Heat transfer analysis of magnetohydrodynamic Casson fluid through a porous medium with constant proportional Caputo derivative: Fid-Bau Portal

Heat transfer analysis of magnetohydrodynamic Casson fluid through a porous medium with constant proportional Caputo derivative

Aleem, Maryam / Asjad, Muhammad Imran / Akgül, Ali

Abstract

This article aims to investigate free convection of a Casson fluid past a vertical plate embedded in porous medium with invariant wall temperature. It is assumed that the fluid can conduct electricity and it is flowing across a porous medium. The partial differential equations governing the model are made dimensionless by using dimensionless parameters. The Laplace transform method is applied to get analytical results. Furthermore, the hybrid fractional model is developed and the exact solutions for momentum and energy equations are acquired. The obtained results are compared with classical ones and the effect of hybrid fractional parameters are analyzed graphically by using MathCad software. Skin friction and heat transfer rate $N u$ is analyzed for small and large times and for hybrid fractional parameter $β$ . We also have seen the increasing velocity profiles for buoyancy parameter Gr, whereas temperature of the fluid decreases for Pr $Pr$ . The rate of heat transfer $(N u)$ and skin friction $(C_{f})$ can be minimized by increasing the values of $β$ . Furthermore, the constant proportional Caputo derivative model exhibits more decay in velocity in comparison with classical model given in Khalid et al. Therefore, the constant proportional Caputo differential model demonstrates better memory function than the classical one. Moreover, the obtained results are identical to already published results of Khalid et al. and Imran et al.