Numerical simulations and modeling of MHD boundary layer flow and heat transfer dynamics in Darcy-forchheimer media with distributed fractional-order derivatives

In this study, we extend the application of an existing Cattaneo heat flux model integrated with magnetohydrodynamic (MHD) Maxwell boundary layer flow using distributed fractional-order derivatives. This offers a novel approach for the use of disturbed order along with the midpoint quadrature rule, not previously considered in the literature for such phenomena. Moreover, the application of a variable heat flux with distributive order fractional constitutive equation, also an unexplored area in the literature, adds to the novelty of our study. We investigate the dynamics of the model over a flat surface in the presence of variable heat flux and Darcy-Forchheimer media. The governing equations, along with their respective initial and boundary conditions, are derived and solved using the finite difference method employing the L1 scheme. A benchmark 'exact solution' is obtained for a simplified version of the problem and a numerical solution is provided for a more complex, realistic version. The accuracy of our numerical scheme is validated by comparing results with the benchmark solution, and a mesh independence study further validates our code. Our study uncovers unique insights into the influence of various physical parameters on the velocity and temperature boundary layer thickness, as well as the flow and heat transfer mechanisms, elucidating the rheological characteristics of the system.