Analysis of Poiseuille flow of a reactive Power law fluid between parallel plates

This study is about the behavior of a fully developed incompressible reactive Power law fluid in steady flow between two insulated parallel plates. Both plates are kept at the same temperature, T₀. It is assumed that the heat is generated by a chemical reaction term, which is uniformly distributed throughout the volume along with the viscous heating due to the reactive nature of the fluid. The chemical reaction is assumed to be strongly exothermic under Arrhenius Kinetics. An exact solution for the velocity profile is constructed from the nonlinear momentum equations, while approximate solutions for the nonlinear energy equation is obtained by using the Homotopy Perturbation technique. The behavior of the velocity and temperature are discussed for different dimensionless parameters involved in the governing equations. Graphical representations and discussions are also presented. An interesting situation observed is that the shear thinning/thickening behavior in our problem is not true for all values of the Power law index. In Poiseuille flow the behavior of the fluid depends not only on the Power law index, but also on the pressure gradient and the gap between the parallel plates. For certain values of the Power law index and pressure gradient, we observe the same behavior of shear thinning/thickening as quoted in the literature, but below these critical values the behavior is reversed as shown graphically.