The process of heat transfer by natural convection in a square enclosure the temperature of one of whose walls varies by sine law

The unsteady-state natural convection in a square enclosure arranged at an angle $\alpha$ ($0$ to $90^\circ$) to the horizontal is numerically investigated. One of the sides of the enclosure is maintained at a constant temperature, and the other, opposite side, at a temperature, which varies by the sine law and, on the average during a period, is lower than that of the side with constant temperature. The other two sides of the enclosure are taken to be adiabatic. Numerical solutions are obtained for the Grashof number of $5\times10^5$ and the Prandtl number equal to unity, in a wide range of variation of the oscillation frequency of the temperature of one of the walls of the square enclosure. The results are obtained using the control volume approach on the basis of the SIMPLER algorithm.