A mathematical model of mass transport in a long permeable tube with radial convection

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Abstract
Laplace transforms and regular double asymptotic expansions are used to solve the problem of ordinary chemical mass transport in a permeable tube, where there is small radial convection through the membrane wall and where the length-to-diameter ratio is large. The system is taken to be dilute and Newtonian and the solution is found to higher order in two small parameters. Results indicate that the exit concentration decreases markedly as the diameter, membrane permeability and tube length increase, and that changes in mass transport owing to variations in radial convection are much more significant than those due to the same order of magnitude changes in the resistance of the chemical solute to passage through the membrane (transmittance). In addition, the maximum effects of changes in the radial convection and transmittance are not at the membrane itself (r = 1), but rather roughly at radial values of 0·6 and 0, respectively.