A numerical investigation is performed to study the effect of thermal radiation on magnetohydrodynamic (MHD) free convection flow along a vertical flat plate in presence of variable thermal conductivity in this paper. The governing equations of the flow and the boundary conditions are transformed into dimensionless form using appropriate similarity transformations and then solved employing the implicit finite difference method with Keller-box scheme. Results for the details of the velocity profiles, temperature distributions as well as the skin friction, the rate of heat transfer and surface temperature distributions are shown graphically. Results reveal that the thermal radiation is more significant in MHD natural convection flow during thermal conductivity effect is considered. To illustrate the accuracy of the present results, the results for the local skin fraction and surface temperature distribution excluding the extension effects are compared with results of Merkin and Pop designed for the fixed value of Prandtl number and a good agreement were found.
Steady two-dimensional Magneto hydrodynamic free convection flow with thermal radiation in the presence of magnetic field along a vertical flat plate is concerned in the present study. The fluid is taken to be gray, absorbing-emitting radiation. The non-linear governing equations have been transformed by the usual similarity transformation to a system of ordinary differential equations. These dimensionless similar equations are then solved numerically employing the Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Finally the effects of the pertinent parameters are examined. Keywords: MHD flow; radiation; magnetic field; kinematic viscosity; thermal diffusivity. DOI: http://dx.doi.org/10.3329/diujst.v6i2.9346 DIUJST 2011; 6(2): 55-62
In this paper, the influence of Joule heating and magneto-hydrodynamics on mixed convection in a lid-driven cavity along with a heated hollow circular plate placed at the centre of the square cavity is investigated. The governing equations which are derived by considering the effects of both Joule heating and magneto-hydrodynamics are solved via the penalty finite-element method with the Galerkin-weighted residual technique. The effects of the Richardson number and Hartmann number arising from the MHD and Joule heating on the flow and heat transfer characteristics have been examined. The results show that the flow behavior, temperature distribution and heat transfer inside the cavity are strongly affected by the presence of the magnetic field. On the other hand, only the temperature distribution and heat transfer inside the cavity are strongly affected by the Joule heating parameter. The results also show that if the Hartmann number is increased from 5 to 100 then the heat transfer detraction is 20%, and if the Joule heating parameter is increased from 1 to 5 then the heat transfer detraction is 58%. In addition, multiple regressions among the various parameters are obtained.
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