In this study, an entropy generation minimization, EGM, technique is applied as a unique measure to study the thermodynamic losses caused by heat transfer and pressure drop in cylindrical pin-fin heat sinks. The use of EGM allows the combined effect of thermal resistance and pressure drop to be assessed through the simultaneous interaction with the heat sink. A general expression for the entropy generation rate is obtained by considering the whole heat sink as a control volume and applying the conservation equations for mass and energy with the entropy balance. Analytical/empirical correlations for heat transfer coefficients and friction factors are used in the optimization model, where the characteristic length is used as the diameter of the pin and reference velocity used in Reynolds number and pressure drop is based on the minimum free area available for the fluid flow. Both in-line and staggered arrangements are studied and their relative performance is compared on the basis of equal overall volume of heat sinks. It is shown that all relevant design parameters for pin-fin heat sinks, including geometric parameters, material properties and flow conditions can be simultaneously optimized.
Khan et al. (Tue,) studied this question.