Article,
Conjugated Graetz Problems—I: General Formalism and a Class of Solid-Fluid Problems
Chemical Engineering Science, 36 (8): 1381--1391 (1981)
DOI: 10.1016/0009-2509(81)80172-8
Abstract
Conjugated Graetz problems arise where two (or more) phases, with at least one phase in fully developed flow, exchange energy or mass across an intervening surface. In these problems the temperature or concentration fields are coupled through the conjugating conditions which express the continuity of fluxes and the rate of transfer. A general formalism is presented first for the analysis of these problems, employing a matrix differential operator with respect to the radial variable and following the decomposition technique of 1–3. The aforementioned operator is shown to be symmetric in its domain, possessing a denumerable set of eigenvalues and a complete set of eigenvectors. A class of solid-fluid problems, involving the removal of heat from a heated solid cylinder by a surrounding annular-flow fluid, is then discussed in detail; analytical solutions are obtained by expansion in terms of the above eigenvectors. These solid-fluid problems may be viewed as extensions of the extended, one-phase, Graetz problem with prescribed wall flux 2.
