Revolutionizing energy flow: Unleashing the influence of MHD in the presence of free convective heat transfer with radiation

This study investigates the complex interplay between radiation and magneto-flow on a porous, perpendicular plate immersed in a viscoelastic Maxwell fluid. The significance lies in understanding how the Lorentz force shapes dynamics and energy transfer in such systems, which is crucial for various industrial applications. Utilizing a comprehensive model that accounts for heat generation and absorption, we transform partial differential equations into ordinary ones through flow similarity analysis, providing valuable insights into the system's behavior. Employing the bvp4c solver in MATLAB, we evaluate velocity and energy profiles in Maxwell fluid flow. Graphical representations allow for a thorough examination of the influence of thermophysical parameters. Our findings reveal an intensified velocity profile attributed to prolonged material relaxation times.Furthermore, temperature profiles progressively increase with higher radiation and porous parameters. These results hold significant implications for industrial applications, particularly in Maxwell fluids' heat transport studies. Insights from this research can inform the design and optimization of systems such as ovens, boilers, cross-flow heat exchangers, and solar panels, enhancing efficiency and performance. Overall, this study contributes novel insights that advance understanding beyond previous efforts in the literature, paving the way for further exploration in this field. The primary finding of this study indicates that as the Rayleigh number increases, the velocity profile experiences an increase, whereas the temperature profile shows a decrease.