A Comparative Study of Thermoconvective Flows of a Newtonian Fluid Over Three Horizontal Undulated Surfaces in a Porous Medium

Abstract

This paper presents a comparison between the results of three thermoconvective flows of a Newtonian fluid over uniformly heated, undulated horizontal surfaces in a porous medium against the background of the results of a flat plate. The undulations are assumed to have sinusoidal, sawtooth, and triangular waveforms. A system of nonlinear coupled partial differential equations arising in the study is solved using the Keller–Box method. Streamlines and isotherms have been plotted and analyzed to examine the effect of parameters on the fluid dynamics and heat transfer. At large surface amplitudes, secondary flow is observed in the cases of sinusoidal and triangular waveforms, but not in the cases of a sawtooth surface and a flat plate. The magnitude of the slip velocity at the horizontal surface is greatest for the sine waveform, while it is least in the case of triangular. The flat plate does not support slip in the velocity to the extent seen in the case of undulated surfaces. The variation of the mean Nusselt number and mean skin friction with surface amplitude and the Rayleigh number indicate that heat transfer and viscous friction at the boundary increase with individual and collective increases in the values of the amplitude and the Rayleigh number. Further, the mean Nusselt number and mean skin friction are found to be maximum for the sinusoidal surface and minimum for the triangular one. The heat transfer and skin friction by the flat surface are much less than that of all three undulated surfaces.