Abstract A numerical model of non-isothermal pervaporation was developed to investigate the development of the velocity, concentration and temperature fields in rectangular membrane module geometry. The model consists of the coupled Navier–Stokes equations to describe the flow field, the energy equation for the temperature field, and the species convection-diffusion equations for the concentration fields of the solution species. The coupled nonlinear transport equations were solved simultaneously for the velocity, temperature and concentration fields via a finite element approach. Simulation test cases for trichloroethylene/water, ethanol/water and iso-propanol/water pervaporation, under laminar flow conditions, revealed temperature drop axially along the module and orthogonal to the membrane surface. The nonlinear character of the concentration and temperature boundary-layers are most significant near the membrane surface. Estimation of the mass transfer coefficient assuming isothermal assumption conditions can significantly deviate from the non-isothermal predictions. For laminar conditions, predictions of the feed-side mass transfer coefficient converged to predictions from the classical Lévêque solution as the feed temperature approached the permeate temperature.