Fully-developed natural convection in a periodic array of pin-fins

The pin-fin heat exchangers/sinks show better performance over other conventional heat exchangers/sinks due to its high surface area to volume ratio and finds application in the field of thermal management of modern electronic components. The present study deals with the two-dimensional numerical investigation of natural convection in an array of periodically in-line mounted square pin-fins. The effect of variation in geometric parameters on the fluid flow and heat transfer has been investigated for different Grashof number. Both the Navier-Stokes and energy equations have been solved using second order spatial and temporal discretizations in the framework of finite difference method. Periodic boundary conditions have been employed for velocity, temperature and pressure. Numerical simulation has been carried out using MAC algorithm for a range of geometrical pitch ranging between 1.5 and 3.0. A Prandtl number of 0.7 (corresponding to air) has been used. The results show that the flow becomes unsteady and periodic oscillatory above a critical Grashof number. This critical value of Grashof number is found to decrease with increasing fin spacing. The Nusselt number is also found to increase with increase in Grashof number for a particular pitch whereas a decrease in Nusselt number is observed with increase in pitch at constant Grashof number.