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Hybrid Methods in Engineering

ISSN Imprimir: 1099-2391
ISSN On-line: 2641-7359

Archives: Volume 1, 1999 to Volume 4, 2002

Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v1.i4.50
12 pages

A NEW SOLUTION OF THE EXTENDED GRAETZ PROBLEM WITH AXIAL CONDUCTION AND VARIABLE WALL TEMPERATURE

G. Elmor Filho
Departamento de Engenharia Quimica (DE-5), Institute Militar de Engenharia (IME); Curso de Pos-Graduacao em Tecnologia de Processos Quimicos e Bioquimicos (TPQB), Departamento de Engenharia Quimica, Escola de Quimica, Centre de Tecnologia, FURJ, Brazil
E. M. Queiroz
Curso de Pas-Graduacao em Tecnologia de Processes Quimicos e Bioquimicos (TPQB), Departamento de Engenharia Quimica, Escola de Quimica, Bloco E, Centro de Tecnologia, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil
Affonso Silva Telles
Curso de Pos-Graduagao em Tecnologia de Processos Quimicos e Bioquimicos (TPQB), Departamento de Engenharia Quimica, Escola de Quimica, Centre de Tecnologia, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

RESUMO

An analytical solution for the extended Graetz problem with axial heat conduction is presented. The method is applicable to a fully developed flow in a circular tube subject to more general, first-kind wall boundary conditions as a function of the axial distance. The solution is generated using a convenient complete basis for the set of square integrable functions in R, orthogonal to the Hermite polynomials. Thus, the solution for the temperature profile is obtained by the infinite series of products of functions, resulting in the decomposition of the energy equation into a set of ordinary differential equations, each of which depends only upon the two previous equations. This fact allows the set to be solved successively. Representative curves illustrating the variations of the temperature surfaces, bulk temperature, heat flux, and Nusselt numbers with pertinent parameters are obtained.