Laminar natural convection inside the open, forward-facing stepped rectangular enclosure with a partition and time-variant temperature on the stepped top wall

A finite difference based numerical study of two dimensional laminar natural convection inside the open rectangular forward stepped enclosure with sinusoidal time-variant temperature on the top wall is presented by vorticity-stream function approach. The enclosure is divided by a vertical partition at the middle with a central opening. The aspect ratio of the enclosure is 1.6. The top wall is constructed with a step of 20% of height of the enclosure. Except the top wall, all the outer walls are assumed as hot and maintained at constant temperature. The parameters governing the study are the amplitude (0 < a < 0.5) and the period (0.001 <τ < 0.8) of the variable temperature, the Rayleigh number (104 < Ra < 106), Prandtl number (Pr = 0.71), and the step. The effect of the amplitude and period on the heat transfer inside the enclosure is examined for constant temperature (a = 0) and varying temperature (a ≠ 0 and τ ≠ 0). The details of fluctuating flow and temperature fields are analyzed and the periodic results are elucidated with streamlines, isotherms and Nusselt number. The result indicates that the heat transfer increases with increasing amplitude and decreases with increasing period of oscillating temperature on the top wall. The heat transfer increases when buoyancy is increased through Rayleigh number. The provision of step increases the heat transfer on the right side of the upper wall due to the increasing buoyancy.