New theory for forced convection through porous media by fluids with temperature-dependent viscosity

A theoretical analysis is performed to predict the effects of a fluid with temperature-dependent viscosity flowing through an isoflux-bounded porous m edium channel. For validation purposes, the thermo-hydraulic behavior of th is system is obtained also by solving numerically the differential balance equations. The conventional procedure for predicting the numerical pressure -drop along the channel by using the global Hazen-Dupuit-Darcy (HDD) model (also known as the Forchheimer-extended Darcy model), with a representative viscosity for the channel calculated at maximum or minimum fluid temperatu res, is shown to fail drastically. Alternatively, new predictive theoretica l global pressure-drop equations are obtained using the differential form o f the HDD model, and validated against the numerical results. Heat transfer results from the new theory in the form of Nusselt numbers, are compared w ith earlier results for Darcy flow models (with and without viscosity varia tion), and validated by using the numerical results. Limitations of the new theory are highlighted and discussed.