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, the effects of the Copper ratio constituting the upper face of a tilted Printed Circuit Board (PCB) on the natural convective heat transfer concerning an electronic equipment containing a quad flat non-lead type (QFN32) package are examined.
Abstract: The main objective of this work is to examine the effects of the Copper ratio constituting the upper face of a tilted Printed Circuit Board (PCB) on the natural convective heat transfer concerning an electronic equipment containing a quad flat non-lead type (QFN32) package Calculations are done by means of the finite volume method for several positions of electronic device on the PCB which is inclined with respect to the horizontal at an angle ranging from 0° (horizontal position) to 90° (vertical position) with a step of 15° The power generated by the QFN32 varies between 01 and 08 W, and 10 Copper ratio varying between 026% and 3945% are considered These ranges correspond to the normal operating of the active electronic device for the intended applications The study shows that the thermal behavior of the distinct areas of the active package is affected by the Copper ratio Correlations are proposed, allowing determination of the average convective heat transfer coefficient on the different areas of the QFN32 device, according to the considered values of the Copper ratio, the PCB’s inclination angle and the generated power They optimize its design while controlling its temperature during operation The results of this survey provide a better modeling of this conventional arrangement widely used in electronic applications
9 citations
TL;DR: In this paper, a study on laminar free convection within a square cavity filled with a fluid saturated porous medium is presented, where macroscopic flow equations are obtained by volume-averaging local instantaneous continuity and momentum equations.
Abstract: This work presents a study on laminar free convection within a square cavity filled with a fluid saturated porous medium. Macroscopic flow equations are obtained by volume-averaging local instantaneous continuity and momentum equations. The so-called “two-energy equation model” is used, in which distinct macroscopic equations are applied to the working fluid and the solid material. Transport equations are discretized using the control-volume method and the system of algebraic equations is relaxed via the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm. The effect of Ram on Nuw correctly predicted the enhancement of passive heat transfer across the cavity for increasing Ram. Increasing ks/kf enhances the conduction transport through the solid material and, consequently, dampens the overall Nusselt number, defined here as the ratio between conduction and convection mechanisms over conduction transport only. Further, results indicate that by increasing the void space within the porous m...
8 citations
Cites background from "Entropy Generation During Natural C..."
...In addition, several important works on porous cavities have been published lately, involving sinusoidal heating at the walls [14], conjugate heat transfer [15], entropy generation [16], application to food processing [17], lid-driven cavity flows [18], works using the heatline approach [19, 20], double-diffusion effects [21], and multigrid convergence accelerator methods [22], to mention a few....
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TL;DR: In this paper, the authors analyzed the effect of the motion of horizontal and vertical walls on the entropy generation and heat transfer in a porous square cavity during mixed convection, and the results were presented using streamfunction (ψ), local entropy generation due to fluid friction, isotherms (θ), and local entropy generated due to heat-transfer contours.
Abstract: The aim of the present investigation is to analyze the effect of the motion of horizontal (cases 1a–1d) and vertical walls (case 2a–2c) on the entropy generation and heat transfer in a porous square cavity during mixed convection. The cavity is subject to the thermal boundary conditions such as the hot bottom wall, cold side walls, and thermally insulated top wall. Analysis has been done for various fluids with Prandtl number, Prm = 0.026–7.2, Grashof number, Gr = 105, Reynolds number, Re = 10–100, and Darcy number, Dam = 10−4–10−2. Numerical results are presented using streamfunction (ψ), local entropy generation due to fluid friction (Sψ), isotherms (θ), and local entropy generation due to heat-transfer (Sθ) contours. In addition, the total entropy generation (Stotal), average Bejan number (Beav), and overall heat-transfer rate at the hot bottom wall are analyzed and discussed.
6 citations
Cites background from "Entropy Generation During Natural C..."
...[21] studied the entropy generation in porous square cavities for various thermal boundary conditions....
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TL;DR: The correlations proposed in this work allow calculating the convective heat transfer coefficient in any area of the considered assembly according to the generated power and the tilt inclination, and allow increasing reliability and better thermal control of this conventional device widely used in electronics for many engineering applications.
Abstract: Heat exchanges occurring between the electronic assemblies and their environment are an essential data in order to control their temperature, enhance their performance and improve their reliability. In this survey, the average natural convective heat transfer coefficient is determined for an assembly constituted by a Quad Flat Non-lead QFN64 generating a high power ranging from 0.1 to 1.0 W during operation. It is welded on a PCB which may be inclined with respect to the horizontal plane by an angle varying between 0° and 90°. The calculations done by means of the finite volume method show how the free convective heat transfer on every part of this electronic assembly is influenced by these physical parameters. The correlations proposed in this work allow calculating the convective heat transfer coefficient in any area of the considered assembly according to the generated power and the tilt inclination. These original and unpublished tools allow increasing reliability and better thermal control of this conventional device widely used in electronics for many engineering applications.
6 citations
25 Jul 2021
TL;DR: In this article, the authors studied the entropy production of conjugate heat transfer in a porous cavity with respect to heat source and solid wall locations, and the results showed that the maximum values of the entropy generated from fluid friction develop close to the cavity wall-fluid interfacial, while the maximum value of the heat transfer developed nearby the heat source region.
Abstract: In this research, the entropy production of the conjugate heat transfer in a porous cavity with respect to heat source and solid wall’s locations has been studied numerically. Three different cases of the cavity with finite walls thickness and heat source locations are considered in the present study. For both cases one and two, the cavity considered has a vertical finite walls thickness, while the cavity with the horizontal finite walls thickness is considered for case three. For cases one and two, the left sidewall of the cavity is exposed to heat source, whereas the rest of this wall as well as the right sidewall are adiabatic. The upper and lower cavity walls are adiabatic. For case three, the lower wall is exposed to a localized heat source, while the rest of it is assumed adiabatic. The upper wall is cold, whereas the left and right sidewalls are adiabatic. The flow and thermal fields properties along with the entropy production are computed for the modified Rayleigh number (150 ? Ram? 1000), thermal conductivity ratio (1 ? Kr? 10), heat source length (0.2 ? B ? 0.6), aspect ratio (0.5 ? AR ? 2) and walls thickness (0.1 ? D1? 0.2 and 0.1 ? D2? 0.2) respectively. The results show that, the maximum values of the entropy generated from fluid friction develop close to the cavity wall-fluid interfacial, while the maximum values of the entropy generated from heat transfer develop nearby the heat source region. The average Bejan number (Beav) is higher than (0.5) for cases one and two. While for case three, it was found to be less than (0.5). Also, the results show that as the modified Rayleigh number, thermal conductivity ratio, heat source length and aspect ratio increased, the fluid flow intensity in the cavity increased. While, it decreased when the walls thickness increased. From theresults, it is concluded that case three gives a higher heat transfer enhancement. The obtained results are compared against another published results and a good agreement is found between them.
5 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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