Simulation of Mixed Convection Air Cooling of Protruding Heat Sources Mounted on One Side of a Vertical Channel

A numerical study of steady, laminar, two-dimensional mixed convection air cooling of identical as well as non-identical rectangular protruding heat sources located on one side of a vertical channel is presented in this paper. The stream function-vorticity-temperature approach with the finite-difference-based methodology implementing higher order upwind scheme has been applied. Three cases have been considered, namely (i) when the number of identical chips is two; (ii) when the number varies from 3 to 10; and finally, (iii) when five chips of different heights but of same width are placed in various orders. For the case of two chips the effects of Re, Gr/Re² (that is, Richardson number), dimensionless separation distance between the chips (d/H), dimensionless chip height (h/H) and width (w/H) on the average Nusselt number of each chip have been investigated. A correlation based on regression analysis is also presented for each parameter. With increase in Reynolds number the average Nusselt number of both chips increases. Similar trend is seen when the separation distance between two chips is raised. It is also observed that as the number of chips escalates from 2 to 10, the average Nusselt number of downstream chips becomes smaller than that of the upstream chips, the rate of drop being much sharper near the channel inlet. A regression-analysis based composite correlation each for average Nusselt number of Chip 1 (lower chip) and Chip 2 (upper chip) as a function of Reynolds number, Richardson number, separation distance between the chips, chip height and width has been obtained for the 2-chip case. The model also predicts maximum chip temperature in an array of ten chips. Finally, for five non-identical chips having same width but different heights the simulation reveals that the chips placed in increasing order of their heights in the direction of air flow are cooled better as compared to any other pattern of placement of the chips.