Nonzero Finite Wall Resistance Solution With Constant Dialyzate for Various Mass Transfer Quantities

Abstract

This article deals with the theoretical investigations into dialytic mass transfer in parallel-plate hemodialyzers. The theoretical solutions presented are closed-form analytical solutions involving only exponential and algebraic polynomial functions, and are simple, economical, and convenient to use. With the help of Laplace transforms and the Galerkin method, the expressions for mixed mean concentration, local fluid-wall Sherwood number, logarithmic fluid-wall Sherwood number, local fluid Sherwood number, logarithmic fluid Sherwood number, clearance, and local concentration have been obtained. Data obtained in the present contribution are compared with earlier results and are found to be in the excellent agreement. Two solutes, urea and vitamin B12, were considered. It is observed from the above-mentioned comparison that the effect of variable dialyzate concentration on various mass transfer quantities is significant in the case of uremic small molecules. In the case of uremic middle molecules, the nonuniform concentration distribution in the dialyzate channel is only slightly affected.