Exact solutions for a class of heat and mass transfer problems

Abstract

A number of heat and mass transfer problems of chemical engineering interest involve the convective diffusion equation of the form where θ = θ(X1, X2). 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.

Slip-flow heat transfer in microtubes with axial conduction and viscous dissipation – An extended Graetz problem

“…Note that eigenfunctions F m (h) are not mutually orthogonal (by referring to the standard SturmLiouville problem) since the eigenvalues occur non-linearly. To determine the coefficients A m , similar procedure to that of Davis [26] is implemented. By using the inlet boundary condition, Eq.…”

“…Accordingly, the linearly independent eigenfunctions become non-orthogonal [16]. This interesting problem has been studied by many researchers for macrochannels both analytically [17][18][19][20][21][22][23][24][25][26] and computationally [27,28] for more than three decades ago. More recently, Hadjiconstantinou and Simek [29] studied the effect of axial conduction for thermally fully-developed flows in micro and nano channels; and Jeong and Jeong [30] studied the effect of axial conduction together with viscous dissipation in slit channels with micro spacing for thermally developing flow.…”

Mass transfer in laminar flow between parallel permeable plates

“…We have used the confluent hypergeometric function in the solution of (6) and higher eigenvalues were obtained with no difficulty. Use of the confluent hypergeometric function has been made by Lauwerier (1950) for the solution of Poiseuille flow in a pipe with constant concentration boundary condition and more recently by Davis (1973) for the solution of related problems in pipes and channels. Solutions are also developed in which the eigenvalues and eigenfunctions are written as power series in Sh, (the wall Sherwood number) for small Sh, and 1/(2 + Sh,) for large Sh,.…”

Asymptotic Nusselt numbers for Newtonian flow through a parallel-plate channel with recycle

“…The extended Graetz problem concerns furthermore the effects of axial conduction in the Graetz problem [l, 2]. The conjugated Graetz problem extends above problems from a single phase (or single stream) situation to a multiphase (or multi-stream) situation [1][2][3][4].…”