# Effects of radiation and magnetic field on mixed convection flow of non-Newtonian power-law fluids across a cylinder in the presence of chemical reaction

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## Abstract

The effects of thermal radiation, magnetic field and chemical reaction on momentum, heat and mass transfer of mixed convection flow of a non-Newtonian power-law fluid across a horizontal cylinder are presented. Governing equations have been reduced to a set of dimensionless equations using appropriate transformations. The resulting equations are solved employing an implicit finite difference method up to the point of boundary layer separation. For the non-Newtonian fluids, the Nusselt number and the Sherwood number demonstrate completely different characteristics from the Newtonian fluids near the front stagnation point. The magnetic field parameter produces lower skin friction, heat transfer, and mass transfer, whereas these are increased for the thermo-solutal parameter and the mixed convection parameter. The skin friction and the Nusselt number are found to decrease and the Sherwood number increases with an increase of the Schmidt number and the chemical reaction parameter. Moreover, the conduction-radiation parameter generates higher skin friction and mass transfer and lower heat transfer rate.

## Nomenclature

*B*_{0}Strength of magnetic field

*C*Concentration of the fluid

*C*_{f}Local skin friction

*D*Coefficient of mass diffusivity

*F*Dimensionless stream function

*g*Acceleration due to gravity

*K*Fluid consistency index for power-law fluid

*k*^{*}Rosseland mean absorption coefficient

*M*Magnetic field parameter

*N*Thermo-solutal convection parameter

*Nu*Local Nusselt number

*n*Flow-index for power-law fluid

- Pr
Generalized Prandtl number

*q*_{r}Radiative heat-flux along the

*y*-direction*R*Radius of the cylinder

*Re*Generalized Reynolds number

*Ri*Mixed convection parameter

*R*_{d}Conduction-radiation parameter

*Sc*Schmidt number

*Sh*Local Sherwood number

*T*Temperature

*T*_{∞}Ambient temperature

*u*Velocity component in the

*x*-direction*u*_{e}Local velocity at the outer boundary of the edge

*v*Velocity component in the

*y*-direction*X*Dimensionless distance (=

*x/R*)*x*Distance along the surface of the cylinder from the forward stagnation point

*Y*Dimensionless distance normal to the surface of the cylinder

*y*Distance normal to the surface of the cylinder

## Greek symbols

- Ω
Chemical reaction parameter

*α*Thermal diffusivity

*β*_{C}Volumetric coefficient of concentration expansion

*β*_{T}Volumetric coefficient of thermal expansion

*θ*Dimensionless temperature

*κ*_{c}Thermal conductivity

*κ*_{r}Rate of chemical reaction

*ρ*Density of the fluid

*σ*_{c}Electrical conductivity

*σ**Stefan–Boltzman constant

*ϕ*Dimensionless concentration

*ψ*Stream function

## Subscripts

*w*Wall condition

*∞*Ambient condition

## Notes

## References

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