Dynamic Interactions: Non-Integer-Order Heat-Mass Transfer in Magnetohydrodynamic Flow of Non-Newtonian Fluid over Inclined Plates

The heat and mass transfer phenomenon in the presence of a moving magnetic field has a wide range of applications, spanning from industrial processes to environmental engineering and energy conversion technologies. Understanding these interactions enables the optimization of various processes and the development of innovative technologies. This manuscript is about a non-integer-order heat-mass transfer model for Maxwell fluid over an inclined plate in a porous medium. The MHD flow of non-Newtonian fluid over the plate due to the natural convection of the symmetric temperature field and general motion of the inclined plate is investigated. A magnetic field is applied with a certain angle to the plate, and it can either be fixed in place or move along with the plate as it moves. Our model equations are linear in time, and Laplace transforms form a powerful tool for analyzing and solving linear DEs and systems, while the Stehfest algorithm enables the recovery of original time domain functions from their Laplace transform. Moreover, it offers a powerful framework for handling fractional differential equations and capturing the intricate dynamics of non-Newtonian fluids under the influence of magnetic fields over inclined plates in porous media. So, the Laplace transform method and Stehfest’s numerical inversion algorithm are employed as the analytical approaches in our study for the solution to the model. Several cases for the general motion of the plate and generalized boundary conditions are discussed. A thorough parametric analysis is performed using graphical analysis, and useful conclusions are recorded that help to optimize various processes and the developments of innovative technologies.