Skin-friction for unsteady free convection MHD flow between two heated vertical parallel plates

Abstract

Unsteady viscous incompressible free convection flow of an electrically conducting fluid between two heated vertical parallel plates is considered in the presence of a uniform magnetic field applied transversely to the flow. The induce field along the lines of motion varies transversely to the flow and the fluid temperature changing with time. An analytical solution for velocity, induced field and the temperature distributions are obtained for small and large magnetic Reynolds numbers. The skin-friction at the two plates is obtained. Velocity distribution, induced field and skin-friction are plotted against the distance from the plates. It has been observed that with the increase in Rm, the magnetic Reynolds number, at constant M, the Hartmann number, leads to an increase in the skin-friction gradually. But with the increase in M, at constant Rm, the skin-friction decreases.Posmatra se nestacionarna viskozna nestisljiva konvekcija elektroprovodnog fluida u prisustvu magnetnog polja upravnog na ravan tecenja. Indukovano polje duz linija kretanja varira poprecno na ravan tecenja, a temperatura fluida se menja tokom vremena. Dobijena su analiticka resenja za brzinu, indukovano polje i raspored temperature za male i velike magnetne Rejnoldsove brojeve. Dobijeno je trenje na zidovima dve ploce. Distribucija brzine, indukovano polje i trenje na zidu su prikazani u funkciji rastojanja od plovca. Uoceno je da porast magnetnog Rejnoldsovog broja, Rm, pri konstantnom Hartmanovom broju, M, vodi ka postepenom porastu trenja na zidu. Medjutim, porast M, pri konstantnom Rm, dovodi do smanjenja trenja na zidu.