A theory of convective heat transfer in a rotating hydromagnetic viscous flow

Abstract

An initial value investigation is made of the combined effects of the free and forced convection in rotating hydromagnetic viscous fluid flows under the action of a uniform transverse magnetic field. The hydromagnetic flow is generated in the uniformly rotating fluid bounded between two rigid non-conducting paralled plates by small non-torsional oscillations of the lower plate, and in addition, the plates are maintained at a constant temperature gradient in a direction parallel to the plane of the plates. The exact solutions of the velocity field and the temperature distribution are obtained by the Laplace transform method combined with the theory of residues. It is shown that the solutions consists of the steady-state and the transient components. The time required for the transient effect to decay is discussed in detail, and the ultimate steady-state is shown to be composed of boundary layers on the plates and an interior flow. Attention is focused upon the physical nature of the solutions, and the structure of the various kinds of boundary layers formed on the plates. The final steady-state velocity, temperature and shear stresses are numerically discussed for different values of the Grashof number and frequency of the plate.