The transient unbounded flow of a stratified viscous fluid over an oscillating permeable boundary has been considered. The viscosity and the density of the fluid have been assumed to decay exponentially in the direction normal to the bounding permeable wall. The initial value problem associated with the resulting diffusion equation, subject to the Beavers-Joseph boundary condition, has been solved analytically. The solution for the transient velocity has been expressed in terms of error and exponential functions of complex arguments. The effects of fluid stratification and the bounding porous medium on the fluid velocity have been analyzed.
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