A Semi-Empirical Heat Transfer Model for Forced Convection in Pin-Fin Heat Sinks Subjected to Nonuniform Heating

This paper presents a cost effective semi-empirical analytical model for convective heat transfer in pin-fin heat sinks subjected to nonuniform heating set by a circular hot gas impinging jet. Based on empirical correlations taken from the open literature, temperature variations in the heat sink are obtained from the finite volume solution of the semi-empirical model. Based on a purpose-built experimental setup, measurements of a substrate temperature are performed using an infrared camera. These, along with the convective fluid temperature measured at the exit of the pin-fin array, are compared against analytical model predictions, with overall good agreement achieved. Subsequently, the influences of the convection Reynolds number, substrate thickness, and thermal conductivity of material on the distribution of substrate temperature are quantified by the validated model. It is demonstrated that the present model is capable of predicting local thermal behaviors such as the footprints of the pin fins. In addition, with the spreading resistance captured accurately, the model can be used for the design optimization of pin-fin/substrate systems subjected to nonuniform heating.