Flow and Heat Transfer of a Second Grade Fluid Between Two Stretchable Rotating Disks

The steady laminar flow and heat transfer of a non-Newtonian second grade fluid between two stretchable, co-axially rotating disks is considered. Using similarity transformations, partial differential equations governing the flow, are reduced to a set of highly coupled and nonlinear ordinary differential equations. These developed nonlinear equations are then integrated analytically using an effective analytical method called homotopy analysis method to obtain series solutions. The convergence of the obtained series solutions are also analyzed. Results obtained using 20th-order homotopy approximations, for different cases, such as the disks rotating in same (opposite) sense with same (different) angular velocities are shown graphically and discussed in detail for various parameters of interest, such as, stretching parameter, Reynolds number, non-Newtonian viscoelastic parameter. Of particular interest are the values of F′′(0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F''(0)$$\end{document} and -G′(0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-G'(0)$$\end{document}. And -G′(0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-G'(0)$$\end{document} found to be decreasing function of the non-Newtonian viscoelastic parameter K whereas the values of F′′(0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F''(0)$$\end{document} decreases with K, except when both the disk stretches and Ω=0,0.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega =0, 0.5$$\end{document}.