Influence of temperature-dependent conductivity on convective heat transfer in a vertical duct

Abstract

An analysis has been carried out to study the flow and heat characteristics of a Newtonian fluid in a vertical rectangular duct. One of the vertical walls of the duct is cooled to a constant temperature, while the other wall is heated to constant but different temperature. The thermal conductivity is assumed to vary as a linear function of temperature. The basic equations governing the flow and heat transfer are highly non-linear coupled partial differential equations. Numerical solution of the problem is obtained by using finite difference method of second-order accuracy. The effects of various physical parameters such as conductivity parameter BK (-1 ? BK ? 1:0), Grashof number Gr (1:0 ? Gr ? 25:0), Brinkman number Br (0:01 ? Br ? 2:0), and aspect ratio A (0:5 ? A ? 2:0), which determine the velocity and temperature contours, are shown pictorially. Results are also presented for the skin friction, volumetric flow rate, and heat transfer rate for representative values of different key parameters. It is found that the intensity of the velocity contours is dense in the lower half region of the duct for negative values of conductivity variation parameter and in the upper region of the duct for positive values of conductivity variation parameter. The 3D contours on temperature are concave for negative values of BK and convex for positive values of BK. © 2018 by Begell House, Inc.