Unsteady MHD flow of a Casson fluid over a melting surface modeling using conformable fractional derivatives and variable thermal conductivity

• Fractional Casson model captures memory effects in unsteady MHD melting flow • Nonlinear radiation and chemical reaction effects on heat and mass transport • Magnetic and porous resistances regulate velocity, temperature and concentration • Similarity reduction and bvp4c shooting used to solve the nonlinear system • Results support applications in porous media and thermal processing systems This is done by a fraction derivative method to study unsteady magnetohydrodynamic flow between a melting under a sloping contracting sheet using a Casson fluid. The influences of nonlinear radiations and a nonlinear chemical reaction are included and incorporated in a modified non-Newtonian Casson model in the study. The research has a unique advantage by using conformable fractional derivatives to capture the memory and hereditary effects of heat and mass transport phenomenon, which cannot be captured by the standard integer-order models. The governing PDEs of momentum, energy and concentration are recast and transformed into a coupled system of nonlinear ODEs using similarity transformations. The resultant BVP is then numerically solved using the bvp4c solver in combination with a shooting strategy. The sensitivity of the velocity, temperature and the concentration distributions are studied by use of the graphical and tabular analyses to all the important physical parameters of the system. These are the fractional order, magnetic field strength, unsteadiness parameter, porosity, melting parameter and Schmidt number. The graphs are used to show how the magnetic parameter (M) and the permeability parameter (Kp) change velocity, temperature, and concentration profiles. The flow induced resistance by the Lorentz force and the amplification of both thermal and solutal layers, thus, cause decreasing velocity and increased temperature and concentration with increasing M. On the other hand, an increased Kp has a small increase in temperature and concentration boundary layers but it reduces velocity because of the increment in resistance provided by the porous medium. In general, M and Kp play an important role in the flow, heat, and mass transfer properties of the system.