Entropy Generation During Natural Convection in a Porous Cavity: Effect of Thermal Boundary Conditions
02 Aug 2012-Numerical Heat Transfer Part A-applications (Taylor & Francis Group)-Vol. 62, Iss: 4, pp 336-364
TL;DR: In this article, the authors investigated the effect of different boundary conditions on entropy generation, and showed that the entropy generation rates are reduced in sinusoidal heating (case 2) when compared to that for uniform heating with a penalty on thermal mixing, and that there exists an intermediate Da for optimal values of entropy generation.
Abstract: Entropy generation plays a significant role in the overall efficiency of a given system, and a judicious choice of optimal boundary conditions can be made based on a knowledge of entropy generation. Five different boundary conditions are considered and their effect of the permeability of the porous medium, heat transfer regime (conduction and convection) on entropy generation due to heat transfer, and fluid friction irreversibilities are investigated in detail for molten metals (Pr = 0.026) and aqueous solutions (Pr = 10), with Darcy numbers (Da) between 10−5–10−3 and at a representative high Rayleigh number, Ra = 5 × 105. It is observed that the entropy generation rates are reduced in sinusoidal heating (case 2) when compared to that for uniform heating (case 1), with a penalty on thermal mixing. Finally, the analysis of total entropy generation due to variation in Da and thermal mixing and temperature uniformity indicates that, there exists an intermediate Da for optimal values of entropy generation, th...
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01 Jan 1997
TL;DR: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems and discusses the main points in the application to electromagnetic design, including formulation and implementation.
Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.
1,820 citations
TL;DR: In this paper, the authors investigated the entropy generation due to conjugate natural convection-conduction heat transfer in a square domain under steady-state condition, and the results showed that both the average Nusselt number and entropy generation are increasing functions of K ro while they are maxima at some critical values of D.
Abstract: Entropy generation due to conjugate natural convection–conduction heat transfer in a square domain is numerically investigated under steady-state condition. The domain composed of porous cavity heated by a triangular solid wall and saturated with a CuO–water nanofluid. Equations governing the heat transfer in the triangular solid together with the heat and nanofluid flow in the nanofluid-saturated porous medium are solved numerically using the over-successive relaxation finite-difference method. A temperature dependent thermal conductivity and modified expression for the thermal expansion of nanofluid are adopted. A new criterion for assessment of the thermal performance is proposed. The investigated parameters are the nanoparticles volume fraction φ (0–0.05), modified Rayleigh number Ra (10–1000), solid wall to base-fluid saturated porous medium thermal conductivity ratio K ro (0.44, 1, 23.8), and the triangular solid thickness D (0.1–1). The results show that both the average Nusselt number and the entropy generation are increasing functions of K ro , while they are maxima at some critical values of D . It is also found that the addition of nanoparticles increases the entropy generation. According to the new proposed criterion, the results show that the largest solid thickness ( D = 1.0) and the lower wall thermal conductivity ratio manifest better thermal performance.
142 citations
TL;DR: In this article, the entropy generation in natural convection of nanofluid in a wavy cavity using a single-phase model was analyzed using the finite difference method of the second-order accuracy.
Abstract: Purpose
The main purpose of this numerical study is to study on entropy generation in natural convection of nanofluid in a wavy cavity using a single-phase nanofluid model.
Design/methodology/approach
The cavity is heated non-uniformly from the wavy wall and cooled from the right side while it is insulated from the horizontal walls. The physical domain of the problem is transformed into a rectangular geometry in the computational domain using an algebraic coordinate transformation by introducing new independent variables ξ and η. The governing dimensionless partial differential equations with corresponding initially and boundary conditions were numerically solved by the finite difference method of the second-order accuracy. The governing parameters are Rayleigh number (Ra = 1000-100000), Prandtl number (Pr = 6.82), solid volume fraction parameter of nanoparticles (φ = 0.0-0.05), aspect ratio parameter (A = 1), undulation number (κ = 1-3), wavy contraction ratio (b = 0.1-0.3) and dimensionless time (τ = 0-0.27).
Findings
It is found that the average Bejan number is an increasing function of nanoparticle volume fraction and a decreasing function of the Rayleigh number, undulation number and wavy contraction ratio. Also, an insertion of nanoparticles leads to an attenuation of convective flow and enhancement of heat transfer.
Originality
The originality of this work is to analyze the entropy generation in natural convection within a wavy nanofluid cavity using single-phase nanofluid model. The results would benefit scientists and engineers to become familiar with the flow behaviour of such nanofluids, and will be a way to predict the properties of this flow for the possibility of using nanofluids in advanced nuclear systems, in industrial sectors including transportation, power generation, chemical sectors, ventilation, air-conditioning, etc.
128 citations
TL;DR: It is found that the applied magnetic field can suppress both the natural convection and the entropy generation rate, and the nanoparticles addition can be useful if a compromised magnetic field value represented by a Hartman number of 30 is applied.
Abstract: This paper investigates the entropy generation and natural convection inside a C-shaped cavity filled with CuO-water nanofluid and subjected to a uniform magnetic field. The Brownian motion effect is considered in predicting the nanofluid properties. The governing equations are solved using the finite volume method with the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm. The studied parameters are the Rayleigh number (1000 ≤ Ra ≤ 15,000), Hartman number (0 ≤ Ha ≤ 45), nanofluid volume fraction (0 ≤ φ ≤ 0.06), and the cavity aspect ratio (0.1 ≤ AR ≤ 0.7). The results have shown that the nanoparticles volume fraction enhances the natural convection but undesirably increases the entropy generation rate. It is also found that the applied magnetic field can suppress both the natural convection and the entropy generation rate, where for Ra = 1000 and φ = 0.04, the percentage reductions in total entropy generation decreases from 96.27% to 48.17% for Ha = 45 compared to zero magnetic field when the aspect ratio is increased from 0.1 to 0.7. The results of performance criterion have shown that the nanoparticles addition can be useful if a compromised magnetic field value represented by a Hartman number of 30 is applied.
120 citations
TL;DR: In this paper, a numerical study is made on the mixed convection of copper-water nanofluid inside a differentially heated skew enclosure, where the finite volume based SIMPLEC algorithm is used to solve the transformed equations for fluid flow and heat transfer equations in the computational domain.
Abstract: A numerical study is made on the mixed convection of copper–water nanofluid inside a differentially heated skew enclosure. Co-ordinate transformations are used to transform the physical domain to the computational domain in an orthogonal co-ordinate. The finite volume based SIMPLEC algorithm is used to solve the transformed equations for fluid flow and heat transfer equations in the computational domain. The fluid flow and heat transfer characteristics are studied for a wide range of skew angles ( 30 ° ⩽ λ ⩽ 150 ° ) , nanoparticle volume fraction ( 0.0 ⩽ ϕ ⩽ 0.2 ) and Richardson number ( 0.1 ⩽ Ri ⩽ 5 ) at a fixed value of Reynolds number. The entropy generation and Bejan number are evaluated to demonstrate the thermodynamic optimization of the mixed convection. It is shown that the heat transfer rate increases remarkably by the addition of nanoparticles. The flow field is sensible to the skew angle variation. Our results show that the heat transfer augmentation through nanoparticles with lower rate in entropy generation enhancement can be achieved in a skewed cavity.
76 citations
References
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TL;DR: In this article, the heat transfer and pressure drop characteristics of a double-pipe pin fin heat exchanger have been experimentally derived and the empirical correlations previously validated with the experimental data were used in order to develop a mathematical model for the optimization of the actual heat exchange.
Abstract: Pin fins are widely used as effective elements for heat transfer enhancement. For this reason, extensive work is being carried out to select and optimize pin fins for various applications. Any optimization procedure would lead to desirable results only if the parallel heat transfer and pressure drop are considered. In the present study, the heat transfer and pressure drop characteristics of a double-pipe pin fin heat exchanger have been experimentally derived. The empirical correlations previously validated with the experimental data were used in order to develop a mathematical model for the optimization of the actual heat exchanger. The optimization model was developed on the basis of the entropy generation minimization for different heat exchanger flow lengths and different pin length. The conclusions are derived on the basis of the behavior of the entropy generation NS number as a function of Re. It is shown that not all definition forms for the entropy generation number leads to the right conclusions.
80 citations
01 Mar 1992
TL;DR: In this paper, a two dimensional cavity filled with a uniform heat generating, saturated porous medium has been studied and the results are presented in terms of the isotherms and stream functions, the temperature variation and maximum temperature in the cavity and heat transfer from the vertical walls.
Abstract: Steady natural convection heat transfer in a two dimensional cavity filled with a uniform heat generating, saturated porous medium has been studied. The boundary conditions were: Two isothermal walls at different temperatures, two horizontal adiabatic walls. The aspect ratio was varied from 0.1 to 10 and the Rayleigh number from 100 to 108. The results are presented in terms of the isotherms and stream functions, the temperature variation and maximum temperature in the cavity and heat transfer from the vertical walls. The study indicates that asymmetric vertical boundary conditions with θ h >0 has an important effect on the temperature and flow fields as well as on the heat transfer characteristics of the cavity with highly asymmetric results. Various heat transfer modes are identified dependent on the Rayleigh number and the aspect ratio.
67 citations
TL;DR: In this article, the authors investigated possible improvements in the geometry design of a monolithic solid oxide fuel cells through analysis of the entropy generation terms, and calculated different contributions to the local rate of entropy generation using a computational fluid dynamic (CFD) model of the fuel cell, accounting for energy transfer, fluid dynamics, current transfer, chemical reactions and electrochemistry.
Abstract: The aim of the paper is to investigate possible improvements in the geometry design of a monolithic solid oxide fuel cells (SOFCs) through analysis of the entropy generation terms. The different contributions to the local rate of entropy generation are calculated using a computational fluid dynamic (CFD) model of the fuel cell, accounting for energy transfer, fluid dynamics, current transfer, chemical reactions and electrochemistry. The fuel cell geometry is then modified to reduce the main sources of irreversibility and increase its efficiency.
59 citations
"Entropy Generation During Natural C..." refers methods in this paper
...The EGM approach has been applied to optimize natural convection systems [24, 25], pin-fin heat sinks [26], fuel cells [27], heat exchangers [28, 29], environmental control of aircraft [30, 31], combustion in porous media [32], etc....
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01 Dec 1976
TL;DR: In this paper, the authors discuss the magnitudes of convection, extensions of Lapwood's work, the departure of permeable media in geothermal areas from simple homogeneous isotropic systems, and stability analysis for boundary conditions 1 and 2 from convection theory.
Abstract: The question of the depth reached by groundwater in natural recharge to a geothermal field is of interest for geothermal development, since it can affect the nature of the recharge regime during withdrawal, and the volume of water within reach during exploitation. Also, useful inferences may be drawn about the large-scale permeability of the system if the groundwater flow regime is understood. Evidence for the presence of thermal convection in the groundwater now appears to be well-established, although topographic effects may also be important (Studt and Thompson 1969, Healy and Hochstein 1973). Two regions which serve particularly well as illustrations are (1) the Imperial Valley of Southern California and (2) the Taupo Volcanic Zone of New Zealand. Both exhibit a number of quite well-defined zones of anomalously high heat flow (geothermal fields), separated by distances of 10 to 15 Km, the intervening areas usually having very low heat flow. In (1) the upper flow boundary is practically impermeable while, in (2), flow through the upper boundary is almost unimpeded. Idealized conditions which correspond approximately to these cases were introduced by Lapwood (1948); these will be designated as boundary conditions 1 and 2 respectively. This paper discusses the magnitudes of convectionmore » parameters, extensions of Lapwood’s work, the departure of permeable media in geothermal areas from simple homogeneous isotropic systems, and stability analysis for boundary conditions 1 and 2 from convection theory. 11 refs., 1 fig.« less
49 citations
TL;DR: In this article, the authors address two basic issues in the thermodynamic optimization of environmental control systems (ECS) for aircraft: realistic limits for the minimal power requirement, and design features that facilitate operation at minimal power consumption.
Abstract: This paper addresses two basic issues in the thermodynamic optimization of environmental control systems (ECS) for aircraft: realistic limits for the minimal power requirement, and design features that facilitate operation at minimal power consumption. Four models are proposed and optimized. In the first, the ECS operates reversibly, the air stream in the cabin is mixed to one temperature, and the cabin experiences heat transfer with the ambient, across its insulation. The cabin temperature is fixed. In the second model, the fixed cabin temperature is assigned to the internal solid surfaces of the cabin, and a thermal resistance separates these surfaces from the air mixed in the cabin. In the third model, the ECS operates irreversibly, based on the bootstrap air cycle. The fourth model combines the ECS features of the third model with the cabin-environment interaction features of the second model. It is shown that in all models the temperature of the air stream that the ECS delivers to the cabin can be optimized for operation at minimal power. The effect of other design parameters and flying conditions is documented. The optimized air delivery temperature is relatively insensitive to the complexity of the model; for example, it is insensitive to the size of the heat exchanger used in the bootstrap air cycle. This study adds to the view that robustness is a characteristic of optimized complex flow systems, and that thermodynamic optimization results can be used for orientation in the pursuit of more complex and realistic designs.
49 citations
"Entropy Generation During Natural C..." refers methods in this paper
...The EGM approach has been applied to optimize natural convection systems [24, 25], pin-fin heat sinks [26], fuel cells [27], heat exchangers [28, 29], environmental control of aircraft [30, 31], combustion in porous media [32], etc....
[...]