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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01 Jan 1992
11 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 article, the authors study heat transfer kinetics at the fiber scale in order to describe injection of liquid metal through a fibrous perform initially situated in a preheated mold, which is one of the various methods used to produce metal matrix composite materials (MMCs).
Abstract: Purpose – To study heat transfer kinetics at the fiber scale in order to describe injection of liquid metal through a fibrous perform initially situated in a preheated mould, which is one of the various methods used in order to produce metal matrix composite materials (MMCs).Design/methodology/approach – The first part presents a preliminary study in a static case to describe heat transfer kinetics between a fiber and the matrix in the case of a sudden contact of both components initially set up at different temperatures. This model enables to study the influence of the various parameters of the problem on heat transfer kinetics with phase change. In the second part, we present a modeling which takes into account the metal convection within the pores of the preform.Findings – The numerical results of these two models justify the instantaneous thermal equilibrium assumption classically admitted to describe MMCs manufacturing methods. The results of this dynamic microscopic model are compared with the resul...
9 citations
TL;DR: In this paper, a numerical algorithm based on the body-fitted finite element method (FEM) is proposed to calculate the flow behavior of the isothermal infiltration process in a fibrous preform.
Abstract: The injection of molten metal through a fibrous preform is one of the techniques used to manufacture metal matrix composites (MMCs) The flow of liquid metal through a fibrous preform constitutes a moving boundary problem of fluid mechanics in a porous medium In the present model, the isothermal infiltration process is considered The numerical algorithm, based on the body-fitted finite element method (FEM), can precisely deal with the transient and irregular physical domains and calculate the flow behavior Numerical results show that the infiltration pattern is strongly influenced by the nature of the preform The injection flow rate under constant applied pressure decreases with the infiltration time The effect of the preform orientation on infiltration pattern is also discussed Similarity analysis shows that the infiltration time is inversely proportional to the ratio of applied pressure to liquid viscosity for the same type of preform
9 citations