Heat generation and Joule dissipation influence on Magnetohydrodynamic Cu- H2O and Al2O3-H2O nanofluid convection with nanoparticle volume fraction and ramped and isothermal wall temperature: A finite element approach

Abstract

In high-performance thermal engineering systems such as energy storage units, electronic cooling devices, and rotating heat exchangers, the combined effects of internal heat generation and viscous dissipation play a vital role in modulating heat and mass transfer during hydromagnetic nanofluid flow over vertical surfaces, especially in a rotating frame. Motivated by these practical demands, the present study is devoted to a comprehensive finite element analysis of the combined impact of heat source/sink and Joule heating on magnetohydrodynamic convection of Cu–H₂O and Al₂O₃–H₂O nanofluids, with varying nanoparticle volume fractions under ramped and isothermal wall thermal conditions. A system of nonlinear, dimensionless partial differential equations is numerically solved using the Galerkin-based finite element method (GFEM). Significant observations for the influence of various governing parameters are the elevation of thermal distribution with intensified heat source and Eckert number, while the buoyancy ratio was found to enhance momentum transfer across the fluid domain. Between the two nanofluids, $\mathrm{Cu}-H₂O$ consistently exhibited superior transport characteristics over $\mathrm{Al}₂O₃-H₂O$, attributed to its enhanced thermal conductivity and lower dynamic viscosity. The accuracy of the simulation is validated by benchmarking the computed values of skin friction, Nusselt number, and Sherwood number against established solutions in limiting scenarios, yielding excellent agreement. This study finds critical applications in the design and optimization of rotating chemical reactors, nano-enhanced energy systems, and magnetically controlled thermal processing equipment.