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Numerical investigation on magnetohydrodynamics flow of Casson fluid over a deformable porous layer with slip conditions

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Abstract

The present study makes a numerical assessment of magnetohydrodynamics stream of Casson liquid over a deformable porous layer with slip conditions. The governing ordinary differential equations are settled Runge–Kutta fourth-order method along with the shooting technique. The impact of relevant parameters on the liquid velocity, the solid displacement, the temperature and the concentration are shown graphically, while the mass stream rate is contemplated numerically shown in tabular structure. The present outcomes have been great concurrence with existing assessments under some exceptional cases. We can see that the liquid velocity and solid displacements are rotted for higher estimations of magnetic parameter and the contrary nature found for the impact of Casson parameter. The effect of slip boundary conditions on the fluid velocity, the temperature and the concentration is additionally inspected.

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Abbreviations

\(\mu_{\text{a}}\) :

Apparent viscosity of the fluid in the porous material

\(K\) :

Drag coefficient

\(\mu\) :

Lame constant

\(\theta\) :

Angle of inclination

\(K_{0}\) :

Thermal conductivity

\(\upsilon\) :

Fluid velocity

\(Q_{0}\) :

Constant heat source/sink

\(\phi\) :

Volume fraction of the fluid

\(u\) :

Solid displacement

\(\rho\) :

Fluid density

\(g\) :

Gravity

\(\frac{\partial p}{\partial x}\) :

Pressure gradient

\(\sigma\) :

Electrical conductivity

\(B_{0}\) :

Strength of the magnetic field

\(U\) :

Average velocity

\(\beta\) :

Casson parameter

\(L_{1}\) :

Velocity slip parameter

\(L_{2}\), \(L_{3}\) :

Temperature and concentration slip parameters

\(D_{B}\) :

Thermodiffusion coefficient

\(T\), \(C\) :

Temperature and the concentration

\(T_{\text{w}} ,C_{\text{w}}\) :

Constant temperature and concentration at the walls

\(C_{0}\) :

Ambient concentration

\(R\) :

Chemical reaction

\(\beta\) :

Casson parameter

\(\phi\) :

Volume fraction of the fluid

\(\text{Re}\) :

Reynolds number

\({\text{Fr}}\) :

Froude number

\(\theta\) :

Angle of inclination

\(\delta\) :

Viscous drag coefficient

\(M\) :

Magnetic parameter

\(P\) :

Pressure gradient

\({\text{Br}}\) :

Brinkman number

\(\beta_{1}\) :

Constant heat source parameter

\(U_{1}\), \(U_{2}\) :

Lower and upper plate velocities

\(\gamma\) :

Chemical reaction parameter,

\(\alpha_{1} = \frac{{L_{1} }}{h}\) :

Velocity slip parameter

\(\alpha_{2} = \frac{{L_{2} }}{h}\), \(\alpha_{3} = \frac{{L_{3} }}{h}\) :

Temperature and the concentration slip parameters

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  1. Department of Mathematics, School of Applied Sciences, REVA University, Bengaluru, 560064, Karnataka, India

    M. Krishna Murthy

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Krishna Murthy, M. Numerical investigation on magnetohydrodynamics flow of Casson fluid over a deformable porous layer with slip conditions. Indian J Phys 94, 2023–2032 (2020). https://doi.org/10.1007/s12648-019-01668-4

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