Influence of the main parameters of a parallel-plate dialyser under laminar flow conditions
A mathematical model describing the mass transfer in a parallel-plate dialyser with co-current laminar flow in both channels based on the Navier-Stokes equations and Fick's second law was developed. Numerical solutions are presented for pulse- and stepwise concentration changes of the solute in one of the channels using the Laplace transform technique. By simulation the influence of the main design and operational parameters of the dialyser and the most important physical constants for the mass transfer process were investigated. Conclusions with regard to optimum design and operation were drawn and some possibilities for simplifying the model were established
Laminar heat or mass transfer in rectangular channels and in cylindrical tubes for fully developed flow: comparison of solutions obtained for various boundary conditions
Abstract A comparison is made of results obtained with various boundary conditions at the wall of the channels. By comparing blood Sherwood numbers for finite wall resistance with those for constant concentration boundary condition only a small variation is found for various points along the blood channel.
Numerical inversion of the Laplace transform: an explicit closed-form expression for the time-domain solution
Abstract A method for the numerical inversion of Laplace transforms that yields time-domain solutions in the explicit form f ( t ) = P n ( t )e − t /τ , where P n ( t ) is an n th order polynomial, is described and successfully applied to a wide variety of transfer functions having chemical engineering applications.