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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The impact of heat source on magnetohydrodynamic oscillatory flow of a chemically reacting viscoelastic fluid in an asymmetric wavy channel is analysed. The governing flow equations are transformed into ODEs by utilizing proper nondimensional variables. The subsequent ordinary differential equations are solved analytically. The effects of different flow parameters on the fluid flow, thermal and species distributions as well as rate of heat and mass transfer coefficients are examined graphically. It is pointed out that the velocity of fluid is parabolic with extreme value along the channel centreline and minimum at the walls. The magnitude of fluid velocity increases with an increase in porous parameter and high heat transport of a system is due to the presence of oscillatory flow. Keywords Visco-elastic fluid • Heat source • MHD • Oscillatory flow • Asymmetric channel List of symbols a 1 , b 1 Amplitudes of the wavy walls a, b Amplitude ratios B 0 Electromagnetic induction C * Fluid concentration C 1 , C 2 Concentrations at walls C P Specific heat at constant pressure d 1 + d 2 Width of channel d Mean half width of the channel D a Darcy number g Gravitational force Gc Modified Grashof number Gr Grashof number H o Intensity of magnetic field H 1 , H 2 Inner and outer walls K Porous medium shape factor Kr Chemical reaction parameter k * Porous permeability coefficient k Thermal conductivity M Hartmann number Nu Nusselt number Pe Peclet number p Pressure Q Heat source parameter q Radiative heat flux Re Reynolds number R Radiation parameter Sc Schmidt number Sh Sherwood number T Fluid temperature T 1 , T 2 Temperatures at walls t Time U Flow mean velocity u Axial velocity Greek symbols θ Fluid temperature β T Coefficient of thermal expansion β C Coefficient of mass expansion μ Coefficient of viscosity μ e Magnetic permeability σ c Conductivity of the fluid ρ Fluid density υ Kinematics viscosity coefficient

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