Magneto-Hydro-Dynamic Generator with Joule Heating and Viscous Dissipation: An Analytic Investigation of Mixed Convection Flow

This study investigates mixed convection heat transfer in the vertical channel of magneto-hydro-dynamic (MHD) generators, considering the effects of magnetic fields, Joule heating, and viscous dissipation. The key objectives are to derive an accurate analytical solution for the complex non-linear heat transfer equations and provide insights into optimizing MHD generator design. An innovative mathematical approach involving differential transforms and power series expansions is utilized to solve the coupled partial differential equations. Validation is conducted by comparing results to existing numerical and analytical research. Parametric analysis of dimensionless quantities reveals that increasing the Hartmann number enhances fluid velocity in the channel core but suppresses temperature near the walls due to the magnetic damping effect. Higher Λ (ratio of buoyancy forces to viscous forces) values decrease both velocity and temperature profiles. The magnetic field effectively regulates flow and thermal behavior. Joule heating power rises with a higher Hartmann number but declines as Λ increases due to heightened viscous dissipation. These outcomes elucidate the impacts of critical parameters on heat transfer characteristics and performance. The robust analytical approach and findings pave the pathway for the optimized design of efficient MHD generators. Further work can examine additional configurations and parametric effects to deepen understanding of magneto-hydrodynamic mixed convection phenomena.