Chemical entropy generation and magnetohydrodynamic effects on the unsteady heat and fluid flow through a porous medium have been numerically investigated. The entropy generation due to the use of a magnetic field and porous medium effects on heat transfer, fluid friction, and mass transfer have been analyzed numerically. Using a similarity transformation, the governing equations of continuity, momentum, and energy and concentration equations, of nonlinear system, were reduced to a set of ordinary differential equations and solved numerically. The effects of unsteadiness parameter, magnetic field parameter, porosity parameter, heat generation/absorption parameter, Lewis number, chemical reaction parameter, and Brinkman number parameter on the velocity, the temperature, the concentration, and the entropy generation rates profiles were investigated and the results were presented graphically.

The present work, the entropy generation due to radiation and variable viscosity magnetohydrodynamic effects with a porous medium in a circular pipe, has been obtained and studied numerically. The governing continuity, momentum, and energy equations in cylindrical coordination are converted into a system of nonlinear ordinary differential equations by means of similarity transformation. The resulting system of coupled nonlinear ordinary differential equations is solved numerically by a Runge‐Kutta method and shooting technique. Numerical results are presented for velocity, temperature profiles, pressure profile, entropy generation rates, and Bejan number for different physical parameters of the problem. Also, the effects of the pertinent parameters on the skin friction and the rate of heat transfer are obtained and discussed numerically and illustrated graphically.

This paper describes the studied effects of thermal radiation and chemical reaction on unsteady MHD non-Newtonian (obeying Walter's B model) fluid in porous medium. The resulting problems are solved numerically. Graphical results for various interesting parameters are presented. Also the effects of the different parameters on the skin-friction and the heat fluxes are obtained and discussed numerically.

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In this paper, we discuss thin-film nanofluid sprayed in non-Darcian, magnetohydrodynamic, embedding in a porous medium flow and thermal radiation with heat transfer generation on a stretching cylinder. The spray rate is a function of film size. A comparative study is made for the nanoparticles, namely, copper oxide (CuO), alumina oxide (Al O 2 3 ), and iron oxide (Fe O ) 3 4 . The governing continuity, momentum, and energy equations of the nanofluid are reduced using similarity transformation and converted into a system of nonlinear ordinary differential equations, which are solved numerically. Numerical solutions are obtained for the velocity and temperature fields as well as for the skin-friction coefficient and Nusselt number. The pressure distribution and spray rate are also calculated. The results are presented in graphical forms to study the effects of various parameters. K E Y W O R D Snanofluid, porous medium, spray, stretching cylinder, temperature buoyancy, thermal radiation, thin film