Modified Hazen-Dupuit-Darcy Model for Forced Convection of a Fluid With Temperature-Dependent Viscosity

We investigate numerically the global pressure-drop of fluids with temperature dependent viscosity, flowing through a porous medium channel bounded by two parallel isoflux surfaces. By reviewing the development of the Hazen-Dupuit-Darcy (HDD) equation we bring to light the inappropriateness of the model in estimating the global pressure-drop of fluids with temperature dependent viscosity. Albeit this observation, we tested the accuracy of the HDD model in comparison with numerical results by using three alternatives, namely (1) fluid viscosity determined at the average bulk temperature, (2) fluid viscosity determined at the log-mean bulk temperature and (3) fluid viscosity replaced by a channel-length averaged fluid viscosity. The HDD model is inadequate because the temperature dependent fluid viscosity surprisingly affects both, viscous and form, global drag terms. We propose and validate a new global model, which accounts for the effects of temperature dependent viscosity in both drag terms of the original HDD model