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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30 Oct 2018
TL;DR: In this paper, the inherent irreversibility in a buoyancy induced magnetohydrodynamic (MHD) couple stressfluid through non-Darcian porous medium was investigated.
Abstract: This paper investigates the inherent irreversibility in a buoyancy induced magnetohydrodynamic (MHD) couple stress
fluid through non-Darcian porous medium. It is assumed that the fluid exchanges heat with the ambient following Newtonian
law. The governing Navier-Stoke and energy equations are formulated and non-dimensionalied, the approximate solutions for
the velocity and temperature profiles are obtained via Adomian decomposition method. The results are used to calculate the
entropy generation rate, and Bejan number. The effects of Buoyancy force, suction/injection, Hartman number and other flow
parameters on velocity, temperature, entropy generation rate, and Bejan number are analyzed and discussed graphically. The
results show that increase in Buoyancy force and suction/injection increases fluid velocity and temperature.Entropy generation
rate becomes higher as the values of Buoyancy force, suction/injection parameter, and Hartman number increases
2 citations
Cites background from "Entropy Generation During Natural C..."
...Other studies on the analysis of entropy generation in various fluid flows can be found in [1, 5, 6, 8, 13, 20, 28]....
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TL;DR: In this paper , a two-phase lattice Boltzmann scheme was developed for the two phase CuO-H2O nanomagnetic fluid (ferrofluid) under a non-uniform variable magnetic field.
Abstract: In this study, a new lattice Boltzmann scheme is developed for the two-phase CuO–H2O nanomagnetic fluid (ferrofluid) under a non-uniform variable magnetic field. It introduces the second-order external force term including both MHD (magnetohydrodynamic) and FHD (ferrohydrodynamic) into the lattice Boltzmann equation. The square cavity and a heat source inside the circular cavity with natural convections of nanofluid are investigated, respectively. The effects of Rayleigh number ( Ra), the volume fraction of nanoparticles ( φ), Hartmann number ( Ha) generated by MHD, and magnetic number ( MnF) generated by FHD on the nanofluid flow and heat transfer properties, as well as the total entropy generation ( Stot) have been examined. The two-phase lattice Boltzmann model has demonstrated that it is more accurate in predicting the heat transfer of nanofluid than the single-phase model. Consequently, the results calculated by the single-phase and the two-phase methods show the opposite trends. It indicates that nanoparticles could enhance heat transfer with maximum values of 1.78% or deteriorate heat transfer with maximum values of 14.84%. The results of the circular cavity show that Ha could diminish the flow intensity, whereas MnF could enhance it. The average Nusselt number ( Nuave) on the heat source decreases with the augments of Ha and MnF but increases with Ra. An optimal volume fraction φ = 1% for heat transfer is obtained except for Ra = 104. Stot achieves the maximum value at Ha = 40 when Ra = 105. It increases with a rise of Ra but reduces with an increment of φ.
2 citations
TL;DR: In this paper, the authors showed that radiative heat transfer is negligible with respect to natural convective exchanges in the operating power range (0.01-0.1W).
Abstract: Embarked Quad Flat Non-lead (QFN) electronic devices are equipped with a significant number of sensors used for flight parameters measurement purposes. Their accuracy directly depends on the package thermal state. Flight safety therefore depends on the reliability of these QFNs, whose junction temperature must remain as low as possible while operating. The QFN64 is favored for these applications. In the operating power range considered here (0.01-0.1W), the study shows that radiative heat transfer is negligible with respect to natural convective exchanges. It is then essential to quantify the convective heat transfer coefficient on its different areas so that the arrangement is properly dimensioned. This is the objective of this work. The device is welded on a PCB which may be inclined with respect to the horizontal plane by an angle ranging from $0^{\circ}$
to $90^{\circ}$
. Numerical approach results are confirmed by thermal and electrical measurements carried out on prototypes for all power-inclination angle combinations. The correlations here proposed help determine the natural convective heat transfer coefficient in any area of the assembly. This work allowed to thermally characterize and certify a new QFN64 package equipped with sensors designed for aeronautics, currently under industrialization process.
1 citations
TL;DR: Ren et al. as discussed by the authors presented a simulation of magnetohydrodynamics and demonstrated the effect of magnetic field on the natural convection of CuO-H2O nanofluid inside a circular enclosure.
Abstract: No AccessTechnical NotesNumerical Simulation of Magnetohydrodynamics Natural Convection of CuO-H2O Nanofluid Inside Circular EnclosureJiyun Ren, Ruibo Jin, Yang Liu, Dingbiao Wang and Zunlong JinJiyun RenZhengzhou University, 450001 Zhengzhou, People’s Republic of China*Graduate Student, Department of Thermal Engineering, School of Mechanical and Power Engineering; .Search for more papers by this author, Ruibo JinUniversity of Electronic Science and Technology of China, 611731 Chengdu, People’s Republic of China†Undergraduate Student, Department of Electronic Information Engineering, Glasgow College; .Search for more papers by this author, Yang LiuZhengzhou University, 450001 Zhengzhou, People’s Republic of China‡Graduate Student, Department of Chemical Process Machinery, School of Mechanical and Power Engineering; .Search for more papers by this author, Dingbiao WangZhengzhou University, 450001 Zhengzhou, People’s Republic of China§Professor, Institute of Process Energy Saving and Advanced Equipment Research, School of Mechanical and Power Engineering; .Search for more papers by this author and Zunlong JinZhengzhou University, 450001 Zhengzhou, People’s Republic of China¶Professor, Institute of Thermal Engineering, School of Mechanical and Power Engineering; (Corresponding Author).Search for more papers by this authorPublished Online:16 Feb 2022https://doi.org/10.2514/1.T6468SectionsRead Now ToolsAdd to favoritesDownload citationTrack citations ShareShare onFacebookTwitterLinked InRedditEmail About References [1] Ho C. 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See also AIAA Rights and Permissions www.aiaa.org/randp. TopicsAerodynamicsAeronautical EngineeringAeronauticsBuoyancyComputational Fluid DynamicsEquations of Fluid DynamicsFluid DynamicsFluid Flow PropertiesFluid MechanicsLattice Boltzmann MethodsMagnetohydrodynamicsPlasma PhysicsSpace Science and TechnologyVortex Dynamics KeywordsNanofluidsNatural ConvectionHartmann NumbersImmersed Boundary MethodEnergy Transfer MechanismsEntropy GenerationLBMIsothermsSpecific Heat CapacityNanoparticlesAcknowledgmentsWe gratefully acknowledge the financial support for this project from the National Natural Science Foundation of China (grant no. 21676257).PDF Received31 August 2021Accepted7 January 2022Published online16 February 2022
1 citations
TL;DR: In this paper , the Darcy-Brinkman-forchheimer model was used to study the thermal convection in square-shaped, porous enclosures demonstrating the impact of cavity orientation.
Abstract: The scope of the present investigation is to explore the thermal convection in square-shaped, porous enclosures demonstrating the impact of cavity orientation. The differential equations controlling the fluid flow and energy transfer are solved using the finite volume framework. The Darcy-Brinkman-Forchheimer model is selected for porous medium. The investigation is executed for modified Rayleigh number (Ra m ) from 10 2 to 10 4 . The orientation of the enclosure is varied from the horizontal position ( γ = 0°) to the vertical position ( γ = 90°) at an interval of 15°. The flow pattern and the heat transfer are examined using the traditional method of streamlines and isotherms. The Nusselt number (Nu m ) is employed to measure the transport of energy by thermal convection. The results indicate that the Nu m varies with the change in the Ra m and cavity orientation. When the cavity is rotated from the horizontal position to the vertical position, the thermal convection increases up to a critical inclination angle ( γ c ). However, the heat transfer by convection declines beyond the critical inclination angles. It is noted that the critical inclination angle varies with the change in the Ra m . The enhancement in energy transport by convection varies with Ra m . The augmentation in thermal convection is measured by the heat transfer enhancement parameter ( ξ ). The augmentation in energy transport is maximum for lower Ra m = 10 2 ( ξ = 34.9 %) and minimum for higher Ra m = 10 4 ( ξ = 24.3 %). This investigation helps in designing a thermal system that results in the optimum utilization of energy resources.
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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 ]....
[...]
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]....
[...]
...(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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