Analysis of Radiative Heat Transfer Changes in the Flow Dynamics of Maxwell and Casson Nanofluids over a Vertically Aligned Plate with Internal Heat Generation

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Abstract
This study presents a comprehensive numerical investigation of radiative heat transfer and flow dynamics involving Maxwell and Casson nanofluids flowing past a vertically aligned plate, incorporating the effects of internal heat generation. These non-Newtonian fluids exhibiting memory and yield stress behaviors are examined to understand their influence on velocity, temperature, and concentration profiles under coupled thermal and solutal gradients. The governing partial differential equations representing momentum, energy, and mass conservation are transformed into coupled nonlinear ordinary differential equations using similarity variables. These are solved using the fourth-order Runge-Kutta method with a MATLAB-based shooting technique. Key dimensionless parameters such as the Prandtl number, Grashof number, Biot number, heat source parameter, Nusselt number, Sherwood number, and skin friction coefficient are analyzed. The results show that internal heat generation significantly increases fluid temperature and velocity while reducing nanoparticle concentration and thermal transfer efficiency. Furthermore, elevated Biot numbers and thermal radiation broaden the thermal boundary layer, adversely affecting heat transfer. These findings have practical implications for engineering applications such as electronic cooling systems, chemical reactors, biomedical devices, and thermal insulation design. The insights gained enable improved modeling and thermal regulation in systems requiring efficient heat and mass transfer under non-Newtonian fluid behavior and internal heat sources.

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