Exponential nonuniform wall heating of a square cavity and natural convection

Abstract

The process of a nonuniform wall heating of a square cavity and the resulting natural convection phenomenon is numerically analyzed within the present work. While the left vertical wall of the cavity is exposed to a nonuniform heating source, the right opposite wall is uniformly cooled and the other horizontal walls are kept adiabatic. The paramount importance of the problem is the transfer of heat and mixing as a consequence of the triggered fluid convection through the cavity. A finite element technique is employed for the simulation of thermally driven flow. Numerical accuracy of the method is initially justified through validation of the benchmark results of the traditional natural convection due to a constantly heated wall. Then a nonuniform wall heating is adopted such that the heating position center varies on the vertical wall controlled by a position parameter. Numerical heat flows and stream flows together with the local/average values of Nusselt number are displayed graphically with changing position parameter and Rayleigh number. A visual analysis of the heat transport and mixing via the natural convection is made. It is anticipated that the heating position has heat transfer enhancing impact if the center of heating is closer to the upper horizontal wall. The formation of thinner boundary layer and thermal layer as a consequence of nonuniform surface heating leads to redistribution of streamlines and temperatures. The best heat transfer rate is obtained as the heating takes place near the top wall of the heated boundary.