Analytical Solutions of Fractional Walter's B Fluid with Applications

FractionalWalter's LiquidModel-B has been used in thiswork to study the combined analysis of heat andmass transfer togetherwith magnetohydrodynamic (MHD) flow over a vertically oscillating plate embedded in a porous medium. A newly defined approach of Caputo-Fabrizio fractional derivative (CFFD) has been used in the mathematical formulation of the problem. By employing the dimensional analysis, the dimensional governing partial differential equations have been transformed into dimensionless form. The problem is solved analytically and solutions of mass concentration, temperature distribution, and velocity field are obtained in the presence and absence of porous and magnetic field impacts. The general solutions are expressed in the format of generalized Mittag- Leffler function M-Omega 2,(Omega 1)Omega 3 (chi) and Fox-H function H-p,q1+1(l,p) satisfying imposed conditions on the problem. These solutions have combined effects of heat andmass transfer; this is due to free convections differences betweenmass concentration and temperature distribution. Graphical illustration is depicted in order to bring out the effects of various physical parameters on flow. From investigated general solutions, the well-known previously published results in the literature have been recovered. Graphs are plotted and discussed for rheological parameters.