Natural convection from inclined plates to gases and liquids when both sides are uniformly heated at the same temperature

Steady, laminar natural convection from inclined thin plates immersed in an unbounded fluid space is studied numerically. The salient feature of the study is that the upper and lower sides of the plate are simultaneously heated at the same uniform temperature. A specifically developed computer-code based on the SIMPLE-C algorithm is implemented for solving the coupled system of mass, momentum, and energy conservation equations. Numerical simulations are performed for representative combinations of (a) the inclination angle of the plate with respect to the gravity vector, tit, sweeping from 0 degrees to 75 degrees, (b) the Rayleigh number, Ra, ranging from 10 to the smaller Ra between 10(7) and the critical value that marks the onset of longitudinal vortices above the plate, and (c) the Prandtl number, Pr, spanning from 0.7 to 140. Resorting on the computed velocity and temperature fields, all possible heat transfer avenues are explored and analyzed in detail. Comparisons with the standard case of one-sided heating of the plate when the other side is thermally insulated are executed and discussed at length. It is found that the heat transfer rate at the two sides of the plate increases with increments in the Rayleigh number and/or the Prandtl number, while decreases with widening the inclination angle of the plate. In addition, a noteworthy fact is that the heat transfer performance of the lower side of the plate is practically independent of the heat activity at the upper side of the plate, i.e., when both sides are heated at the same temperature or when one side is heated while the other is thermally insulated. Conversely, in most cases the amount of heat exchanged at the upper side of the plate diminishes when the lower side is heated instead of being thermally insulated. Comprehensive correlation equations for the three emerging average Nusselt numbers are developed for purposes of engineering analysis and design. (C) 2011 Elsevier Masson SAS. All rights reserved.