Free convection fluctuating flow on a horizontal magnetized plate

Abstract

The free convection flow of electrically conducting fluid along a semi-infinite horizontal magnetized plate is analysed, when the plate temperature oscillates about a constant mean. The basic steady flow is purely buoyancy induced, while the oscillations in the plate temperature cause a time-dependent boundary layer flow and heat transfer. The unsteady boundary layer equations are linearized and the first two approximations are considered. Two separate solutions valid for high and low frequency ranges are obtained by series expansion method in terms of frequency parameters. For very high frequencies, the oscillatory flow pattern is of ‘shear-wave’ type unaffected by the mean flow. The skin friction in the very high frequency solution has a phase lag of 45° while the phase of heat transfer oscillations is ahead of the plate temperature fluctuations by π/4.