Convection in a vertical duct under the chemical reaction influence using Robin boundary conditions

Abstract

Convective flow with chemical reaction in a vertical duct using third kind boundary conditions is investigated. The heat is exchanged from the walls of the duct and the external fluid. The equations of balance are written in dimensionless form taking into account the effect of viscous dissipation. The inclusion of viscous dissipation reflects the transformation of original balance equations into nonlinear equations. Hence the closed form solutions are not possible. Therefore, the balance equations are resolved by the classical explicit Runge–Kutta method combined with shooting method which can be employed for various magnitudes of Brinkman number. The solutions obtained numerically are justified by solving the balance equations analytically using the perturbation technique which is applicable only for Brinkman numbers to be less than one. The flow profiles are shown graphically for different values of the thermal and solutal Grashof numbers, Biot numbers, Brinkman number, and chemical reaction parameter. The impacts of physical characteristics on the friction factor and Nusselt number are also evaluated and the results are tabulated. The solutions received by perturbation technique and Runge-Kutta method are equal when Br = 0 and as the Brinkman number increases, the error also increases.