Department of Mathematics, Assuit University, Faculty of Science, Assuit, Egypt.
Department of Mathematics, South Valley University, Faculty of Science, Qena, Egypt.
Department of Mathematics, Aswan University, Faculty of Science, Aswan, Egypt.
Numerical investigation for heat transfer with steady MHD natural convection cooling of a localized heat source at the bottom wall of an enclosure filled with nanofluids subjected to changeable thermal boundary conditions at the sidewalls has been studied in the a presence of inclined magnetic field. Finite difference method was employed to solve the dimensionless governing equations of the problem. The effects of governing parameters, namely, Hartmann number, solid volume fraction, the different values of the heat source length and the different locations of the heat source on the streamlines and isotherms contours as well as maximum temperature, Nusselt number and average Nusselt number along the heat source were considered. The present results are validated by favorable comparisons with previously published results. The results of the problem are presented in graphical and tabular forms and discussed. It is found that an increase in the Hartmann number results in a clear reduction in the rate of heat transfer; however, the increase in Rayleigh number enhances the nanofluid flow and heat transfer rate.