Forced convection of Casson fluid flow in a porous heated channel under magnetic field considering Joule heating using the double-distribution Lattice Boltzmann method

This study numerically investigates forced convection of Casson fluid through a porous heated channel under an inclined magnetic field with Joule heating using a double-distribution-function lattice Boltzmann method based on the D2Q9 lattice. A spatially uniform magnetic field inclined at 45° to the channel axis is imposed to account for magnetic-field orientation effects within the considered configuration. The Darcy–Forchheimer formulation is employed to represent porous-medium resistance, while the Lorentz force associated with the inclined magnetic field and Joule heating are incorporated into the momentum and thermal transport models, respectively. The effects of Reynolds number, Casson parameter, Hartmann number, Darcy number, and Joule heating parameter on the hydrodynamic and thermal characteristics are systematically examined. The results show that increasing the Reynolds number strengthens axial momentum transport, accelerates hydrodynamic development, and increases the local heat-transfer rate, while reducing the bulk mean temperature because of the shorter residence time of the fluid. Increasing the Casson parameter reduces the apparent viscous resistance, resulting in higher fluid velocity, lower pressure loss, and thinner thermal boundary layers. An increase in Hartmann number strengthens electromagnetic damping, suppresses fluid motion, increases pressure loss, and weakens convective heat transfer. In contrast, increasing the Darcy number reduces porous resistance, enhances fluid velocity and convective transport, and decreases the pressure loss. The local Nusselt number is highest near the channel entrance and decreases downstream as the thermal boundary layer develops. Increasing the Joule heating parameter produces a pronounced rise in bulk mean temperature and elevates the temperature throughout the channel, with the effect becoming more evident downstream due to the accumulation of internally generated thermal energy. The numerical formulation is validated against established benchmark results for Rayleigh–Bénard convection, showing a maximum relative deviation of approximately 5.09% in the average Nusselt number, together with good agreement in the characteristic flow structure. These findings demonstrate the coupled roles of non-Newtonian rheology, magnetic damping, porous resistance, and electromagnetic heating in controlling flow development and heat transfer in porous heated channels.