A Comparison of Approximate and Exact Solutions for Homogeneous Irreversible Chemical Reaction in the Laminar Boundary Layer

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Chemical Engineering Communications


A comparison of approximate and exact solutions for homogeneous irreversible chemical reaction in the laminar boundary layer flow has been made. By using the Method of Weighted Residuals, approximate analytical expressions for the velocity and concentration profiles were developed for the case of a laminar boundary layer flow over a flat plate at zero incidence angle, where isothermal, homogeneous, nth order chemical reaction takes place. Both the Subdomain and Galerkin methods were employed to examine the influence of the choice of the weighting function on the predictions, and to provide a means for improving the solutions systematically. The problem was also solved numerically for the case of first order reaction by using a similarity solution for the hydrodynamic flow and a power series expansion method for the mass transfer. The analytical results were compared with the exact solutions in order to evaluate the accuracy of the approximate analytical solutions. The Method of Weighted Residuals provided approximate solutions that are qualitatively correct and, within limits, quantitatively accurate. The resulting approximate expressions can be used to give quick estimates for reactions investigated herein and to predict the results for higher order reactions when there are no exact solutions. © 1990, Taylor & Francis Group, LLC. All rights reserved.