Effects of thermal radiation and Ohmic dissipation on MHD Casson nanofluid flow over a vertical non-linear stretching surface using scaling group transformation

• Increase in the thermal radiation and magnetic field parameters there is decrease in the momentum boundary layer thickness.
• Reduction in the Nusselt and Sherwood numbers with increase in the thermal radiation parameter.
• Increasing the thermophoretic parameter there is decrease in the Nusselt number.
• Increase in the Sherwood number with increase in the value of the Brownian motion parameter.
• Nusselt number decreases with increase in the Brownian motion parameter.

The problem of steady magnetohydrodynamic boundary layer flow of a Casson nanofluid over a vertical stretching surface with non-linear stretching velocity and suction has been investigated numerically. We have incorporated the combined effects of thermal radiation and the Ohmic dissipation with thermophoresis and Brownian motion on heat and mass transfer in Casson nanofluid. The governing equations are reduced to a system of nonlinear ordinary differential equations with associated boundary conditions by applying scaling group transformations. The reduced nonlinear ordinary differential equations are then solved numerically by Runge–Kutta–Fehlberg fifth-order method with shooting technique. The effects of magnetic field, Prandtl number, Ohmic dissipation, Brownian motion parameter, thermophoresis parameter and Lewis number on the local Nusselt and local Sherwood numbers are analyzed. It is found that the velocity decreases with increase in the buoyancy parameter whereas it decreases with Rayleigh number. Further, temperature decreases with increase in the radiation parameter whereas opposite effect is seen with increase in the magnetic parameter. Further, the local Nusselt number decreases with increase in the Brownian motion parameter and thermophoresis parameter, whereas opposite trend of these parameters is seen on the local Sherwood number.

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