Effect of chemical reaction, heat source/sink, and thermal diffusion on transient natural convection through a tube

Abstract

A semi-analytical investigation of the effect of a chemical reaction and thermal diffusion on transient natural convection flow of a viscous incompressible binary fluid with heat source/sink in a vertical and infinite tube is presented. The equations for the model are simplified with the help of the Laplace transform, solved analytically to obtain solutions whose expressions are given in modified Bessel functions. These solutions are then inverted numerically using the Riemann sum approximation method. An exhaustive model analysis is achieved by exhibiting the temperature, concentration, and velocity profiles graphically.Also, numerical values are displayed in tabular form for the Nusselt number, Sherwood number, and the shear stress. Furthermore, a version of the governing equations which are independent of time is solved analytically. The obtained results are found to coincide with the results of the time-dependent problem at an appreciable value of time. A close examination of the results reveals that raising the generative chemical reaction parameter strengthens both the concentration and momentum of the flow while they are weakened with a surge of the destructive chemical reaction. As the heat source intensifies, both fluid temperature and velocity are elevated while the species concentration is abated with the reversed phenomenon occurring as the