Flowing research of non-newtonian fluid in between two parallel plates

In the study, non-Newtonian fluid flow in between two parallel plates at same temperatures is considered. The equations of motion are derived for third grade fluids. Acceleration terms, viscous term, third grade fluid terms are calculated for cartesian coordinates. The equations represent two dimensional steady flow.First the equations of motion are derived. Perturbation methods are employed in search of approximate solutions.The simplest perturbation expansion, namely the pedestrian expansion, is used. The velocity distribution and the temperature distribution are calculated approximately. Third grade fluid with temperature dependent viscosity is accommodated in the analysis. Reynolds model and Vogel model are used to account for the temperature dependent viscosity. Approximate analytical solutions for the velocity and temperature profiles are found using perturbation techniques. It is found that the influence of non-Newtonian parameter and viscosity index is more pronounced in the region of the plate surfaces where rate of fluid strain and temperature gradients are high.