Spectral Collocation Analysis of Entropy Generation in Coupled Heat and Mass Transfer Boundary Layer Flow

Abstract

This study presents a spectral collocation analysis of entropy generation in a laminar boundary layer flow with coupled heat and mass transfer. The model considers a steady, two-dimensional, incompressible, and Newtonian flow over a flat plate with constant thermophysical properties and negligible pressure gradient. Through similarity transformations, the governing equations for momentum, energy, and species concentration are reduced to a system of coupled nonlinear ordinary differential equations. The resulting boundary value problem is solved using the Spectral Collocation Method with Chebyshev polynomials, which ensures high numerical accuracy and rapid convergence. Entropy generation arising from thermal gradients, viscous dissipation, and mass diffusion is quantified, and the effects of key dimensionless parameters, including the Prandtl number, Schmidt number, and Brinkman number, are systematically investigated. The results show that entropy generation is highest near the wall due to steep velocity, temperature, and concentration gradients and decreases rapidly across the boundary layer. Increasing Prandtl and Schmidt numbers enhances thermal and concentration gradients, leading to higher irreversibility, while the Brinkman number significantly increases entropy generation through viscous heating. Bejan number analysis indicates that thermal irreversibility dominates near the surface, whereas viscous and diffusion effects become more pronounced away from the wall. Although based on an idealized boundary layer configuration, the findings provide meaningful insight into energy degradation and coupled transport mechanisms, with potential relevance to near-surface environmental and atmospheric processes. The study demonstrates the effectiveness of spectral methods for accurately resolving nonlinear transport phenomena.