Thermal investigation for electrified convection flow of Newtonian fluid subjected to damped thermal flux on a permeable medium

The main purpose of this manuscript is to study an unsteady, MHD and free convection flow with the thermal transport for an electrical conducted, incompressible, and linearly viscous fluid flow close to a moving vertical plate in the existence of an exponential heating process. The flow area is considered permeable half-space as well as the utilization of an electromagnetic field perpendicular to fluid motion. The Caputo time-fractional derivative is utilized to present a heat flux constitutive-equation through a weak memory. The Laplace transformation technique is utilized to achieve the exact solutions of the dimensionless governing equations for the temperature field, Nusselt number, fluid velocity, and skin friction coefficient and stated in connection with Wright functions as well as a generalized G-Lorenzo-Hartley function. As a limiting case, a comparison with (Awan et al 2019 Chin. J. Phys. 60 98–106) equation (38) is done to verify the applied technique as well as for validity of our results. The influences of a variety of fractional as well as material factors are pictured with MathCad15. For low estimations of time, Fluid temperature and velocity are increased by decreasing fractional factor γ and both illustrate a contrary behavior for larger estimations of the time $t_1.$ The fluid velocity is decreased through the large estimations of the magnetic factor $M_1.$ (paper)