Pressure drop-flow rate equation for adiabatic capillary flow with a pressure- and temperature-dependent viscosity

1981 ◽  
Vol 21 (2) ◽  
pp. 65-68 ◽  
Author(s):  
Morton M. Denn
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Rate Equation ◽  
Capillary Flow ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Drop Flow ◽  
Dependent Viscosity

Predicting Inlet Temperature Effects on the Pressure-Drop of Heated Porous Medium Channel Flows Using the M-HDD Model

2004 ◽  
Vol 126 (2) ◽  
pp. 301-303 ◽  
Author(s):  
Arunn Narasimhan ◽  
Jose´ L. Lage
Keyword(s):  
Porous Medium ◽  
Pressure Drop ◽  
Inlet Temperature ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Viscosity Effects ◽  
Nonisothermal Flows ◽  
Nonlinear Temperature ◽  
Global Pressure ◽  
Dependent Viscosity

A Modified Hazen-Dupuit-Darcy (M-HDD) model, incorporating nonlinear temperature-dependent viscosity effects, has been proposed recently for predicting the global pressure-drop of nonisothermal flows across a heated (or cooled) porous medium channel. Numerical simulations, mimicking the flow of a liquid with nonlinear temperature-dependent viscosity, are presented now for establishing the influence of inlet temperature on the pressure-drop and on the predictive capabilities of the M-HDD model. As a result, new generalized correlations for predicting the coefficients of the M-HDD model are derived. The results not only demonstrate the importance of fluid inlet temperature on predicting the global pressure-drop but they also extend the applicability of the M-HDD model.

The effects of temperature-dependent viscosity on flow in a cooled channel with application to basaltic fissure eruptions

1995 ◽  
Vol 305 ◽  
pp. 239-261 ◽  
Author(s):  
Jonathan J. Wylie ◽  
John R. Lister
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Theoretical Description ◽  
Steady Flows ◽  
Two Dimensional ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity ◽  
Averaged Model

A theoretical description is given of pressure-driven viscous flow of an initially hot fluid through a planar channel with cold walls. The viscosity of the fluid is assumed to be a function only of its temperature. If the viscosity variations caused by the cooling of the fluid are sufficiently large then the relationship between the pressure drop and the flow rate is non-monotonic and there can be more than one steady flow for a given pressure drop. The linear stability of steady flows to two-dimensional and three-dimensional disturbances is calculated. The region of instability to two-dimensional disturbances corresponds exactly to those flows in which an increase in flow rate leads to a decrease in pressure drop. At higher viscosity contrasts some flows are most unstable to three-dimensional (fingering) instabilities analogous, but not identical, to Saffman-Taylor fingering. A cross-channel-averaged model is derived and used to investigate the finite-amplitude evolution.

New Theory for Forced Convection Through Porous Media by Fluids With Temperature-Dependent Viscosity

2001 ◽  
Vol 123 (6) ◽  
pp. 1045-1051 ◽  
Author(s):  
Arunn Narasimhan ◽  
Jose´ L. Lage ◽  
Donald A. Nield
Keyword(s):  
Pressure Drop ◽  
Numerical Results ◽  
Balance Equations ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Flow Models ◽  
Nusselt Numbers ◽  
Conventional Procedure ◽  
Viscosity Variation ◽  
Dependent Viscosity

A theoretical analysis is performed to predict the effects of a fluid with temperature-dependent viscosity flowing through an isoflux-bounded porous medium channel. For validation purposes, the thermo-hydraulic behavior of this 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 temperatures, is shown to fail drastically. Alternatively, new predictive theoretical global pressure-drop equations are obtained using the differential form of the HDD model, and validated against the numerical results. Heat transfer results from the new theory, in the form of Nusselt numbers, are compared with earlier results for Darcy flow models (with and without viscosity variation), and validated by using the numerical results. Limitations of the new theory are highlighted and discussed.

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

2000 ◽  
Vol 123 (1) ◽  
pp. 31-38 ◽  
Author(s):  
Arunn Narasimhan ◽  
Jose´ L. Lage
Keyword(s):  
Heat Flux ◽  
Pressure Drop ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Bulk Temperature ◽  
Fluid Viscosity ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
New Model ◽  
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. Based on our new model, two regimes are discovered as the surface heat flux increases. In the first regime both drag terms are affected, while in the second regime only the form drag term is affected, prior to the model reaching an inviscid limit. Predictive empirical relations correcting the viscous and form drag terms, complementing the new model, are obtained as functions of the surface heat flux.

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