NATURAL CONVECTION IN A DIFFERENTIALLY HEATED SQUARE CAVITY WITH INTERNAL HEAT GENERATION

Abstract

A high-resolution, finite-difference numerical study is reported on natural convection in a square cavity. The vertical sidewatts of the cavity are differentially heated, and a uniform internal heat generation is also present. Two principal parameters are considered, the internal Rayleigh number Ra_I, which represents the strength of the internal heat generation, and the external Rayleigh number Rag, which denotes the effect due to the differential heating of the side walls. The internal Rayleigh number varies in the range 10¹⁰ Ra_I ≤ 10⁷, while the external Rayleigh number is set at Ra_E = 5 x 10⁷ for most computations. As the relative strength of the internal heat generation increases, the flows near the tap portion of the heated sidewall are directed downward. When the effect of the internal heat generation is dominant, the thermal energy leaves the system for the surroundings over the top portion of the heated wall. Only in the bottom pari of the heated wall is heat transfer directed into the system. These numerical solutions are in qualitative agreement with the available experimental measurements.