The present work is devoted to the numerical study of laminar magnetohydrodynamic (MHD) conjugate natural convection flow from a horizontal circular cylinder taking into account Joule heating and internal heat generation. The governing equations and the associated boundary conditions for this analysis are made nondimensional forms using a set of dimensionless variables. Thus, the nondimensional governing equations are solved numerically using finite difference method with Keller box scheme. Numerical outcomes are found for different values of the magnetic parameter, conjugate conduction parameter, Prandtl number, Joule heating parameter, and heat generation parameter for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and the rate of heat transfer along the surface. It is found that the skin friction increases, and heat transfer rate decreases for escalating value of Joule heating parameter and heat generation parameter. Results are presented graphically with detailed discussion. 1. Introduction Two-dimensional laminar natural convection from a horizontal cylinder under various surface boundary conditions such as isothermal, uniform heat flux, and mixed boundary conditions was investigated by several researchers employing the different numerical techniques. For example, Merkin [1] analysed the free convection boundary layer on an isothermal horizontal cylinder. Kuehn and Goldstein [2] determined numerical solution for the Navier-Stokes equations for laminar natural convection about a horizontal isothermal circular cylinder. They obtained the solutions of the Navier-Stokes and energy equations for natural-convection heat transfer from a horizontal isothermal cylinder and found that boundary layer conditions reached at the lower portion of the cylinder when the Rayleigh number becomes very large. Wang et al. [3] investigated numerical computation of natural convection flow about a horizontal cylinder using splines. They reported some new computations at very high Rayleigh numbers which indicate the existence of attached “separation” vortices in the downstream plume region. The combined effect of conduction and free convection which is known as conjugate free convection has a significant importance in many practical applications. Gdalevich and Fertman [4] investigated conjugate problems of natural convection. Miyamoto et al. [5] investigated the effects of axial heat conduction in a vertical flat plate on free convection heat transfer. They discovered that axial heat conduction in the flat plate
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