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.

NUMERICAL STUDY OF BÉNARD CONVECTION WITH TEMPERATURE-DEPENDENT VISCOSITY IN A POROUS CAVITY VIA LATTICE BOLTZMANN METHOD

2010 ◽  
Vol 21 (11) ◽  
pp. 1407-1419 ◽  
Author(s):  
FUMEI RONG ◽  
ZHAOLI GUO ◽  
TING ZHANG ◽  
BAOCHANG SHI
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Numerical Results ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Average Temperature ◽  
Nusselt Numbers ◽  
Benard Convection ◽  
Dependent Viscosity ◽  
Boltzmann Method

In this paper, the heat transfer characteristics of a two-dimensional steady Bénard convection flow with a temperature-dependent viscosity are studied numerically by the lattice Boltzmann method (LBM). The double-distribution model for LBM is proposed, one is to simulate incompressible flow in porous media and the other is to solve the volume averaged energy equation. The method is validated by comparing the numerical results with those existing literature. The effect of viscosity dependent on temperature is investigated. The average Nusselt numbers for the cases of exponential form of viscosity-temperature and effective Rayleigh number based on average temperature (T ref = 0.5 (Th +Tc)) are compared. A new formula of reference temperature (T ref = Tc +f (b) (Th -Tc)) is proposed and the numerical results show that the average Nusselt numbers predicted by this method have higher precision than those obtained by average temperature.

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.

scholarly journals Influence of Viscous Dissipation on the Exiting Sheet Thickness in the Calendering of Newtonian Fluids

2020 ◽  
Vol 7 ◽  
Keyword(s):  
Mathematical Problem ◽  
Sheet Thickness ◽  
Newtonian Fluids ◽  
Temperature Fields ◽  
Balance Equations ◽  
Initial Thickness ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity ◽  
Velocity Pressure

In this work we treat theoretically the calendering process of Newtonian fluids with finite sheet initial thickness, taking into account that the viscosity of the fluid is a welldefined function of the temperature. We predict the influence of the temperature-dependent viscosity on the exiting sheet thickness in the calendering process. The mass, momentum and energy balance equations, based on the lubrication theory, were nondimensionalized and solved for the velocity, pressure and temperature fields by using perturbation and numerical techniques, where the exiting sheet thickness represents an eigenvalue of the mathematical problem. The numerical results show that the inclusion of temperature-dependent viscosity effect reduces about 20% the leave-off distance in comparison with the case of temperature-independent viscosity.

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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