MHD Maxwell Fluid with Heat Transfer Analysis under Ramp Velocity and Ramp Temperature Subject to Non-Integer Differentiable Operators

The main focus of this study is to investigate the impact of heat generation/absorption with ramp velocity and ramp temperature on magnetohydrodynamic (MHD) time-dependent Maxwell fluid over an unbounded plate embedded in a permeable medium. Non-dimensional parameters along with Laplace transformation and inversion algorithms are used to find the solution of shear stress, energy, and velocity profile. Recently, new fractional differential operators are used to define ramped temperature and ramped velocity. The obtained analytical solutions are plotted for different values of emerging parameters. Fractional time derivatives are used to analyze the impact of fractional parameters (memory effect) on the dynamics of the fluid. While making a comparison, it is observed that the fractional-order model is best to explain the memory effect as compared to classical models. Our results suggest that the velocity profile decrease by increasing the effective Prandtl number. The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity. The incremental value of the M is observed for a decrease in the velocity field, which reflects to control resistive force. Further, it is noted that the Atangana-Baleanu derivative in Caputo sense (ABC) is the best to highlight the dynamics of the fluid. The influence of pertinent parameters is analyzed graphically for velocity and energy profile. Expressions for skin friction and Nusselt number are also derived for fractional differential operators.