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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TL;DR: In this paper, a numerical study is performed on the transient natural convection with a temperature-dependent viscosity inside a square partially porous cavity with a local heat-generating and heat-conducting so
Abstract: A numerical study is performed on the transient natural convection with a temperature-dependent viscosity inside a square partially porous cavity with a local heat-generating and heat-conducting so...
25 citations
Cites background from "Entropy Generation During Natural C..."
...[1] have studied numerically natural convection heat transfer and entropy generation in a square cavity under the effect of different thermal boundary conditions....
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TL;DR: In this article, the second-order finite difference approximation is employed to discretize the governing partial differential equations, and a stream-function velocity formulation is used to solve the coupled non-linear partial differential equation numerically.
Abstract: This work is concerned with the numerical study of laminar, steady MHD mixed convection flow, and entropy generation analysis of A l 2 O 3 -water nanofluid flowing in a lid-driven trapezoidal enclosure. The aspect ratio of the cavity is taken very small. The cavity is differentially heated to study the fluid flow, heat, and mass transfer rate. The adiabatic upper wall of the enclosure is allowed to move with a constant velocity along the positive x-direction. The second-order finite difference approximation is employed to discretize the governing partial differential equations, and a stream-function velocity formulation is used to solve the coupled non-linear partial differential equations numerically. The simulated results are plotted graphically through streamlines, isotherms, entropy generation, Nusselt number, and Sherwood number. The computations indicate that the average Nusselt number and average Sherwood number are decreasing functions of Hartmann number, aspect ratio, and nanoparticle volume fraction. Significant changes in streamlines, temperature and concentration contours for high Richardson number are observed.
23 citations
TL;DR: It is found that the waviness of the solid wall augments the average Nusselt number and minimizes the generation of entropy, and the porosity of the porous layer is a more crucial parameter than its permeability.
Abstract: This paper investigates the natural convection inside a partially layered porous cavity with a heated wavy solid wall; the geometry is encountered in compact heat exchangers. Alumina nanoparticles are included in the water to enhance the heat exchange process. The incidental entropy generation is also studied to evaluate the thermodynamic irreversibility. The nanofluid flow is taken as laminar and incompressible while the advection inertia effect in the porous layer is taken into account by adopting the Darcy–Forchheimer model. The problem is explained in the dimensionless form of the governing equations and solved by the finite element method. The Darcy number (Da), porosity of the porous layer (
$$\varepsilon$$
), number of undulations (N), and the nanoparticles volume fraction (
$$\phi$$
) are varied to assess the heat transfer and the incidental entropy generation. It is found that the waviness of the solid wall augments the average Nusselt number and minimizes the generation of entropy. The results show for some circumstances that the Nusselt number is augmented by 43.8% when N is raised from 0 (flat solid wall) to 4. It is also found that the porosity of the porous layer is a more crucial parameter than its permeability, where a 37.4% enhancement in the Nusselt number is achieved when the porosity is raised from 0.2 to 0.8.
20 citations
TL;DR: In this paper, a Quad Flat Non-Lead-type (QFN32) package is welded on a printed circuit board inclined with respect to the horizontal at an angle ranging from 0° (horizontal position) to 90° (vertical position) by steps of 15°.
Abstract: Correlations allowing the calculations of the convective heat transfer coefficient on all elements of an electronic assembly are proposed in this work. The active element is a Quad Flat Non-Lead-type QFN32 package that may be welded in any position of a printed circuit board (PCB) inclined with respect to the horizontal at an angle ranging from 0° (horizontal position) to 90° (vertical position) by steps of 15°. The power generated by the QFN32 varies between 0.1 W and 0.8 W, corresponding to its normal operating range. Six distinct surfaces are considered in this work and the power exchanged between each of them and the environment is quantified. This survey details a previous one in which it is quantified the global convective heat transfer concerning the whole assembly. The correlations proposed in the present work provide a better modeling of this conventional device widely used in electronic applications. They thus optimize its design while controlling its temperature during operation.
20 citations
References
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Book•
01 Jan 1992TL;DR: In this paper, an introduction to convection in porous media assumes the reader is familiar with basic fluid mechanics and heat transfer, going on to cover insulation of buildings, energy storage and recovery, geothermal reservoirs, nuclear waste disposal, chemical reactor engineering and the storage of heat-generating materials like grain and coal.
Abstract: This introduction to convection in porous media assumes the reader is familiar with basic fluid mechanics and heat transfer, going on to cover insulation of buildings, energy storage and recovery, geothermal reservoirs, nuclear waste disposal, chemical reactor engineering and the storage of heat-generating materials like grain and coal. Geophysical applications range from the flow of groundwater around hot intrusions to the stability of snow against avalanches. The book is intended to be used as a reference, a tutorial work or a textbook for graduates.
5,570 citations
"Entropy Generation During Natural C..." refers background in this paper
...An extensive review of literature on porous media may be found in earlier works [ 8 ]....
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Book•
01 Jan 1984
TL;DR: Second-order Differential Equations in One Dimension: Finite Element Models (FEM) as discussed by the authors is a generalization of the second-order differential equation in two dimensions.
Abstract: 1 Introduction 2 Mathematical Preliminaries, Integral Formulations, and Variational Methods 3 Second-order Differential Equations in One Dimension: Finite Element Models 4 Second-order Differential Equations in One Dimension: Applications 5 Beams and Frames 6 Eigenvalue and Time-Dependent Problems 7 Computer Implementation 8 Single-Variable Problems in Two Dimensions 9 Interpolation Functions, Numerical Integration, and Modeling Considerations 10 Flows of Viscous Incompressible Fluids 11 Plane Elasticity 12 Bending of Elastic Plates 13 Computer Implementation of Two-Dimensional Problems 14 Prelude to Advanced Topics
3,043 citations
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
"Entropy Generation During Natural C..." refers background or methods in this paper
...(5), (9), and (10)] with boundary conditions is solved by using the Galerkin finite element method [41]....
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...(12) and (13), the second term containing the penalty parameter (c) are evaluated with two point Gaussian quadrature (reduced integration penalty formulation, [41])....
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TL;DR: Entropy generation minimization (finite time thermodynamics, or thermodynamic optimization) is the method that combines into simple models the most basic concepts of heat transfer, fluid mechanics, and thermodynamics as mentioned in this paper.
Abstract: Entropy generation minimization (finite time thermodynamics, or thermodynamic optimization) is the method that combines into simple models the most basic concepts of heat transfer, fluid mechanics, and thermodynamics. These simple models are used in the optimization of real (irreversible) devices and processes, subject to finite‐size and finite‐time constraints. The review traces the development and adoption of the method in several sectors of mainstream thermal engineering and science: cryogenics, heat transfer, education, storage systems, solar power plants, nuclear and fossil power plants, and refrigerators. Emphasis is placed on the fundamental and technological importance of the optimization method and its results, the pedagogical merits of the method, and the chronological development of the field.
1,516 citations
"Entropy Generation During Natural C..." refers background in this paper
...The main idea behind thermodynamic optimization is to relate degree of thermodynamic non-ideality of the design to the physical characteristics of the system, such as finite dimensions, shapes, materials, finite speeds, and finite-time of intervals of operation and vary one or more physical characteristics to optimize the design characterized by minimum entropy generation subject to finite-size and finite-constraints [22, 23]....
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TL;DR: In this article, the effects of a solid boundary and the inertial forces on flow and heat transfer in porous media were analyzed, and a new concept of the momentum boundary layer central to the numerical routine was presented.
Abstract: The present work analyzes the effects of a solid boundary and the inertial forces on flow and heat transfer in porous media. Specific attention is given to flow through a porous medium in the vicinity of an impermeable boundary. The local volume-averaging technique has been utilized to establish the governing equations, along with an indication of physical limitations and assumptions made in the course of this development. A numerical scheme for the governing equations has been developed to investigate the velocity and temperature fields inside a porous medium near an impermeable boundary, and a new concept of the momentum boundary layer central to the numerical routine is presented. The boundary and inertial effects are characterized in terms of three dimensionless groups, and these effects are shown to be more pronounced in highly permeable media, high Prandtl-number fluids, large pressure gradients, and in the region close to the leading edge of the flow boundary layer.
1,427 citations
"Entropy Generation During Natural C..." refers methods in this paper
...Under these assumptions and following Vafai and Tien [37] with Forchheimer inertia term being neglected, the governing equations for steady two-dimensional natural convection flow in a porous square cavity using conservation of mass, momentum, and energy may be written with the following dimensionless variables or numbers:...
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...The momentum transfer in porous medium is based on generalized non-Darcy model proposed by Vafai and Tien [37]....
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...Under these assumptions and following Vafai and Tien [37] with Forchheimer inertia term being neglected, the governing equations for steady two-dimensional natural convection flow in a porous square cavity using conservation of mass, momentum, and energy may be written with the following dimensionless variables or numbers: X ¼ x L ; Y ¼ y L ; U ¼ uL a ; V ¼ vL a ; h ¼ T Tc Th Tc P ¼ pL 2 qa2 ; Pr ¼ n a ; Da ¼ K L2 ; Ra ¼ gbðTh TcÞL 3Pr n2 ð1Þ as qU qX þ qV qY ¼ 0 ð2Þ U qU qX þ V qU qY ¼ qP qX þ Pr q 2U qX 2 þ q 2U qY 2 !...
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