An efficient numerical scheme for fractional characterization of MHD fluid model

How to precisely characterize the fractional modeling and physical treatment is an ongoing challenge in fluid mechanics and numerical techniques, especially in nonlinear complex models. A model study is conducted to report fractional time-dependent mixed convection incompressible fluid flow inside a channel. The physical system is under the impacts of viscous dissipation, electrical and magnetic fields. Three fractional operators Atangana Baleanu Caputo (ABC), Caputo Fabrizio (CF), and classical Caputo (CC) are involved into the temporal derivative. Transformations are used to convert the physical model into equivalent fractional partial differential equations (FPDEs). The computational code is developed for finite difference schemes and code validation is made for different fractional operators. The simulations have been performed to check the appropriate fractional operator and a comparison is made to check the accuracy and efficiency. Additionally, a set of graphs is asserted to show the velocity and temperature distribution for various values of parameters. Velocity is analyzed as decreasing function with an enhancement in the Rayleigh number while the higher fractional parameter (α) causes a dominant drop. A dropped velocity is analyzed in the absence of oscillation and enhanced velocity for higher oscillation, while a more dominant increment in the velocity is noted when Λ0 is non-zero. A decrease in the thermal layer is observed for higher Pe, and a more dominant impact is noted for smaller values of the fractional parameter. The pattern of the thermal profile is observed enhancing when there is an involvement of radiative parameter while lower temperature distribution is noted in the absence of the radiative term.