Analytic Approximations for Cooling Turbine Disks

In this paper, we use the homotopy analysis method as a tool to obtain analytic approximations to the nonlinear problem of the cooling of turbine disks with a non-Newtonian viscoelastic fluid. The application of this method is executed via a polynomial exponential basis. The effects on velocity and temperature profiles with variations of the cross viscosity parameter, the Reynolds number, and the Prandtl number are discussed. A comparison with corresponding results of the perturbation method is illustrated and also, as a result of application of the homotopy analysis method, an analytic evaluation for the Nusselt number compared to the perturbation method is achieved. [DOI: 10.1115/1.4006993]