A mathematical model is derived for convective mass and heat transfer between the flows of finely dispersed food media moving in adjacent channels separated by a permeable wall where portions of the fluid phases are exchanged many times between the flows. Numerical solutions are given for a countercurrent flow of a suspension and a liquid. The distribution of the flow velocity and the suspension porosity along the length of the channels is shown as well as the time dependence of the temperature of the flows. (C) 2004 Elsevier Ltd. All rights reserved.