Thermal resistance analysis of pin-fin heat sinks under nonuniform impingement heating

A thermal resistance analysis for pin-fin heat sinks subjected to nonuniform flame impinging-jet heating is presented. Explicit analytical expression of the overall total resistance is obtained by evaluating each of the individual thermal resistances in the circuit, including the spreading resistance, the material resistance, the convective resistance, and the resistance due to fluid temperature rise. Upon modeling the nonuniform heat flux distribution over the entire upper surface of the substrate due to flame impinging-jet heating with an exponential function, the spreading resistance within a circular plate is obtained analytically. To verify the assumptions/approximations made in the analogy model, the results predicted by the thermal resistance analogy model are compared with those obtained from a three-dimensional numerical model, with overall good agreement achieved. The interaction of heat conduction in the substrate and heat convection in the fluid flow is then investigated using the analogy model. Obtained results demonstrate that increasing the rate of convection heat transfer decreases the spreading resistance in the substrate. Furthermore, an optimal substrate thickness is found to exist when the lateral spreading of heat in the substrate is balanced by that conducted through the thickness direction of the substrate.