Magnetohydrodynamic conjugate free convection flow from an isothermal horizontal circular cylinder

Abstract

The problem of steady, laminar, two-dimensional conjugate heat transfer through an incompressible and electrically-conducting fluid from an isothermal horizontal circular cylinder in the presence of a uniform magnetic field acting normal to the cylinder has been studied. An extensive literature review is introduced with the endeavor of the present study at the very beginning of the thesis. The detailed derivation of the governing equations for the flow field and heat transfer from standard vector form to the case by case is presented. The developed governing equations and the associated boundary conditions for this analysis are transferred to dimensionless forms using a suitable transformation. Implicit finite difference method with Keller-box scheme has been applied to solve the problem and the method of numerical solution is also discussed completely. Firstly, Magnetohydrodynamic (MHD) conjugate free convection flow from an isothermal horizontal circular cylinder is investigated. Numerical outcomes are found for different values of the Magnetic parameter, conjugate conduction parameter and Prandtl number for the velocity profiles and the temperature distributions within the boundary layer as well as the skin friction coefficients and the rate of heat transfer along the surface. Results are presented graphically and discussed. Secondly, the numerical solutions are obtained for the problem of MHD- conjugate natural convection flow from a horizontal cylinder taking into account Joule heating and internal heat generation. The effects of the Magnetic parameter, conjugate conduction parameter, Prandtl number, Joule heating parameter and heat generation parameter are analysed for the skin friction coefficients and the rate of heat transfer along the surface and the velocity and the temperature within the boundary-layer. It is found that the skin friction increases, and heat transfer rate decreases for escalating value of Joule heating parameter and heat generation parameter. Thirdly, the effects of the stress work and viscous dissipation on MHD-conjugate free convection flow from an isothermal horizontal circular cylinder is studied. Numerical results for the Prandtl number, magnetic parameter, conjugate conduction parameter, stress work parameter, temperature ratio parameter and viscous dissipation parameter are found for the velocity profiles, temperature distributions, coefficient of skin friction and heat transfer rate. Like other literature, it is found that the effects of the viscous dissipation are smaller than stress work on the flow field and heat transfer. Finally, MHD-conjugate free convective heat transfer analysis from isothermal horizontal circular cylinder with temperature dependent viscosity is considered. The velocity profiles, temperature distributions, the skin friction coefficient and the rate of heat transfer are computed and discussed in detail for various values of viscosity variation parameter, magnetic parameter, conjugate conduction parameter and Prandtl number. It is observed that the velocity increases and the temperature decreases within the boundary layer for increasing values of the viscosity variation parameter. Comparisons are performed with available results reported by previous investigations in all cases and the results show excellent agreement.