Natural Convection in a Square Enclosure With a Partially Heated Wall Section Covered by a Blind-Like Attachment in Which There Is a Linearly Varying Heat Generation Rate

Abstract

Natural convective heat transfer across a square enclosure with one vertical wall partially heated to a uniform high temperature and with the opposite vertical wall cooled to a lower uniform temperature has been numerically investigated. The remaining wall sections are adiabatic. The heated wall section is covered at the top and in the front by thin straight walls that offer no resistance to heat transfer. There is heat generation in vertical portion of this covering wall that is parallel to the heated wall section. The present work was undertaken as part of a wider study of the effect of window coverings on the heat transfer rate from windows, particularly for the case where the window is hotter than the room air. The situation being considered here is an approximate model of a window covered by a plane (roller) blind. In such situations there is often effectively heat generation in the blind as a result of the absorption of solar radiation. However, because of the sun angle and the effect of building overhangs, this heat generation is often not uniform along the blind. To study this effect, the case where there is a linearly varying rate of heat generation in the barrier (the “blind”) with the highest rate of heat generation at the bottom of the barrier and with no heat generation at the top has been considered. The flow in the enclosure has been assumed to be laminar and two-dimensional. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces. The governing equations have been written in dimensionless form and have been solved using a finite-element method. The solution has the Rayleigh number, the Prandtl number, the dimensionless distance of the barrier from the hot vertical surface, the mean dimensionless rate of heat generation in the barrier, and the dimensionless size of the heated wall section as parameters. Results have only been obtained for a Prandtl number of 0.7. The effect of the other dimensionless variables on the heat transfer rate from the hot wall section has then been numerically determined.