Lattice Boltzmann Modeling of Conjugate Heat Transfer for Power-Law Fluids: Symmetry Breaking Effects of Magnetic Fields and Heat Generation in Inclined Enclosures

Conjugate heat transfer in non-Newtonian fluids is a fundamental phenomenon in thermal management systems. This study investigates the combined effects of magnetic field topology, heat absorption/generation, the thermal conductivity ratio, enclosure inclination, and power-law rheology using the lattice Boltzmann method. The parametric analysis shows that increasing the heat generation coefficient from −5 to +5 reduces the average Nusselt number by up to 97% for the pseudo-plastic fluids and up to 29% for the Newtonian fluids, while entropy generation increases by 44–86% depending on the thermal conductivity ratio. Increasing the inclination angle from 0° to 90° weakens convection and reduces heat transfer by nearly 77%. Magnetic field strengthening (Ha = 0–45) decreases the Nusselt number by 20–55% depending on the barrier temperature. Among all tested conditions, the highest thermal performance (maximum heat transfer and minimum entropy generation) occurs when using a pseudo-plastic fluid (n = 0.75), exhibiting high wall conductivity (TCR = 50) and heat absorption (HAPC = −5), a cold obstacle (θb=0), and zero inclination (λ = 0°), as well as in the absence of the magnetic field effects. These quantitative insights highlight the controllability of the conjugate heat transfer and irreversibility in the power-law fluids under coupled magnetothermal conditions.