Abstract
In this paper the effect physical parameters on flow variables of unsteady, incompressible, electrically conducting viscoelastic fluid flowing between a pair of infinite vertical Couette porous channel walls embedded in a porous medium is analyzed. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall varies periodically. The temperature difference between the two walls is high enough due to thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. This technique is applied on partial differential equations that are difficult to solve. These partial differential equations are reduced to a set of ordinary differential equations in dimensionless form and thus they can be solved analytically. The effects of physical parameters on the flow variables are studied and the results have been discussed. The physical parameters considered include Hartmann number, viscoelastic parameter, Permeability of porous medium, chemical reaction parameter, radiative parameter, thermal Grashof number for heat transfer, modified Grashof number for mass transfer, frequency parameter, Prandtl number, mass diffusivity and Schmidt number. The flow variables considered include velocity, temperature and concentration. The theoretical results have been supported by simulation study. The observations include: (i) velocity decreases with increasing values of frequency, Hartmann number and viscoelastic parameter (ii) velocity increases with increasing values of temperature, thermal Grashof number, modified Grashof number and permeability of porous medium, (iii) the temperature decreases near the moving channel wall when the radiative parameter increases (iv) the temperature approaches to zero in the region near to the boundary layer of the stationary channel wall when the radiative parameter increases (v) concentration decreases with an increment in both chemical reaction and Schmidt number and (vi) The velocity of fluid increases as thermal Grashof number and modified Grashof number increases.
Highlights
The change of shear stress versus strain rate inside a fluid depending on viscosity can be classified as a linear, nonlinear or plastic response
If the shear stress is linearly proportional to the strain rate it is known as Newtonian fluid, and the constant of proportionality is called as the coefficient of dynamic viscosity
The effects of thermal radiation, chemical reaction, permeability of porous medium and electrically conducting viscoelastic fluid in vertical Couette channel wall embedded in a porous medium are important they have not been considered in these studies [15]
Summary
The change of shear stress versus strain rate inside a fluid depending on viscosity can be classified as a linear, nonlinear or plastic response. To fill the gap in this study it has been considered the effects of thermal radiation, chemical reaction, Permeability of porous medium and electrically conducting viscoelastic fluid. The effects of thermal radiation, chemical reaction, permeability of porous medium and electrically conducting viscoelastic fluid in vertical Couette channel wall embedded in a porous medium are important they have not been considered in these studies [15]. The main objective of the present study is to analyze the effect of physical parameters on flow variables of unsteady, incompressible, and electrically conducting viscoelastic fluid on free convection oscillatory fluid flow bounded between two infinite vertical Couette channel walls embedded in a porous medium when the temperature and concentration oscillates with time in the presence of thermal radiation, chemical reaction and permeability of porous medium
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