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The two dimensional heat transfer of a free convective-radiative MHD (magnetohydrodynamics) flows with variable viscosity and heat source of a viscous incompressible fluid in a porous medium between two vertical wavy walls was investigated. The fluid viscosity is assumed to vary as an exponential function of temperature. The flow is assumed to consist of a mean part and a perturbed part. The perturbed quantities were expressed in terms of complex exponential series of plane wave equation. The resultant differential equations governing the flow were non-dimensionalised and solved using Differential Transform Method (DTM). The numerical computations were presented in tabular and graphical forms for various fluid parameters. It shows that an increase in radiation, variable viscosity and permeability parameters cause a rise in velocity profile. Nusselt number increases with increase in heat source and decreases with increase in radiation parameter at both walls.

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Purpose The purpose of this paper is to consider heat and mass transfer on magnetohydrodynamics (MHD) Williamson fluid flow over a slendering stretching sheet with variable thickness in the presence of radiation and chemical reaction. All pertinent flow parameters are discussed and their influence on the hydrodynamics, thermal and concentration boundary layer are presented with the aid of the diagram. Design/methodology/approach The governing partial differential equations are reduced into a system of ordinary differential equations with the help of suitable similarity variables. A discrete version of the homotopy analysis method (HAM) called the spectral homotopy analysis method (SHAM) was used to solve the transformed equations. SHAM is efficient, and it converges faster than the HAM. The SHAM provides flexibility when solving linear ordinary differential equations with the use of the Chebyshev spectral collocation method. Findings The findings revealed that an increase in the variable thermal conductivity hike the temperature and the thermal boundary layer thickness, whereas the reverse is the case for velocity close to the wall. Originality/value The uniqueness of this paper is the exploration of combined effects of heat and mass transfer on MHD Williamson fluid flow over a slendering stretching sheet. The Williamson fluid term in the momentum equation is expressed as a linear function and the viscosity and thermal conductivity are considered to vary in the boundary layer.

The numerical analysis for transfer of heat by natural convection on an unsteady Magnetohydrodynamic flow of non-Newtonian fluids through porous channel is considered. Equations governing the model are formulated, simplified and non-dimensionalised. The solution is obtained by employing Crank Nicolson's type of finite difference discritization. Velocity as well as the temperature distributions for both Prandtl-Eyring and Eyring-Powell non-Newtonian fluid models are examined. Comparism between these two diverse liquid models is made with their graphical illustrations on velocity and temperature profiles. It is observed that the velocity is higher for Prandtl Eyring model than Eyring Powell model. Also, the temperature variation for Prandtl number in Eyring-Powell fluid is a little slower than that of Prandtl-Eyring fluid.