**39**, 1, pp. 111-122, 1991

### Magnetohydrodynamic Unsteady Free Convection Flow Of a Viscoelastic Fluid Along a Vertical Plate

The unsteady free convection flow of an incompressible electrically conducting viscoelastic fluid past an oscillating vertical plate in the presence of a transverse magnetic field has been studied. The flow phenomena have been characterized by the nondimensional numbers *P* (Prandtl number), *G* (Grashof number), *m* (magnetic number), *ω* (frecuency number) and *k* (viscoelastic parameter). It is found that the temperature profile may be compared with a damped harmonic wave propagating in a direction perpendicular to the plate. The dimensionless temperature as well as the thermal boundary layer δ_{T} increase with the decrease of *P*. The effects of *P*, *G* and *m* on the velocity field *u _{r}* and velocity boundary layer thickness

*δ*for the viscoelastic fluid are similar to that for a Newtonian fluid. As

*k*increases,

*u*and

_{r}*b*increase simultaneously. Opposite effects are noticed at a certain distance away from the plate. The skin friction

*r*at the plate is estimated for different values of

_{r}*P*,

*G*,

*m*and

*k*.

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