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.
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
The present article deals with variable viscosity on the peristaltic transport of bile in an inclined duct under the action of slip boundary conditions. The wall geometry is described by the sinusoidal wave propagating in the axial direction with different amplitude and with constant speed. The flow of fluid is examined in a wave frame of reference, moving with the velocity of the wave. Mathematical modeling of the problem includes equations of motion and continuity. The fluid flow is investigated by converting the equations into a non-dimensionalized form simplified considering long wavelength and low Reynolds number approximation. The analytic expressions for axial velocity, pressure gradient, and pressure rise over a single wavelength cycle are obtained. The impact of various parameters such as slip parameter, viscosity parameter, angle of inclination, gravity parameter and amplitude ratio on axial velocity, pressure gradient and pressure rise are discussed in detail by plotting graphs in MATLAB R2018b software. In this article, a comparison of linear and nonlinear variation of viscosity of bile has been made. It is concluded that velocity and pressure rise is more in case linear variation of viscosity, whereas more pressure gradient is required in case of nonlinear variation of viscosity.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.