Statistics of Mathematical Two-Scale Closure of Momentum, Heat and Charge Transport Problems With Stochastic Orientation of Porous Medium Capillaries

2001 ◽  
Author(s):  
V. S. Travkin ◽  
K. Hu ◽  
I. Catton
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Volume Averaging ◽  
Governing Equations ◽  
Rigorous Approach ◽  
Flow And Heat Transfer ◽  
Model Flow ◽  
History Of ◽  
Transport Problems

Abstract The history of stochastic capillary porous media transport problem treatments almost corresponds to the history of porous media transport developments. Volume Averaging Theory (VAT), shown to be an effective and rigorous approach for study of transport (laminar and turbulent) phenomena, is used to model flow and heat transfer in capillary porous media. VAT based modeling of pore level transport in stochastic capillaries results in two sets of scale governing equations. This work shows how the two scale equations could be solved and how the results could be presented using statistical analysis. We demonstrate that stochastic orientation and diameter of the pores are incorporated in the upper scale simulation procedures. We are treating this problem with conditions of Bi for each pore is in a range when Bi ≳ 0.1 which allows even greater distinction in assessing an each additional differential, integral, or integral-differential term in the VAT equations.

Exact Closure Procedures of Hierarchical VAT Capillary Thermo-Convective Problem for Turbulent and Laminar Regimes

2001 ◽  
Author(s):  
V. S. Travkin ◽  
K. Hu ◽  
I. Catton
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Turbulent Transport ◽  
Volume Averaging ◽  
Turbulent Regime ◽  
Rigorous Approach ◽  
Flow And Heat Transfer ◽  
Pore Level ◽  
Scale Properties ◽  
The Many

Abstract Volume Averaging Theory (VAT), an effective and rigorous approach for study of transport (laminar and turbulent) phenomena, is used to model flow and heat transfer in porous media. The modeling is based on a simple pore level network. The primary difficulties in applying VAT to straight capillary networks, the many unknown integral and differential terms that are needed for closure, are overcome. VAT based modeling of pore level transport in straight capillaries results in two sets of scale governing equations. One scale is the upper scale VAT equations which describe ensemble properties for flow and heat transfer in porous media. The other scale is the lower scale laminar and turbulent transport equations that represent flow and heat transport in each straight pore capillary. It is how the unknown VAT terms in the upper scale equations can be estimated using the relationships between upper scale properties and lower scale properties. Exact closures and mathematical procedures are developed for the turbulent regime, extending the previous laminar regime work. Numerical results for turbulent and laminar transport in straight capillary porous media are shown in this paper.

Compact Modeling of Fluid Flow and Heat Transfer in Straight Fin Heat Sinks

2004 ◽  
Vol 126 (2) ◽  
pp. 247-255 ◽  
Author(s):  
Duckjong Kim ◽  
Sung Jin Kim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Heat Sink ◽  
Volume Averaging ◽  
Thermal Design ◽  
Heat Sinks ◽  
Compact Modeling ◽  
Flow And Heat Transfer

In the present work, a compact modeling method based on a volume-averaging technique is presented. Its application to an analysis of fluid flow and heat transfer in straight fin heat sinks is then analyzed. In this study, the straight fin heat sink is modeled as a porous medium through which fluid flows. The volume-averaged momentum and energy equations for developing flow in these heat sinks are obtained using the local volume-averaging method. The permeability and the interstitial heat transfer coefficient required to solve these equations are determined analytically from forced convective flow between infinite parallel plates. To validate the compact model proposed in this paper, three aluminum straight fin heat sinks having a base size of 101.43mm×101.43mm are tested with an inlet velocity ranging from 0.5 m/s to 2 m/s. In the experimental investigation, the heat sink is heated uniformly at the bottom. The resulting pressure drop across the heat sink and the temperature distribution at its bottom are then measured and are compared with those obtained through the porous medium approach. Upon comparison, the porous medium approach is shown to accurately predict the pressure drop and heat transfer characteristics of straight fin heat sinks. In addition, evidence indicates that the entrance effect should be considered in the thermal design of heat sinks when Re Dh/L>∼O10.

Thermal Optimization of Microchannel Heat Sink With Pin Fin Structures

2003 ◽  
Author(s):  
Duckjong Kim ◽  
Sung Jin Kim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Heat Sink ◽  
Volume Averaging ◽  
Heat Sinks ◽  
Pumping Power ◽  
Heat Transfer Characteristics ◽  
Pin Fin ◽  
Flow And Heat Transfer

In the present work, a novel compact modeling method based on the volume-averaging technique and its application to the analysis of fluid flow and heat transfer in pin fin heat sinks are presented. The pin fin heat sink is modeled as a porous medium. The volume-averaged momentum and energy equations for fluid flow and heat transfer in pin fin heat sinks are obtained using the local volume-averaging method. The permeability, the Ergun constant and the interstitial heat transfer coefficient required to solve these equations are determined experimentally. To validate the compact model proposed in this paper, 20 aluminum pin fin heat sinks having a 101.43 mm × 101.43 mm base size are tested with an inlet velocity ranging from 1 m/s to 5 m/s. In the experimental investigation, the heat sink is heated uniformly at the bottom. Pressure drop and heat transfer characteristics of pin fin heat sinks obtained from the porous medium approach are compared with experimental results. Upon comparison, the porous medium approach is shown to predict accurately the pressure drop and heat transfer characteristics of pin fin heat sinks. Finally, surface porosities of the pin fin heat sink for which the thermal resistance of the heat sink is minimal are obtained under constraints on pumping power and heat sink size. The optimized pin fin heat sinks are shown to be superior to the optimized straight fin heat sinks in thermal performance by about 50% under the same constraints on pumping power and heat sink size.

scholarly journals Thermal Non-Equilibrium Heat Transfer Modeling of Hybrid Nanofluids in a Structure Composed of the Layers of Solid and Porous Media and Free Nanofluids

Energies ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 541 ◽  
Author(s):  
Ali J. Chamkha ◽  
Sina Sazegar ◽  
Esmael Jamesahar ◽  
Mohammad Ghalambaz
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Conjugate Heat Transfer ◽  
Hybrid Nanofluid ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Clear Space ◽  
Hybrid Nanofluids ◽  
Solid Block ◽  
Non Equilibrium

The free convection heat transfer of hybrid nanofluids in a cavity space composed of a clear flow, porous medium and a solid part is addressed. The cavity is heated from the bottom and cooled from the top. The side walls are well insulated. The upper part of the cavity is a clear space with no porous or solid materials and is filled with hybrid nanofluid. The bottom part is divided into two parts of a porous space saturated with the hybrid nanofluid and a solid thermal conductive block. There are conjugate heat transfer mechanisms between the solid block and the porous medium filled with the hybrid nanofluid as well as the hybrid nanofluid in the clear space. For the porous medium model, the local thermal non-equilibrium effects are considered. The hybrid nanofluids contain copper (20 nm) and alumina nanoparticles (40 nm) hybrid nanoparticles. The governing equations for the flow and heat transfer of the hybrid nanofluid in the clear space and the porous medium are introduced. Considering the conjugate heat transfer between the solid block and the hybrid nanofluid fluid in the pores and the porous matrix, appropriate boundary conditions for heat channeling are utilized. The governing equations are transformed into non-dimensional form to generalize the model. The finite element method is employed to solve the equations. The grid check and validation procedure are performed. Subsequently streamlines, isotherms, and Nusselt number are studied as important aspects of flow and heat transfer in the cavity. The increase in the portion of the clear flow part in the cavity enhances heat transfer due to better hybrid nanofluid circulation.

Pseudoplastic natural convection flow and heat transfer in a cylindrical vertical cavity partially filled with a porous layer

2019 ◽  
Vol 30 (3) ◽  
pp. 1096-1114 ◽  
Author(s):  
Kasra Ayoubi Ayoubloo ◽  
Mohammad Ghalambaz ◽  
Taher Armaghani ◽  
Aminreza Noghrehabadi ◽  
Ali J. Chamkha
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Free Convection ◽  
Porous Layer ◽  
Power Law ◽  
Convection Flow ◽  
Governing Equations ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Vertical Cavity

Purpose This paper aims to theoritically investigate the free convection flow and heat transfer of a non-Newtonian fluid with pseudoplastic behavior in a cylindrical vertical cavity partially filled with a layer of a porous medium. Design/methodology/approach The non-Newtonian behavior of the pseudoplastic liquid is described by using a power-law non-Newtonian model. There is a temperature difference between the internal and external cylinders. The porous layer is attached to the internal cylinder and has a thickness of D. Upper and lower walls of the cavity are well insulated. The governing equations are transformed into a non-dimensional form to generalize the solution. The finite element method is used to solve the governing equations numerically. The results are compared with the literature results in several cases and found in good agreement. Findings The influence of the thickness of the porous layer, Rayleigh number and non-Newtonian index on the heat transfer behavior of a non-Newtonian pseudoplastic fluid is addressed. The increase of pseudoplastic behavior and increase of the thickness of the porous layer enhances the heat transfer. By increase of the porous layer from 0.6 to 0.8, the average Nusselt number increased from 0.15 to 0.25. The increase of non-Newtonian effects (decrease of the non-Newtonian power-law index) enhances the heat transfer rate. Originality/value The free convection behavior of a pseudoplastic-non-Newtonian fluid in a cylindrical enclosure partially filled by a layer of a porous medium is addressed for the first time.

scholarly journals Comparison of Numerical Models of Flow and Heat Transfer Through Porous Medium in a Vertical Channel

2021 ◽  
Vol 850 (1) ◽  
pp. 012023
Author(s):  
G Trilok ◽  
N Gnanasekaran
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Equilibrium Model ◽  
Vertical Channel ◽  
Modelling Technique ◽  
Local Thermal Equilibrium ◽  
Pore Density ◽  
Thermal Models ◽  
Flow And Heat Transfer

Abstract Porous medium modelling technique has opened up ways for number of numerical studies to investigate the performance of many devices that involve heat exchanging process. Such modelling technique not only avoids huge cost and time as compared to experimental analysis but also makes computationally less time-consuming as in case of numerical simulation by exact geometry modelling of porous materials. In this regard the present paper analyses two different thermal models namely local thermal equilibrium model and local thermal non equilibrium model along with two different flow models namely Darcy flow model and Darcy extended Forchheimer model. Suitability of the mentioned models in predicting heat transfer through metal foam and wire mesh porous medium is examined subjected to variations in structural aspects of the porous medium that could be primarily represented by variation in porosity and pore density. For this purpose, a vertical channel subjected to constant heat flux capable of housing porous medium reported in literature is numerically modelled and air flow is numerically simulated through the channel. A variety of structural configuration (combination of different porosity and pore density) of the mentioned porous media are considered and among the mentioned flow and thermal models, best suited models for predicting flow and heat transfer through such medium are identified with appropriate justifications. It is revealed from the present study that, Darcy-Forchheimer and LTNE models are best suited to predict flow and heat transfer through porous media than the basic Darcy and LTE models.

Compact Modeling of Fluid Flow and Heat Transfer in Pin Fin Heat Sinks

2004 ◽  
Vol 126 (3) ◽  
pp. 342-350 ◽  
Author(s):  
Duckjong Kim ◽  
Sung Jin Kim ◽  
Alfonso Ortega
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Heat Sink ◽  
Volume Averaging ◽  
Heat Sinks ◽  
Compact Modeling ◽  
Pumping Power ◽  
Pin Fin ◽  
Flow And Heat Transfer

In this work, a novel compact modeling method based on the volume-averaging technique is presented. Its application to the analysis of fluid flow and heat transfer in pin fin heat sinks are further analyzed. The pin fin heat sink is modeled as a porous medium. The volume-averaged momentum and energy equations for fluid flow and heat transfer in pin fin heat sinks are obtained by using the local volume-averaging method. The permeability, the Ergun constant, and the interstitial heat transfer coefficient required to solve these equations are determined experimentally and correlations for them are presented. To validate the compact model proposed in this paper, 20 aluminum pin fin heat sinks having a 101.43 mm×101.43 mm base size are tested with an inlet velocity ranging from 1 m/s to 5 m/s. In the experimental investigation, the heat sink is heated uniformly at the bottom. Pressure drop and heat transfer characteristics of pin fin heat sinks obtained from the porous medium approach are compared with experimental results. Upon comparison, the porous medium approach is shown to predict accurately the pressure drop and heat transfer characteristics of pin fin heat sinks. Finally, for minimal thermal resistance, the optimum surface porosities of the pin fin heat sink are obtained under constraints on pumping power and heat sink size. The optimized pin fin heat sinks are shown to be superior to the optimized straight fin heat sinks in thermal performance by about 50% under the same constraints on pumping power and heat sink size.

A critical review on the applications of fluid-structure interaction in porous media

2019 ◽  
Vol 30 (1) ◽  
pp. 308-327 ◽  
Author(s):  
Khalil Khanafer ◽  
K. Vafai
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Porous Medium ◽  
Porous Media ◽  
Biomedical Applications ◽  
Arterial Wall ◽  
Content Type ◽  
Future Studies ◽  
Structure Interaction ◽  
Flow And Heat Transfer

Purpose This study aims to investigate a critical review on the applications of fluid-structure interaction (FSI) in porous media. Design/methodology/approach Transport phenomena in porous media are of continuing interest by many researchers in the literature because of its significant applications in engineering and biomedical sectors. Such applications include thermal management of high heat flux electronic devices, heat exchangers, thermal insulation in buildings, oil recovery, transport in biological tissues and tissue engineering. FSI is becoming an important tool in the design process to fully understand the interaction between fluids and structures. Findings This study is structured in three sections: the first part summarizes some important studies on the applications of porous medium and FSI in various engineering and biomedical applications. The second part focuses on the applications of FSI in porous media as related to hyperthermia. The third part of this review is allocated to the applications of FSI of convection flow and heat transfer in engineering systems filled with porous medium. Research limitations/implications To the best knowledge of the present authors, FSI analysis of turbulent flow in porous medium never been studied, and therefore, more attention should be given to this area in any future studies. Moreover, more studies should also be conducted on mixed convective flow and heat transfer in systems using porous medium and FSI. Practical implications The wall of the blood vessel is considered as a flexible multilayer porous medium, and therefore, rigid wall analysis is not accurate, and therefore, FSI should be implemented for accurate predictions of flow and hemodynamic stresses. Social implications The use of porous media theory in biomedical applications received a great attention by many investigators in the literature (Khanafer and Vafai, 2006a; Al-Amiri et al., 2014; Lasiello et al., 2016a, Lasiello et al., 2016b; Lasiello et al., 2015; Chung and Vafai, 2013; Mahjoob and Vafai, 2009; Yang and Vafai, 2008; Yang and Vafai, 2006; Ai and Vafai, 2006). A comprehensive review was conducted by Khanafer and Vafai (2006b) summarizing various studies associated with magnetic field imaging and drug delivery. The authors illustrated that the tortuosity and porosity had a profound effect on the diffusion process within the brain. AlAmiri et al. (2014) conducted a numerical study to investigate the effect of turbulent pulsatile flow and heating technique on the thermal distribution within the arterial wall. The results of that investigation illustrated that local heat flux variation along the bottom layer of the tumor was greater for the low-velocity condition. Yang and Vafai (2006) presented a comprehensive four-layer model to study low-density lipoprotein transport in the arterial wall coupled with a lumen (Figure 1). All the four layers (endothelium, intima, internal elastic lamina and media) were modeled as a homogenous porous medium. Originality/value Future studies on the applications of FSI in porous media are recommended in this review.

Flow and heat transfer of nanofluid in a channel partially filled with porous media considering turbulence effect in pores

2020 ◽  
Vol 98 (3) ◽  
pp. 297-302 ◽  
Author(s):  
Ali Asghar Sedighi ◽  
Zeynab Deldoost ◽  
Bahram Mahjoob Karambasti
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Skin Friction Coefficient ◽  
Clear Fluid ◽  
Flow And Heat Transfer ◽  
Turbulence Effect ◽  
Flow Cross

The flow and heat transfer of Al2O3–water nanofluid in a channel partially filled with porous media is investigated numerically. The turbulence effect in the porous media is taken under consideration in this article. A simple case is simulated first to evaluate the accuracy of the results in comparison with the available data. The turbulent kinetic energy profile is investigated at a flow cross section. The results show that the maximum turbulent kinetic energy occurs in the clear fluid region in the vicinity of the porous media region. The turbulent kinetic energy is a decreasing function of the porosity of the porous medium. The effect of porosity on the variation of turbulent kinetic energy decreases with the increase in the porosity of the porous medium. The turbulent kinetic energy in clear fluid and porous media regions decreases with the increase in nanofluid concentration from 0.01 to 0.03, and it increases with the increase in nanofluid concentration from 0.03 to 0.05. The temperature of the nanofluid increases with the increase in the nanofluid concentration and decrease in the porosity of porous media. It is shown that for this case, with the increase in nanofluid concentration and porosity of porous media, the skin friction coefficient increases and the Nusselt number decreases.

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