Computational study of thermal influence in axial annular flow of a reactive third grade fluid with non-linear viscosity

Abstract

This study numerically investigates the mass and heat transfer in a pressure induced flow of a reactive third-grade fluid with Reynolds’ viscosity model through a fixed cylindrical annulus, neglecting material consumption. The coupled nonlinear system of equations governing the flow are obtained in cylindrical coordinates and further cast into dimensionless forms via standard transformation. With graphical illustrations, the influence of salient physical parameters on the axial temperature and flow velocity are studied. Critical conditions are discussed using shooting method. The numerical solutions show very good agreement with those previously obtained from two-term series expansion as a special case. The effects of emerging parameters on the thermal critical characteristics are also discussed in detail. The results obtained are validated with relevant published articles in the literature. The quantitative effects of a state variable and several dimensionless parameters such as pressure gradient, numerical exponent of viscosity, an exponent of the pre-exponential factor, cylinder ratio, viscous heating parameter, and the material parameter accounting for the non-Newtonian nature of the fluid, on the activation energy, Frank-Kamenetskii parameter and Maximum inner cylinder temperature are explored. Keywords: Third-grade fluid, Thermal explosions, Heat generation, Temperature dependent viscosity, Transition, Concentric circular cylinders, 2010 Mathematical Subject Classification: 80A25, 76A05