Local Rayleigh and Nusselt Numbers for Cartesian convection with temperature-dependent viscosity

1996 ◽  
Vol 23 (18) ◽  
pp. 2445-2448 ◽  
Author(s):  
S. Honda
Keyword(s):  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Nusselt Numbers ◽  
Dependent Viscosity

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.

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.

scholarly journals Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1300
Author(s):  
Evgenii S. Baranovskii ◽  
Vyacheslav V. Provotorov ◽  
Mikhail A. Artemov ◽  
Alexey P. Zhabko
Keyword(s):  
Nonlinear Boundary ◽  
Galerkin Approximation ◽  
Large Data ◽  
Temperature Dependent ◽  
Weak Formulation ◽  
Temperature Dependent Viscosity ◽  
Pipeline Network ◽  
Flux Boundary Conditions ◽  
Creeping Flows ◽  
Dependent Viscosity

This paper deals with a 3D mathematical model for the non-isothermal steady-state flow of an incompressible fluid with temperature-dependent viscosity in a pipeline network. Using the pressure and heat flux boundary conditions, as well as the conjugation conditions to satisfy the mass balance in interior junctions of the network, we propose the weak formulation of the nonlinear boundary value problem that arises in the framework of this model. The main result of our work is an existence theorem (in the class of weak solutions) for large data. The proof of this theorem is based on a combination of the Galerkin approximation scheme with one result from the field of topological degrees for odd mappings defined on symmetric domains.

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