Natural Convection Heat and Momentum Transfer in Rectangular Enclosures Heated at the Lower Portion of the Sidewalls and the Bottom Wall and Cooled at the Remaining Upper Portion of the Sidewalls and the Top Wall

Abstract

Laminar natural convection inside air-filled, rectangular enclosures heated from below and cooled from above, with the lower portions of both sidewalls maintained at the temperature of the bottom wall, and the remaining upper portions of the sidewalls maintained at the temperature of the top wall, is studied numerically. A control volume formulation of the finite-difference method is used for the solution of the mass, momentum, and energy transfer governing equations. Simulations are performed for height-to-width aspect ratios of the cavity from 1 to 5, Rayleigh numbers based on the height of the cavity from 5 × 10² to 5 × 10⁶, and values of the heated fractions of both sidewalls from 0 to 1. It is found that when the heated portions of the two sidewalls are different in length, a steady-state solution is reached, with a basic three-cell flow pattern. In contrast, when the heated fractions of the sidewalls are the same, the asymptotic solution may be either stationary, with a flow field consisting of two pairs of superimposed roll cells, or periodic, with a flow pattern consisting of a primary cell and two secondary cells that pulsate about the center of the enclosure. Dimensionless heat transfer correlating equations are proposed.