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 temperat ure dependent viscosity, flowing through a porous medium channel bounded by two parallel isoflux surfaces. By reviewing the development of the Hazen-D upuit-Darcy (HDD) equation we bring to light the inappropriateness of the m odel in estimating the global pressure-drop of fluids with temperature depe ndent viscosity. Albeit this observation we tested the accuracy of the HDD model in comparison with numerical results by using three alternatives, nam ely (1) fluid viscosity determined at the average bulk temperature, (2) flu id viscosity determined at the log-mean bulk temperature and (3) fluid visc osity replaced by a channel-length averaged fluid viscosity. The HDD model is inadequate because the temperature dependent fluid viscosity surprisingl y affects both, viscous and form, global drag terms. We propose and validat e a new global model, which accounts for the effects of temperature depende nt viscosity in both drag terms of the original HDD model. Based on our new model, two regimes are discovered as the surface heat flux increases. In t he first regime both drag terms are affected, while in the second regime on ly the form drag term is affected prior to the model reaching an inviscid l imit. Predictive empirical relations correcting the viscous and form drag t erms, complementing the new model, are obtained as functions of the surface heat flux.