Parallel Plate Flow of a Third-Grade Fluid and a Newtonian Fluid With Variable Viscosity

Steady-state parallel plate flow of a third-grade fluid and a Newtonian fluid with temperature-dependent viscosity is considered. Approximate analytical solutions are constructed using the newly developed perturbation-iteration algorithms. Two different perturbation-iteration algorithms are used. The velocity and temperature profiles obtained by the iteration algorithms are contrasted with the numerical solutions as well as with the regular perturbation solutions. It is found that the perturbation-iteration solutions converge better to the numerical solutions than the regular perturbation solutions, in particular when the validity criteria of the regular perturbation solution are not satisfied. The new analytical approach produces promising results in solving complex fluid problems.