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Exact solutions for a class of heat and mass transfer problems
Author(s) -
Davis E. James
Publication year - 1973
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450510506
Subject(s) - mass transfer , boundary value problem , a priori and a posteriori , convection , heat transfer , thermodynamics , mathematics , convective heat transfer , class (philosophy) , numerical analysis , churchill–bernstein equation , exact solutions in general relativity , mathematical analysis , physics , computer science , philosophy , epistemology , artificial intelligence , reynolds number , turbulence , nusselt number
A number of heat and mass transfer problems of chemical engineering interest involve the convective diffusion equation of the form\documentclass{article}\pagestyle{empty}\begin{document} \[u(x_2 )\frac{{\partial \theta }}{{\partial x_1 }} = \kappa \,\nabla ^2 \theta + G)x_1, x_2 )\] \end{document}where θ = θ(X 1 , X 2 ). Exact solutions for such problems are developed in terms of well‐known functions which have been thoroughly studied in recent years. Several problems which have appeared in the literature, solved by completely numerical methods, are re‐examined and new problems are discussed and solved. The results of the present analysis are compared with those obtained by other methods where possible. The problem of axial diffusion of heat or mass is solved in terms of known functions. The present formulation is shown to be particularly useful in the analysis of conjugated boundary value problems, i. e. for problems involving heat or mass transfer across an interface where the interfacial boundary condition is not known a priori but is related to the temperature or concentration fields in the adjacent phases.