A Local Thermal Non-Equilibrium Solution Based on the Brinkman–Forchheimer-Extended Darcy Model for Thermally and Hydrodynamically Fully Developed Flow in a Channel Filled with a Porous Medium

2021 ◽  
Author(s):  
Yuan Yi ◽  
Xiaohui Bai ◽  
Fujio Kuwahara ◽  
Akira Nakayama
Keyword(s):  
Porous Medium ◽  
Equilibrium Solution ◽  
Fully Developed Flow ◽  
Darcy Model ◽  
Non Equilibrium

Modified Reynolds Equation for Aerostatic Porous Radial Bearings With Quadratic Forchheimer Pressure-Flow Assumption

2007 ◽  
Author(s):  
Rodrigo Nicoletti ◽  
Zilda C. Silveira ◽  
Benedito M. Purquerio
Keyword(s):  
Mathematical Modeling ◽  
Porous Medium ◽  
Linear Model ◽  
Dynamic Characteristics ◽  
Reynolds Equation ◽  
Dimensional Parameter ◽  
Pressure Flow ◽  
Darcy Model ◽  
Linear Effects ◽  
Modified Reynolds Equation

The mathematical modeling of aerostatic porous bearings, represented by the Reynolds equation, depends on the assumptions for the flow in the porous medium. One proposes a modified Reynolds equation based on the quadratic Forchheimer assumption, which can be used for both linear and quadratic conditions. Numerical results are compared to those obtained with the linear Darcy model. It is shown that, the non-dimensional parameter Φ, related to non-linear effects, strongly affects the bearing dynamic characteristics, but for values of Φ > 10, the results tend to those obtained with the linear model.

Local Thermal Non-equilibrium Analysis of Boundary Layer Flow of Carreau Fluid Over a Wedge in a Porous Medium

2021 ◽  
Author(s):  
Ramesh Kudenatti ◽  
Sandhya L
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Layer Flow ◽  
Fluid Phase ◽  
Equilibrium Analysis ◽  
Local Thermal Equilibrium ◽  
Carreau Fluid ◽  
Layer Flow ◽  
Non Equilibrium

Abstract This work examines the steady two-dimensional mixed convection boundary layer flow of non-Newtonian Carreau fluid embedded in a porous medium. The impermeable wedge is at rest over which the momentum and thermal boundary layers form due to motion of Carreau fluid with a large Reynolds number. We consider local thermal non-equilibrium for which the temperature of the solid porous medium is different from that of fluid phase, and hence, a single heat-transport equation is replaced by a two-temperature model. The governed equations for flow and heat transfer are converted into a system of ordinary differential equations using a similarity approach. It is observed that local thermal non-equilibrium effects are dominant for small interphase heat transfer rate and porosity scaled conductivity parameters. It is shown that the temperature at any location of the solid porous medium is always higher than that of fluid phase. When these parameters are increased gradually the local thermal equilibrium phase is recovered at which the temperatures of the fluid and solid are identical at each pore. Similar trend is noticed for both shear-thinning and shear-thickening fluids. The results further show that heat exchange between the fluid and solid porous medium is similar to both assisted and opposed flows and Carreau fluid. The velocity and temperature fields for the various increasing fluid index, Grashof number and permeability show that the thickness of the momentum and thermal boundary layer is thinner.

Non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium

2019 ◽  
Vol 29 (8) ◽  
pp. 2524-2544 ◽  
Author(s):  
Mikhail A. Sheremet ◽  
Ioan Pop ◽  
A. Cihat Baytas
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Volume Fraction ◽  
Good Control ◽  
Solid Matrix ◽  
Content Type ◽  
Practical Applications ◽  
Nanofluid Viscosity ◽  
Non Equilibrium

Purpose This study aims to numerically analyze natural convection of alumina-water nanofluid in a differentially-heated square cavity partially filled with a heat-generating porous medium. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been considered for the description of the nanoparticles transport effect in the present study. Local thermal non-equilibrium approach for the porous layer with the Brinkman-extended Darcy model has been used. Design/methodology/approach Dimensionless governing equations formulated using stream function, vorticity and temperature have been solved by the finite difference method. The effects of the Rayleigh number, Ostrogradsky number, Nield number and nanoparticles volume fraction on nanofluid flow, heat and mass transfer have been analyzed. Findings It has been revealed that the dimensionless heat transfer coefficient at the fluid/solid matrix interface can be a very good control parameter for the convective flow and heat transfer intensity. The present results are original and new for the study of non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium. Originality/value The results of this paper are new and original with many practical applications of nanofluids in the modern industry.

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