Heat Sink Fin Temperature Distribution

BLUF - I solved a heat sink fin heat transfer problem by hand, coded a MATLAB FEM solver, and used Abaqus for FEA to verify the results.

One primary bottleneck for compute performance is thermals. Pushing performance on CPUs and GPUs is proportional to power supplied, which consequently produces heat. Attaching thermally conductive elements to convect the heat into the chip's ambience alleviates the issue. Quantifying how is where engineering insight can be applied for iteratively finding an optimal design.

Hand Calculations

Using initial and boundary conditions as a starting point, I wrote the formulation for iteratively solving the temperarture distribution of a fin.

heat_sink_fin_transient.pdf

Results

The plots below accept the convection coefficient as an input parameter, which is determined by the heat sink coating and coolant liquid.

Increasing convection coefficient makes the fin cool faster along the fin's length

Increasing the convection coefficient gives diminshing returns for heat transfer

Thermal FEA - Abaqus

Solving for temperature and heat flux analytically is feasible for simple geometries. Complex geometries and assemblies of multiple different materials call for FEA software. I used Abaqus to model the fin of a heat sink and tested various temperatures and conditions.

Nodal temperature distribution for a higher base fin temperature and lower convection coefficient

Heat flux for a higher base temperature and lower convection coefficient

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