Numerical Solution for Heat and Mass Transfer of Developing Laminar Mixed Convection of Two-Dimensional Inclined Parallel Plates

Abstract

Two-dimensional, developing laminar mixed convection of a binary non-reacting gas mixture flowing in an inclined channel is investigated. A steady state condition is focused through the present study. Thermal boundary conditions of the channel are that one is uniform wall heat flux while the other is uniform wall temperature. Moreover, the walls of channel have different constant species concentrations. The numerical method, called implicit finite difference method, is applied to find hydraulic and heat transfer parameters, consisting of axial and transverse velocities, temperature, and mass fraction. The developments of these parameter profiles, presented in terms of dimensionless form, are observed and discussed. The analytical solution is also presented for fully developed region. The results show that thermal and solutal buoyancy parameters strongly affect on the axial velocity profile. The flow reversal is found near the constant temperature wall for some conditions. If the inclination angle increases, the flow reversal can clearly be observed nearer the inlet of channel. The dimensionless mass fraction, expressing the concentration of focused gas species, and the dimensionless temperature, reflecting the temperature of mixture in the channel, are also interested in this study. The dimensionless mass fraction and the dimensionless temperature profiles continuously change to be linear as distance along the flow direction increase. Based on the condition in this study, the dimensionless mass fraction profile can reach the fully developed condition faster than the dimensionless axial velocity and the dimensionless temperature profiles.