A comprehensive investigation of natural convection inside a partially differentially heated cavity with a thin fin using two-set lattice Boltzmann distribution functions

Abstract Natural convection occurs in many engineering systems such as electronic cooling and solar collectors. Nusselt number ( Nu ) is one of the most important parameters in these systems that should be under control. This investigation is a comprehensive heat transfer analysis for partially differentially heated cavities with a small thin fin mounted on the hot wall of the cavity to increase or decrease the Nu . A Boussinesq approximation was utilized to model the buoyancy-driven flow. Two sets of distribution functions for the lattice Boltzmann method are used to resolve the continuity, momentum and energy equations. A total of 180 cases were analyzed to determine the average maximum and minimum Nu for the hot section of the cavity. For the cases investigated, the hot and cold sections were assumed to comprise approximately 30% of the vertical walls. After obtaining the velocity and temperature distributions for the cavity, three different Rayleigh numbers, i.e., 10 4 , 10 5 and 10 6 , were used to provide streamlines and isotherms for a number of cases. The average and normalized Nusselt numbers were then computed and compared graphically for all of the cases investigated. The results indicated that by choosing the appropriate position for the fin, the average Nu could be increased by more than 150%.