Conjugate Heat Transfer CHT Analysis on a Graphics Card

Aim : To perform a Conjugate Heat Transfer (CHT) Analysis on a Graphics Card.

Theory :

Conjugate Heat Transfer (CHT) Analysis:

Conjugate Heat Transfer analysis is used for the processes that involve variation of temperatures with respect to solids and fluids, due to thermal interaction between them. A typical example would be a heating or cooling of a solid by the flow of air.

The exchange of heat between two bodies is known as the heat transfer and the rate of heat transferred is directly proportional to the temperature difference between them. Heat transfer in solids are usually occured by conduction whereas in the case of fluids heat transfer occurs by convection. Efficiently combining heat transfers between solids and fluids are the key to design effective coolers, heaters or heat exchangers. Forced convention is the most common way to achieve higher heat transfers. For some applications, the performance are further improved by combining convectionwith phase change(example liquid water to vapour phase change).

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

Accurate description of parameters such as material properties, flow regimes , geometry configurations, selecting correct models based on the physics to be captured, heat transfer modes near the boundaries is needed for the analysis of temperature fields and heat transfer.

Practical CHT problems are used to determine:

• Maximum and minimun temperature in various parts of the system. eg:combustion chamber, gas turbines, chemical vessels etc.
• Temperature Distribution which is related to the thermal stress over a particular wall or system etc.
• Tempearture Response in time-dependent applications such as heating/cooling problem (For example, In the case of cooling a particular system such as engine cooling)
• Overall heat transfer co-efficient.

CHT Analysis of Graphics Card

CHT analysis is performed on an graphics card to determine maximum temperature, hotspots and heat transfer coefficient. Two simulations are performed in this analysis one for the baseline mesh case and for the refined mesh case. We will be comparing the results of these two cases.

We will be going through the common steps used in the CFD analysis.

• Geometry Preparation:

We import the solid model into Ansys Spaceclaim and differentiate different components of the Graphic Card. We will be dividing the graphic card into parts:

• Base.
• Processor.
• Fins.
• Enclosure.

The geometry can be viewed below:

The different parts and enclosure can be seen in the figure below:

Then we will be relating each of the component using share topology to obtain a conformal mesh. By using shared topology we will have the information (i.e in this case heat transfer) transfered accurately between the solid-solid interfaces. Inside the enclosure, flow of air takes place which passes through the graphic card at specific temperature and velocity to cool the graphic card surfaces and maintain a optimal temperature.

In this case study, we will be mainly focusing on CHT analysis taking place between two solid bodies i.e. Processor (Heat Source) and the Fins by conduction process and between a solid and a fluid body i.e. Fins and air by convection process. Fins helps the processor to maintain a safe temperature by increasing the surface area for the heat transfer and air flows over the fin at a certain velocity which helps in maintaining the safe temperature through convective heat transfer taking place between them.

Usually the power consumed by a processor is converted into heat energy. We will be assuming a processor which ideally consumes 50 W. From the geometry the total volume of the processor is `64 mm^3`. Hence we can calculate the heat generation rate of the processor as below:

`50/(64*10^-9) W/m^3 = 781250000 W/m^3`

Baseline Case :

• Meshing

Number of elements : 128205

Element Size: 0.005 m

• Body Sizing : is used for graphic card.

Element Size: 0.015 m

The image of the sectional view of the mesh along with the enclosure for the baseline case can be seen below:

The image of the mesh of graphic card for the baseline case can be seen below:

Mesh quality for the baseline case can be seen in the graph below:

From the above graph we can see the mesh quality is not less than 5% and maximum number of elements falls between 75 ~ 96%. Hence we can conclude that this mesh quality is good and can be proceeded further.

Also we will be naming the various boundaries such as:

• inlets.
• outlet.
• walls.

• Setup:

We will be using a pressure based solver. Also we will be solving for the Energy equation and standard k-epsilon turbulence model. The matrial used for the fluid would be the standard air and for the solid the materials we will be using aluminium for the base, copper for the fins and gold for the processor from the ansys material libary. We will be defining the materials for the respective parts under the command cell zones. Also for the processor we will be selecting the source terms since heat is generated by the processor. The value of the source term is calculated as shown above whose value is set to be `781250000 W/m^3`.

Next we will be moving on to setup the boundary conditions.

• inlet: The type is set to velocity inlet and the velocity magnitude is set to 5 m/s. Also the initial temperature of the incoming air at the inlet is set to 300 K.

• outlet: The type is set to pressure outlet and the guage pressure is to 0 pascal.

• walls: The type is set to wall and wall motion is set to stationary. The shear condition is set to no slip and wall roughness is set to standard.

Then we will be setting up the hybrid initializtion to initialize the solution and create some useful plots such as the temperature contours. Once these details has been set we will be proceeding to solve using steady state with 500 iterations.

Results:

Residual Plots:

Covergence Proof:

From the above plot we can see that the solution has been converged and after certain iterations the trend is repeating. Hence we can conclude that the solution is converged. The convergence criteria used in this case is 1e-03.

Temperature Contour (Front View):

Temperature Contour (Back View):

From the above contour plots we can see that the temperature is maximum at the processor and fins. The maximum temperature obtained in this case is 326.44 K.

Temperature Contour of the Graphic Card:

Temperature Contour of the Graphic Card without fin:

Temperature Contour of the Graphic Card (Back View):

Temperature Contour of the Graphic Card along plane XZ:

Velocity Contour of the Graphic Card along plane XZ:

Wall Heat Transfer Coefficient contour of the Graphic Card along plane XZ:

Wall Heat Transfer Coefficient Contour of the Graphic Card:

Wall Heat Transfer Coefficient Contour of the Graphic Card without Fin:

Refined Case :

• Meshing

Number of elements : 250445

Element Size: 0.005 m

• Body Sizing : is used for graphic card.

Element Size: 0.001 m

• Body Sizing : Another body sizing is used for the processor and the fins as the heat is generated and dissipated through these bodies. Hence a finer mesh size is used for these bodies

Element Size: 0.0008 m

The image of the sectional view of the mesh along with the enclosure for the baseline case can be seen below:

The image of the mesh of graphic card for the baseline case can be seen below:

Mesh quality for the baseline case can be seen in the graph below:

From the above graph we can see the mesh quality is not less than 5% and maximum number of elements falls between 75 ~ 96%. Hence we can conclude that this mesh quality is good and can be proceeded further.

Also we will be naming the various boundaries similar to the previous case such as:

• inlets.
• outlet.
• walls.

• Setup:

We will be using a pressure based solver. Also we will be solving for the Energy equation and standard k-epsilon turbulence model. The matrial used for the fluid would be the standard air and for the solid the materials we will be using aluminium for the base, copper for the fins and gold for the processor from the ansys material libary. We will be defining the materials for the respective parts under the command cell zones. Also for the processor we will be selecting the source terms since heat is generated by the processor. The value of the source term is calculated as shown above whose value is set to be `781250000 W/m^3`.

Next we will be moving on to setup the boundary conditions.

• inlet: The type is set to velocity inlet and the velocity magnitude is set to 5 m/s. Also the initial temperature of the incoming air at the inlet is set to 300 K.

• outlet: The type is set to pressure outlet and the guage pressure is to 0 pascal.

• walls: The type is set to wall and wall motion is set to stationary. The shear condition is set to no slip and wall roughness is set to standard.

Then we will be setting up the hybrid initializtion to initialize the solution and create some useful plots such as the temperature contours. Once these details has been set we will be proceeding to solve using steady state with 500 iterations.

Results:

Residual Plots:

Covergence Proof:

From the above plot we can see that the solution has been converged and after certain iterations the trend is repeating. Hence we can conclude that the solution is converged. The convergence criteria used in this case is 1e-03.

Temperature Contour :

Temperature Contour of the Graphic Card:

Temperature Contour of the Graphic Card without fin:

Temperature Contour of the Graphic Card (Back View):

From the above contour plots we can see that the temperature is maximum at the processor and fins. The maximum temperature obtained in this case is 323.22 K.

Temperature Contour of the Graphic Card along plane XZ:

Velocity Contour of the Graphic Card along plane XZ:

Wall Heat Transfer Coefficient contour of the Graphic Card along plane XZ:

Wall Heat Transfer Coefficient Contour of the Graphic Card:

Wall Heat Transfer Coefficient Contour of the Graphic Card without Fin:

Discussions:

From the temperature contours of the above cases we can observe that the heat is dissipated from the heat source which is the processor to the fins and the base plate. Since fins have a higher thermal conductivity more heat is disspated through the fins rather than the base. At the region of interaction between the fins and air, we can observe that the temperature of the air is increased due to the dissipation of heat from the fins to air by means of forced convection. The initial velocity of the domain was set to 5 m/s. From the above velocity contours we can observe that the velocity decreases near the region of interaction between the solid and fluid. Flow seperations can be observed in the wakes of the graphic card. Maximum fluid velocity is 5.89 m/s (Case 1) and 6.05 m/s (Case 2). From the contours of wall heat transfer coefficients we can observe that the higher values are at the walls of the processors and fins. The maximum value of heat transfer coefficient is 931.88 W/m^2K (Case 1) and 927.29 W/m^2K (Case 2).

Conclusions:

• The simulations for the Base case and the Refined case were done successfully.

• The processor, fins and the base are the areas focused for refining of the mesh as the physics near these components were important to be analysed.

• From the temperature contours, we can say see that the temperature on the fins is approximately equal to to the temperature of the processor. This is an ideal behaviour for the graphic card since fins takes most of the heat generated by the processor. Usually the surface area of the fins is larger which improves the cooling of the graphic card.

• The potential hotspots on the model are processor, fins and the contact region between processor and base.