A numerical study of magneto-hydrodynamic mixed convection in a cavity has been conducted to investigate the behavior of integrated flux of thermal energy, linear momentum and kinetic energy. Shear force through lid motion establishes the forced convection effect and buoyancy force due to differential heating of the moving lid and the stationary interface ensures the natural convection phenomenon. Additionally, conduction through the solid slab with prescribed temperature at its outer surface attached to the cavity induces conjugate heat transfer. In addition, the top and bottom wall throughout the domain are kept insulated and a uniform horizontal magnetic field is applied on the right wall towards left. Fluid flow and heat transfer characteristics are examined for a range of Hartmann number (Ha): 0, 10, 50 and 120 at fixed values of Reynolds number, Grashof number and Prandtl number of 300, 9 × 10^4 and 0.71, respectively. The result shows that the transport of heat in the near wall regions of the fluid domain is primarily governed by diffusion process whereas advection appears stronger in the central region of the cavity. Increase in magnetic field strength from Ha = 0 to 120 gradually suppresses the recirculating structure of the flow signifying a reduction in advective strength as depicted by the decrease in the value of total integrated heat flux from 25 to 6. The reduction in heat flux, momentum fluxes and kinetic energy fluxes with increase in magnetic field has been well correlated in the range of 0 = Ha = 120.

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