Unsteady natural convective flow in an enclosure when there are sharp changes in side-wall temperature

摘要

Natural convective flow in a square enclosure with a section of one of the vertical walls heated and with the opposite wall cooled to a uniform temperature, the remaining walls being adiabatic, has been umerically studied. The temperature of the heated wall section is constant but that of the cold wall aim of the study was to detrmine how the nature of the temperature variation at the cooled surface influences t he heat transfer rate from the hot surface. The flow has been assumed to be laminar and two-dimensional. Fluid propoerties 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 deimensionless form. The resultant equation have been solved using the finte-element method. The solution has the Rayleight number, the Prandtl number, the dimensionless size and position of the heated wall section and the form of the cold wall dimensionless temperature variation with dimensionless time as parameters. Because of the possible applications that motivated the study, results have only been obtained for a Prandtl number of 0.7. The dimensionless cold section temp[erature has been assumed to undergo a sharp rise in value followed a short time later by a sharp drop in its value. Results have then been obtained for modified Ralyeight numbers between 1,000 and 1,000,000 for heated wall sections of various dimensionless size and position.