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 paper, the authors performed dry and wet forward combustion experiments for Turkish heavy oil reservoirs (Raman, Adiyaman and Camurlu and Bati Kozluca) under different experimental conditions.
Abstract: The purpose of this research was to perform dry and wet forward combustion experiments for Turkish heavy oil reservoirs (Raman, Adiyaman and Camurlu and Bati Kozluca) under different experimental conditions. In the experiments, a vertical tube was packed with crushed limestone and saturated with crude oil and water. It was observed that peak temperatures were higher when stabilized combustion was achieved and decreased as the combustion front approached the outlet end of the tube. In wet combustion experiments, the rate of combustion reaction and therefore rate of heat generation were reduced with the resultant drop in peak temperatures. In dry and wet combustion experiments, excess carbon-dioxide productions were observed due to the decomposition of carbonate minerals. Atomic H/C ratio of the fuel consumed decreased as the average peak temperature increased. Fuel consumption rate was higher for dry combustion experiments as the °API gravity of the crude oils increased. A decrease is also observed in fuel consumption rate after the water–air ratio value is reached to optimum value. For high water–air ratio in wet combustion experiments, a general decrease was observed as the °API gravity of the crude oils increased.
47 citations
"Entropy Generation During Natural C..." refers background in this paper
...flooding in porous beds [16], combustion of heavy oils in porous reservoirs [17, 18], etc....
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TL;DR: In this paper, a numerical code is developed in order to evaluate the effects of different parameters of combustion in porous media, including Navier-Stokes, the solid and gas energy and the chemical species transport equations using a multi-step reduced kinetic mechanism.
Abstract: Combustion in Porous Media provides interesting advantages compared with the free flame combustion due to the higher burning rates, increased power dynamic range, the extension of lean flammability limits, and the low emissions of pollutants. A numerical code is developed in order to evaluate the effects of different parameters of combustion in porous media. The governing equations including Navier–Stokes, the solid and gas energy and the chemical species transport equations are solved using a multi-step reduced kinetic mechanism. Flame stabilization and the burner optimization are studied by EGM (Entropy Generation Minimization) method considering the effects of chemical affinities and reaction. It is found that the flames occurring at the upstream half of the porous layer are more stable and more efficient, producing less emissions than those occur at the downstream half of porous layer. Also at a specified equivalence ratio both the heat recirculation efficiency and the Merit number have similar trend by changing the flame location. For a FFL (Fixed Flame Location), there is an optimum value of equivalence ratio at which the burner efficiency is a maximum.
43 citations
TL;DR: In this article, a multi-parameter constrained optimization procedure integrating the design of experiments (DOE), response surface models (RSM), genetic algorithm (GA), mixed integer optimization (MOST), and computational fluid dynamics (CFD) is proposed to design the plate finned heat sinks by minimizing their rates of entropy generation.
Abstract: The multi-parameter constrained optimization procedure integrating the design of experiments (DOE), response surface models (RSM), genetic algorithm (GA), mixed integer optimization (MOST), and computational fluid dynamics (CFD) is proposed to design the plate finned heat sinks by minimizing their rates of entropy generation The results of three cases demonstrate that the combination optimization algorithm is feasible In these cases, the overall rate of entropy generation decreases as the result of introducing the additional constrained variables into the optimization procedure Consequently, the general thermal and fluid performance of the heat sink is dramatically improved Based on the results derived by the optimization, the overall thermal and fluid performance of the plate finned heat sinks with both side and top bypass flow is investigated In addition, two correlations describing Nusselt number and friction factor, as the functions of geometrical and operational parameters, are established by means of the multivariate non-linear regression analysis The specific expressions to compute the thermal resistance and the rate of entropy generation are deduced
41 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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TL;DR: In this paper, a methodology for the analysis of conjugate problems in the convective drying of porous media is presented, where the interface between porous medium and external convective flow is treated as an internal boundary within a two-phase system rather than a geometric limit.
Abstract: A methodology for the analysis of conjugate problems in the convective drying of porous media is presented. In this study, the interface between porous medium and external convective flow is treated as an internal boundary within a two-phase system rather than a geometric limit. The problems of solid drying and convection boundary layer are connected by expressing the continuity of the state variables and their respective fluxes through the interface. The performance of the proposed methodology is evaluated by applying it to wood-drying problems. The analysis of the drying of porous media as a conjugate problem allows the assessment of the effect of the heat and mass transfer within the solid on the transfer in the adjacent fluid, providing good insight on the complexity of the transfer mechanisms.
40 citations
30 Mar 2005
37 citations
"Entropy Generation During Natural C..." refers background in this paper
...A detailed discussion on different viscous dissipation models, their limits of applicability, and other relevant issues on various aspects of modeling viscous dissipation in porous media may be found in earlier works [45, 46]....
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