Heat transfer in heat sinks: An analytical approach based on integral transforms

Heat sinks are crucial components in electronic devices, dissipating heat generated by the device's components. Analyzing heat transfer in heat sinks is crucial for efficient device design. In this article, an analytical approach is proposed for obtaining temperature field in heat sinks. The approach utilizes a 3D formulation for the base and a 2D formulation for the fins, which are solved using the Classical Integral Transform Technique (CITT) and coupled through eigenfunction expansions to determine the interface contact heat fluxes on each fin. An important advantage of the proposed eigenfunction expansion coupling for the interface heat fluxes is that the transform of the interface heat flux is already included in the analytical expressions for the fins and base. This eliminates the need to use the inversion formula, thus avoiding any additional truncation errors and improving the accuracy of the results. The proposed methodology is demonstrated to be effective through different symmetrical and non-symmetrical test cases using CITT and verifying the achieved results with OpenFOAM simulations. The suitability of the partial lumping approach in the fin's thickness for heat sink problems is also demonstrated. The proposed methodology provides a reliable and efficient fully analytical solution for heat sinks used in devices that require heat transfer enhancement applications.