Conjugate Heat Transfer Analysis on a graphics card.
Objective
Simulation of heat dissipation of processor embedded on graphics card.
Introduction
Heat is continuously generated in processor. Increase in temperature of processor affects the performance of the device. Cooling fan and fins are provided on graphics card to cool the processor. Heat is conducted conducted to graphics card while some amount of heat is convected. This simultaneous conduction and covection mode of heat transfer is called conjugate heat transfer (CHT).
Since the governing equations of fluid and solid domains are different, numerical treatment and solution strategy may also differ in individual solution domains. However those solutions required to be coupled at the solid-fluid interface through dynamic update of interface boundary condition. Govering equation for conjugate heat tranfer are:-
Contunity equation
`{∂u}/{∂x}+{∂v}/{∂y}=0`
2-D Momentum equation
`{∂u}/{∂t}+u{∂u}/{∂x}+v{∂u}/{∂y}=−1/ρ{∂p}/{∂lx}+gβ(T−T∞)+v{∂^2u}/{∂y^2}`
2-D Convective heat transfer equation
`{∂T}/{∂t}+u{∂T}/{∂x}+v{∂T}/{∂y}=α{∂^2T}/{∂y^2}+vCp(∂u/∂y)^2`
2-D Heat conduction equation
`ρ_sC_s{∂T_s}/{∂t}=λ_s({∂^2T_s}/{∂x^2}+{∂^2T_s}/{∂y^2})+q_v`
Geometry
Dimension of graphics card.
Enclosure for the graphics card.
Meshing
Meshing of graphics card with mesh size =0.65mm
Meshing of enclosure with mesh size =3mm
Total number of node=89,666
Total number of elements=511,448
Simulation Setup
The model is simulated using k-epsilon turbulent model and run for 500 iterations. Medium inside enclosure is air. Graphics card and processor are assumed to be made up of aluminium and titanium respectively.
Initial Condition
Inlet is velocity inlet and outlet is pressure outlet with zero gauge pressure. The model is run for three different velocity.
Results
Plot for inlet air velocity=5m/s
Residual Plot
From above plot, we can observe that simulation get converged around 150 number of iterations.
Temperature contour of whole graphics card
Temperature contour of processor
Wall heat transfer coefficient of graphics card
Wall heat transfer coefficient in processor
Plot for inlet air velocity=3m/s
Residual Plot
From above plot, we can observe that simulation get converged around 150 number of iterations but fluctuation is more evident.
Temperature contour of whole graphics card
Temperature contour of processor
Wall heat transfer coefficient of graphics card
Wall heat transfer coefficient of processor
Plot for inlet air velocity=1m/s
Residual Plot
From above plot, we can observe that simulation get converged around 150 number of iterations and curve is quite smooth without fluctuation.
Temperature contour of whole graphics card
Temperature contour of processor
Wall heat transfer coefficient of graphics card
Wall heat transfer coefficient of processor
Conclusion
Since, heat generation is in processor and specific heat capacity of titanium is low, high temperature point within the processor. The wall heat transfer coefficient is high at front and side walls of processor because high velocity air directly comes into contact of these surfaces. In all cases, maximum temperature (close to 300.003K) and maximum wall heat transfer coefficient(5870 watt/m2-K) are almost same. This may be because of material properties and effectiveness of fins.