Analysis of Natural Convection Due to Localized Heating in a Shallow Water Layer

Abstract

Natural convection due to localized heating from an array of horizontal cylinders in a shallow water layer has been simulated numerically by approximating the symmetrical region between cylinders as an enclosure with localized heating from a side. Calculations performed for a Rayleigh number range between 103 and 3 X 105 reveal a unicellular vortex motion characterized by three thermal boundary-layer regions (two vertical boundary layers at the sides of the enclosure and a horizontal boundary layer at the air-water interface) In the core region between the boundary layers, the temperature is approximately uniform along horizontal lines but increases slightly along vertical lines to provide a stratified condition. Heat transfer increases with increasing Rayleigh number and decreasing aspect ratio, slightly exceeding that associated with uniform heating from below.