CRITICALITY AND THERMAL EXPLOSION IN THE FLOW OF REACTIVE VISCOUS THIRD GRADE FLUID FLOW IN A CYLINDRICAL PIPE WITH SURFACE COOLING

Abstract

This work investigates the steady state momentum and heat transfer in a fully developed flow of viscous third-grade fluid through a cylindrical pipe, such that the general spatial dependence of viscosity is accounted for. Expression for the velocity profile is constructed analytically and displayed graphically. Comparison with previous documented result through reduction in emergent parameter demonstrates the accuracy of the solution approach. The energy equation with generalized Arrhenius
kinetics is solved for thermal explosion using the Modified Adomian Decomposition semi analytical method. Comparisons are given for sets of results obtained via the Modified Adomian Decomposition Methods against those from other well known methods in the literature. The present study explores the effects of the Biot number Bi ∈ {0,∞} on critical values of emerging parameters (Frank-Kamenetskii parameter, δcr and the dimensionless maximum temperature, θmax cr). The present parametric examination of the effects of Biot number, inhomogeneity of the fluid, heat generating parameter, activation energy parameter (β) and the exponent of the generalized Arrhenius kinetic on the δcr and θmax cr provides quantitative properties for the
sensitized reaction kinetics.