Analysis of mathematical model of fractional viscous fluid through a vertical rectangular channel

Unsteady motion of a viscous fluid passing through a vertical channel with MHD (magnetohydrodynamics) effect has been analyzed in this manuscript. Fractional model is developed by two approaches, namely; Caputo fractional time derivatives with singular kernel and Caputo-Fabrizio fractional time derivatives with non-singular kernel. Analytical solutions have been obtained via Laplace transform method after converting the governing equations into dimensionless form and presented graphical analysis of the obtained results in terms of comparison. The effect of fractional and other flow parameters on temperature, concentration and velocity fields is seen, respectively. As a result, we have found that for the physical model with fractional derivative of Caputo-Fabrizio, temperature, concentration and velocity have greater values in comparison with Caputo one. It is also noted that velocity has shown dual nature for large and small time. Further, rates of heat and mass transfer and skin friction can also be enhanced for the small values of non-integer order parameter and are presented in Table 1.