Abo Bibliothek: Guest

ISSN Druckformat: 1099-2391
ISSN Online: 2641-7359

Archives: Volume 1, 1999 to Volume 4, 2002

# Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v2.i2.20
12 pages

## ANALYTICAL SOLUTION OF THE EXTENDED GRAETZ PROBLEM WITH AXIAL CONDUCTION AND CONVECTIVE BOUNDARY CONDITIONS

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

### ABSTRAKT

This article presents an analytical solution to the extended Graetz problem, in a circular pipe, with axial heat conduction, subjected to boundary conditions of the third kind. A mathematical scheme for solving this type of heat transfer problem was proposed by the present authors [1]. The solution employs a complete basis for the set of square integrable functions, orthogonal to the Hermite polynomials. The temperature profile is obtained as an infinite series of products of functions, resulting in decomposition of the energy equation into a set of ordinary differential equations, each of which depends on the two previous equations only. This allows a straightforward solution of the set of equations. The effects of the external Biot number and the axial conduction in fluid on the surface temperature, bulk temperature, heat flux, and Nusselt number are shown.

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