Time fractional analysis of generalized Casson fluid flow by YAC operator with the effects of slip wall, and chemical reaction in a porous medium

Abstract

The key aim of the present work is to apply the Yang-Abdel-Cattani operator of fractional order derivative with Rabotnov exponential kernel to the mass-heat transfer of the generalized Casson fluid with generalized Fick's and Fourier's laws. The flow is analyzed in a porous medium under the effects of chemical molecular diffusivity, heat generation and slip wall condition on the fluid velocity. The medium through which the fluid is flowing is subjected to the effects of Newtonian heating. The YAC operator of fractional order can describe the generalized memory effects more suitably than the other fractional operators. So for the sake of a better interpretation of the rheological behavior of the Casson fluid we have used the fractional operator of YAC with Rabotnov exponential kernel. The technique of the Laplace transform is used to acquire the exact analytical solution of the problem in the Mittag-Leffler form. Through MathCAD software physical behaviors of various parameters are investigated on the heat, mass and velocity of the fluid during the flow in a porous medium.

Keywords

• Casson fluid
• YAC operator
• Mittag-leffler functions
• Chemical molecular diffusivity
• Newtonian heating, heat source
• Slip wall condition