Exact solutions of an incompressible fluid flow of second order by forced oscillations on the porous boundary

Exact solution of an incompressible fluid of second-order type by causing forced oscillations in the liquid of finite depth bounded by a porous bottom has been obtained. The results presented are in terms of nondimensional elastico-viscosity parameter (β) which depends on the non-Newtonian coefficient and the frequency of excitation (σ) of the external disturbance while considering the porosity (K) of the medium. The flow parameters are found to be identical with that of Newtonian case as β → 0 and K → ∞. It is seen that the effect of α and the porosity of the bounding surface has significant effect on the velocity parameter. Further, the nature of the paths of the fluid particles have also been studied with reference to α and the porosity of the bounding surface.

g(s)

Given history

Retarded history

Retardation factor

Stress tensor

Indeterminate hydrostatic pressure

Velocity component in the i^th direction

Acceleration component in the i^th coordinate

Time parameter

Coefficient of viscosity

Coefficient of elastico-viscosity

Coefficient of cross-viscosity

Nondimensional velocity component along the i^th coordinate

Permeability of material in the dimensional form

Density of the fluid

Nondimensional elastico-viscosity parameter

Nondimensionalised indeterminate hydrostatic pressure

Nondimensionalised acceleration component in i^th direction

Characteristic length

Nondimensionalised porosity factor

Nondimensionalised cross-viscosity parameter

Nondimensional frequency of excitation

Nondimensional external force applied

Phase parameter

Cross-sectional area of the filter bed

Coefficient of viscosity

Flux of the fluid

Velocity vector

Unit vector along the gravitational force

Gravitational force