In this analysis, we present a theoretical study to examine the combined effect of both slip velocity and periodic body acceleration on an unsteady generalized non-Newtonian blood flow through a stenosed artery with permeable wall. A constant transverse magnetic field is applied on the peristaltic flow of blood, treating it as an elastico-viscous, electrically conducting and incompressible fluid. Appropriate transformation methods are adopted to solve the unsteady non-Newtonian axially symmetric momentum equation in the cylindrical polar coordinate system with suitably prescribed conditions. To validate the applicability of the proposed analysis, analytical expressions for the axial velocity, fluid acceleration, wall shear stress and volumetric flow rate are computed and for having an adequate insight to blood flow behavior through a stenosed artery, graphs have been plotted with varying values of flow variables, to analyse the influence of the axial velocity, wall shear stress and volumetric flow rate of streaming blood.

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This study solves the mathematical model for the propagation of harmonic plane waves in a dissipative double porosity solid saturated by a viscous fluid. The existence of three dilatational waves is explained through three scalar potentials satisfying wave equations. Velocities of these waves are obtained from the roots of a cubic equation. Lone shear wave is identified through a vector potential satisfying a wave equation. The displacements of solid particles are expressed through these four potentials. The displacements of fluid particles in pores and fractures can also be expressed in terms of these potentials. A numerical example is solved to calculate the complex velocities of four waves in a dissipative double porosity solid. Each of the complex velocities is resolved to define the phase velocity and quality factor of attenuation for the corresponding wave. Effects of medium properties and wave frequency are analyzed numerically on the propagation characteristics of four attenuated waves. It seems that P1 and S waves are not very sensitive to the pore/fluids characteristics, except the fracture porosity. Hence, the recovery and analysis of slower (P2, P3) waves become more desired to understand the fluid-rock dynamism in crustal rocks.

The study considers the propagation of surface waves on the stress-free surface of a porous solid saturated with non-viscous fluid. The surface pores have the option of being either sealed or fully-opened. With the presence of dilatant cracks, the interior of the porous solid is characterised through three different crack-regimes, based on the connections between embedded cracks. Secular equations are derived in closed form for the propagation of Rayleigh waves in the porous media with sealed or fullyopened surface pores. The velocity of non-dispersive surface waves varies significantly with the density of cracks present. However, aspect (thickness to radius) ratio of (circular) cracks may not have much effect on the velocity of Rayleigh waves. The opening of surface pores may be an important reason for a faster propagation of Rayleigh waves in any realistic elastic medium. Finally, the dilatancy due to the growth of cracks up to their interconnection or drainage may be able to affect the velocity of Rayleigh waves quite significantly.