5}**R_e^0.5**P_r^frac{1}{3}`

Thus Nusselt number for `1` `frac{m}{sec}` `=` `21.3937`

Nusselt number for `2.5` `frac{m}{sec}` `=` `33.827`

Nusselt number for `5` `frac{m}{sec}` `=` `47.838`

Average heat transfer coefficient of the processor for inlet velocity `1` `frac{m}{sec}` `=` `frac{Nu_(Lchar)**K_(air)}{L_(char)}``=``43.143` `frac{W}{m^2K}`

Average heat transfer coefficient of the processor for inlet velocity `2.5` `frac{m}{sec}``=``68.2177` `frac{W}{m^2K}`

Average heat transfer coefficient of the processor for inlet velocity `5` `frac{m}{sec}``=``96.4733``frac{W}{m^2K}`

Source: Simplified Analytical Models for Forced Convection Heat Transfer from cuboids of Arbitrary shape-M.M.YOVANOVICH

 

Comparison of all cases

Mesh refinement	Inlet velocity	Pressure-velocity coupling scheme	Number of elements	Maximum temperature (K)	Average temperature (K)
Baseline mesh	`1 msec^-1`	Coupled	`84494`	378.7989	`312.1207`
First refinement	`1 msec^-1`		`176936`	`387.0458`	`370.3678`
	`2.5``msec^-1`			`352.8055`	`339.7263`
	`5``msec^-1`			`336.8572`	`326.0632`
Second refinement	`1``msec^-1`		`260034`	`386.4317`	`370.1608`
	`2.5msec^-1`			`351.9068`	`339.0548`
	`5msec^-1`			`336.1952`	`325.5599`
Third refinement	`1 msec^-1`		`316756`	`385.6845`	`369.5099`
	`2.5msec^-1`			`353.1334`	`340.198`
	`5msec^-1`			`337.1427`	`326.5421`

 

Average heat transfer coefficient values  

S No	Input velocity	Reynolds number	Maximum temperature (K)	Average temperature (K)	Heat transfer coefficient  (`frac{W}{m^2K}`)
1	`1msec^-1`	`821.50`	`385.6845`	`369.5099`	`43.143`
2	`2.5msec^-1`	`2053.76`	`353.1334`	`340.198`	`68.2177`
3	`5msec^-1`	`4107.52`	`337.1427`	`326.5421`	`96.4733`

 

Conclusion

• The steady-state CHT analysis for the graphics card was carried successfully for inlet velocities ( `1msec^-1`, `2.5msec^-1`, `5msec^-1`)
• The flow is laminar and the no-slip condition combined with viscous effects makes the velocity adjacent to the wall near the cell to be zero.
• The grid independence test was observed by running the simulation for three different mesh refinement, for reducing the computational time and thus achieving the convergence rate faster.
• The flow is uniform, as it reaches the geometry it gets heated by the processor and aluminum fin. The air gets unequally heated in that region leading to the change in profile.
• The maximum temperature plot depends largely upon the inlet velocity of air, which varies inversely. This can be attributed to the fact that the air carries away the heat generated from the processor due to forced convection, thus the higher the velocity of the air more is the heat transfer, which results in a lower maximum temperature as observed during simulation.
• The processor is dissipating a constant TDP value of 150 W, much of the heat is carried away by aluminum fins base and base of the graphics card by conduction.
• The potential hotspot region is identified near the processor region.
• From the vector analysis for the refined mesh, it can be observed that there are recirculation zones at the rear end of the graphics card which can be minimized by changing the design features of the rear end of the graphics card and improving the heat transfer rate which will enhance the life of the graphics card.