Free convection channel flow of couple stress casson fluid: A fractional model using Fourier's and Fick's laws

Fractional calculus is a branch of mathematics that develops from the usual definitions of calculus integral and derivative operators, just as fractional exponents emerge from integer exponents. The fractional derivative has been successfully used to describe various fundamental processes, including coiling polymer, viscoelasticity, traffic construction, diffusive transport, fluid dynamics, electromagnetic theory and electrical networks. However, many researchers do not use fractional derivatives to understand the physical properties of a non-Newtonian fluid that flows over a moving plate. The present paper aims to consider the couple stress Casson fluid between the parallel plates under variable conditions. The flow regime is formulated in terms of partial differential equations. Unlike the published work, this model is fractionalized using Fick's and Fourier's Laws. The system of dimensionless fractional PDEs is solved by using the joint applications of Laplace and Fourier transforms. The influence of several physical parameters, such as the Grashof number, Casson parameter, couple stress parameter etc., on velocity, temperature, and concentration profiles are represented graphically and explained physically. Furthermore, skin friction, Sherwood and Nusselt numbers are numerically calculated and presented in tabular form. It is noted that the influence of physical parameters on skin fraction is opposite to the influence on velocity. Also, the Nusselt number decreases with increasing values of Pr and the Sherwood number increases for decreasing values of Sc. The results show that the velocity of the fluid is the decreasing function of the couple stress parameter and Casson parameter while the increasing function of the permeability parameter and Grashof numbers. It is also worth noting that, unlike the classical model, the present study provides various solutions in the range of an in-between (0, 1], shown in Figures 2, 7, 8) which might be useful for the experimental and numerical solver to compare their results.