Thermal Instability in Reactive Viscous Plane Poiseuille/Couette Flows for Two Extreme Thermal Boundary Conditions
The problem of thermal stability of an exothermic reactive viscous fluid between two parallel walls in the plane Poiseuille and Couette flow configurations is investigated for different thermal boundary conditions. Neglecting reactant consumption, the closed-form solutions obtained from the momentum equation was inserted into the energy equation due to dissipative effect of viscosity. The resulting energy equation was analyzed for critically using the variational method technique. The problem is characterized by two parameters: the Nusselt number (N) and the dynamic parameter. We observed that the thermal and dynamical boundary conditions of the wall have led to a significant departure from known results. The influence of the variable pre-exponential factor, due to the numerical exponent m, also give further insight into the behavior of the system and the results expressed graphically and in tabular forms.