Analytical investigation for cooling turbine disks with a non-Newtonian viscoelastic fluid

The homotopy analysis method (HAM) is used to develop an analytical solution for the cooling of turbine disks with a non-Newtonian viscoelastic fluid. Results are presented for the velocity and temperature fields and the Nusselt   number is determined as a function of the cross viscosity parameter D2D2, the Reynolds number, Re, and the Prandtl number, Pr. The present results corroborate well with the numerical and perturbation results reported in other research literature on the problem. The auxiliary parameter in the homotopy analysis method is derived by using the averaged residual error concept which significantly reduces the computational time. The use of optimal auxiliary parameter provides a superior control on the convergence and accuracy of the analytic solution.