Fractional Modeling of MHD Casson Flow with Heat and Mass Transfer in a Porous Medium Using the Constant-Proportional Caputo Derivative

In this study we developed a new model of fractional magnetohydrodynamic (MHD) polymeric Casson flow, heat and mass transfer from a wall adjacent to a porous medium with viscous dissipation, heat generation and activation energy effects, a problem of relevance to non-Newtonian functional thermal materials processing and smart lubricant manufacturing.Fractional derivatives were used to extend the Casson viscoplastic model (which featured shear-thinning and yield stress effects) in order to represent complex non-Newtonian responses and memory-dependent behaviour.The mathematical formulation was developed using a newly suggested constant-proportional Caputo fractional derivative (CPCFD).The transformed dimensionless fractional governing equations for mass, momentum, energy and species concentration were solved via Laplace integral transform technique (LITT), under suitable boundary conditions.MATHCAD software was used to evaluate solutions for non-dimensional velocity, U temperature, T and concentration, C, with variation in transverse coordinate y and time t.Nusselt number, Sherwood number and skin friction solutions are also presented.The impact of key emerging parameters on these variables was examined.Verification with previous studies neglecting porous media, magnetic field, heat generation, activation energy and viscous heating effects is also included.An increase in activation energy parameter (E a ), i.e., minimum energy threshold required for a chemical reaction to occur, reduces considerably species concentrations.Skin friction, Nusselt number, and Sherwood number were reduced with increasing fractional parameter (a) but increased with time (t).A higher Damköhler number (D v ) increased the dominance of the reaction, increasing species consumption and decreasing concentration.An elevation in fractional derivative parameter (g) improved the system memory effects, suppressed mass diffusion and reduced concentration magnitudes.Fractional calculus enables engineers to define the memory and non-local hereditary effects of polymer chains.Higher Schmidt number (Sc) depleted species diffusion and concentration boundary-layer thickness.Increasing Eckert number (Ec, viscous heating parameter) boosted temperature magnitudes whereas higher permeability parameter reduced them.Higher values of Casson rheological parameter (s) decelerated the flow and increased momentum boundary-layer thickness.An upsurge in magnetic parameter (Ha, i.e., stronger magnetic field intensity and Lorentzian magnetohydrodynamic drag) strongly dampened the flow.Temperature significantly increased with greater heat generation parameter (d).These findings may be beneficial to more sophisticated simulation of industrial viscoplastic functional coating systems.Future work may explore extensions to non-Fourier heat conduction, non-Darcy media, and consider periodic boundary conditions.