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This paper presents a numerical study of the problem of unsteady thermo bioconvection boundary layer flow of a nanofluid containing gyrotactic microorganisms along a stretching sheet under the influence of magnetic field and viscous dissipation. With the help of usual transformation, the governing equations are transformed into unsteady nonlinear coupled partial differential equations. The numerical solution is obtained by using an explicit finite difference scheme. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. From the results it is found that both magnetic parameter and bioconvection Rayleigh number have positive effect on the dimensionless Nusselt number and density number of the motile microorganisms while the opposite behavior became clear in the case of Grashof number and Eckert number. The rescaled velocity, temperature, concentration and the density of motile microorganisms depend strongly on the governing parameters.

The objective of this paper is to examine the effects of variable viscosity, chemical reaction, thermophoresis and heat source or sink on non-Darcy mixed convective heat and mass transfer of a viscous fluid over a semi-infinite porous inclined plate embedded in a saturated porous medium, in the presence of thermal radiation. The partial differential equations, governing the problem under consideration, have been transformed by a similarity transformation into a system of non-linear ordinary differential equations, which are solved numerically by using the fourth-order Rung-Kutta algorithm with shooting iteration technique. The resulting velocity, temperature and concentration distributions are shown graphically for differential values of the parameters entering into the problem. Finally, the numerical values of the skin-friction coefficient, Nusselt number and Sherwood number are also presented and discussed in detials.

SUMMARYIn this paper, a numerical solution of flow and heat transfer in micropolar fluid outside a stretching permeable cylinder with thermal stratification and suction/injection effects. The governing system of partial differential equations is converted to ordinary differential equations by using similarity transformations, which are then solved using numerical technique. The cases of strong concentration of microelement and weak concentration of microelement were considered. Our purpose from this study is to investigate the effects of the governing parameters, namely the suction/injection parameter, thermal stratification parameter, Prandtl number, vortex viscosity parameter and Reynolds number on the velocity profiles, pressure distributions, angular velocity profiles and temperature profiles as well as the skin friction coefficient, dimensionless wall couple stress and the Nusselt number. The numerical results are validated by favorable comparisons with previously published results. The results are shown graphically. The values of the skin friction coefficient, dimensionless wall couple stress and the Nusselt number are presented in tables.

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