Natural Convection in a Corrugated Enclosure With Mixed Boundary Conditions

Abstract

Numerical solutions to the two-dimensional equations governing natural convective flow of air (Prandtl number = 0.71) contained in an enclosure with varying angles of inclination to the horizontal axis have been obtained. The air layer is bounded by a corrugated surface under uniform heat flux conditions, a flat isothermal cooled surface and around the edges by flat adiabatic surfaces. The numerical solutions are obtained in a transformed coordinate system in which the boundaries of the enclosure coincide with coordinate surfaces. The coordinate system is generated with simple algebraic expressions. The numerical scheme is employed in performing parametric heat transfer calculations. The range of parameters investigated include: modified Rayleigh numbers up to 106 , amplitude aspect ratio from 0 to 0.4, inclination angles of 30, 60, and 90 degrees, and number of cycles per unit length of enclosure values of 4/5 and 4. All parameters investigated have varying degrees of influence on the heat transfer and fluid flow. In addition to the usual influence of the modified Rayleigh number on natural convective flows, the region of pseudo-conduction is increased as the enclosure amplitude ratio is increased. The distributions of temperature along the corrugated surface suggest that correlations obtained under isothermal conditions cannot be employed in the design or analysis of the energy transfer system investigated.