Abstract
The study scrutinizes the effects of thermal radiation, heat generation, and induced magnetic field on steady, fully developed hydromagnetic free convection flow of an incompressible viscous and electrically conducting couple stress fluid in a vertical channel. The channel walls are maintained at an isoflux-isothermal condition, such that the left channel wall is maintained at a constant heat flux. In contrast, the right channel wall is maintained at a constant temperature. The governing simultaneous equations are solved analytically utilizing the method of undetermined coefficient, and closed form solutions in dimensionless form have been acquired for the velocity field, the induced magnetic field, and the temperature field. The expression for the induced current density has been also obtained. A parametric study for the velocity, temperature, and induced magnetic field profiles, as well as for the skin-friction coefficient, Nusselt number, and induced current density, is conducted and discussed graphically.
Highlights
The problem of hydromagnetic free convection and heat transfer flow through a vertical channel has drawn much attention due to its possible application in many engineering and technological activities
It was observed that the magnitude of the skin friction on the isoflux channel wall decreases with the increase of the Hartmann number M, magnetic Prandtl number Pm, and radiation parameter R, whereas an increase in the value of the couple stress parameter σ increases the skin friction
The outcomes of the present study are summarized as follows: (1) The velocity of fluid particles decreases with the increase in the radiation parameter, Hartmann number, and magnetic Prandtl number
Summary
The problem of hydromagnetic free convection and heat transfer flow through a vertical channel has drawn much attention due to its possible application in many engineering and technological activities. Studies related to the free convection channel flow and heat transfer characteristic of couple stress fluids find several applications in many industrial processes such as the extrusion of polymer fluids, solidification of liquid crystals, and cooling of metallic plates in bath colloidal solution. Makinde and Eegunjobi [22] contemplated the combined effects of nonlinear thermal radiation, buoyancy forces, thermophoresis, and Brownian motion on the entropy generation rate in hydromagnetic couple stress nanofluid flow through a vertical channel utilizing a shooting technique combined with the Runge–Kutta–Fehlberg method. To the best of the authors’ knowledge, the effects of thermal radiation, heat generation, and an induced magnetic field on hydromagnetic free convection flow of couple stress fluid in an isoflux-isothermal vertical channel have not been reported in the literature. A parametric study was conducted, and the results were portrayed and discussed with the help of graphs
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