Unsteady MHD Flow of a Fractional Casson Fluid in a Porous Channel with Temperature Dependent Properties

This work investigates the unsteady magnetohydrodynamic flow of a fractional Casson fluid through a porous channel with temperature-dependent transport properties. To accurately represent the memory characteristics of viscoelastic fluids, the governing equations for momentum, energy, and species are formulated using Caputo time-fractional derivatives. The novelty of the study is specified in a restricted and verifiable sense: the model combines independently tunable fractional memory in the momentum, thermal, and solutal fields with temperature-dependent viscosity and mass diffusivity in an MHD porous-channel Casson flow, and the resulting variable-coefficient system is solved by a validated compact finite-difference framework. A high-order numerical scheme, combining the L1 approximation in time with a fourth-order compact finite difference method in space, is developed and rigorously validated via the method of manufactured solutions, demonstrating second-order convergence in velocity and near-optimal rates in thermal and solutal fields. Parametric studies reveal that the Casson yield stress and magnetic field significantly impede the flow, while increased porosity enhances it. Significantly, thermal modulation of viscosity and diffusivity introduces strong nonlinear coupling: higher thermal sensitivity reduces wall shear stress and alters heat and mass transfer rates in a non-monotonic manner. The fractional-order parameters are shown to govern the relaxation dynamics of the system, with lower values intensifying memory effects and delaying equilibrium. Thus, the contribution lies not in the isolated use of fractional derivatives, Casson rheology, or MHD, but in their consistent integration with variable transport coefficients and numerical verification in a single computational model. These results provide a foundational framework for modeling and controlling memory-influenced, non-Newtonian transport in engineering applications such as microfluidic actuators, magnetic hyperthermia, and reactive filtration systems.