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 authors have numerically simulated two dimensional mixed convection flow in a sinusoidally heated porous cavity whose two vertical walls (lids) are in motion.
Abstract: In this paper, we have numerically simulated two dimensional (2D) mixed convection flow in a sinusoidally heated porous cavity whose two vertical walls (lids) are in motion. The left vertical wall of the square cavity is maintained at constant cold temperature and the right wall of the cavity is sinusoidally heated, while upper and bottom walls are adiabatic. Three cases are considered depending on the direction of moving walls. We have used streamfunction–vorticity ( ψ – ζ ) formulation of Brinkmann-extended Darcy model to simulate the momentum transfer in the porous medium. The streamfunction–vorticity and the energy equations are all solved as a coupled system of equations for the five field variables consisting of streamfunction, vorticity, two velocities and temperature using compact scheme on nonuniform grids presented in Pandit et al. (2007). The numerical results are analyzed over a range of the key parameters e.g. Richardson number Ri, Darcy number Da, Grashof number Gr, amplitude of the temperature variation and phase deviations. A parametric study is conducted for all cases.
41 citations
TL;DR: In this paper, the authors investigated the effect of four different thermal boundary conditions on natural convection in a fluid-saturated square porous cavity to make a judicious choice of optimal boundary condition on the basis of entropy generation, heat transfer and degree of temperature uniformity.
Abstract: The present work investigates the effect of four different thermal boundary conditions on natural convection in a fluid-saturated square porous cavity to make a judicious choice of optimal boundary condition on the basis of entropy generation, heat transfer and degree of temperature uniformity. Four different heating conditions- uniform, sinusoidal and two different linear temperature distributions are applied on the left vertical wall of the cavity respectively, while maintaining the right vertical wall uniformly cooled and the horizontal walls thermally insulated. The two-phase thermal lattice Boltzmann (TLBM) model for nanofluid is extended to simulate nanofluid flow through a porous medium by incorporating the Brinkman–Forchheimer-extended Darcy model. The close agreement between present LBM solutions with the existing published results lends validity to the present findings. The current results indicate that the uniform and bottom to top linear heating are found to be efficient heating strategies depending on Rayleigh number (103 ≤ Ra ≤ 105) and Darcy number (10−1 ≤ Da ≤ 10−6). It is observed that the nanofluid improves the energy efficiency by reducing the total entropy generation and enhancing the heat transfer rate although its augmentation depends on the optimal volume fraction of nanoparticles.
40 citations
TL;DR: In this paper, the effects of the inclination angle on convection heat transfer and entropy generation characteristics in a two-dimensional square enclosure saturated with water were analyzed numerically and quantitatively.
Abstract: In this paper, we analyze numerically the effects of the inclination angle on natural convection heat transfer and entropy generation characteristics in a two-dimensional square enclosure saturated...
37 citations
TL;DR: In this paper, the analysis of thermodynamic irreversibility generation and the natural convection in inclined partially porous layered cavity filled with a Cu-water nanofromide was performed.
Abstract: The present numerical study investigates the analysis of thermodynamic irreversibility generation and the natural convection in inclined partially porous layered cavity filled with a Cu–water nanof...
31 citations
TL;DR: In this article, the authors analyzed the natural convection heat transfer and irreversibility characteristics in a quadrantal porous cavity subjected to uniform temperature heating from the bottom wall, where the Brinkmann-extended Darcy model is used to simulate the momentum transfer in the porous medium.
Abstract: The purpose of this paper is to analyze the natural convection heat transfer and irreversibility characteristics in a quadrantal porous cavity subjected to uniform temperature heating from the bottom wall.,Brinkmann-extended Darcy model is used to simulate the momentum transfer in the porous medium. The Boussinesq approximation is invoked to account for the variation in density arising out of the temperature differential for the porous quadrantal enclosure subjected to uniform heating on the bottom wall. The governing transport equations are solved using the finite element method. A parametric study is carried out for the Rayleigh number (Ra) in the range of 103 to 106 and Darcy number (Da) in the range of 10−5-10−2.,A complex interaction between the buoyant and viscous forces that govern the transport of heat and entropy generation and the permeability of the porous medium plays a significant role on the same. The effect of Da is almost insignificant in dictating the heat transfer for low values of Ra (103, 104), while there is a significant alteration in Nusselt number for Ra ≥105 and moreover, the change is more intense for larger values of Da. For lower values of Ra (≤104), the main contributor of irreversibility is the thermal irreversibility irrespective of all values of Da. However, the fluid friction irreversibility is the dominant player at higher values of Ra (=106) and Da (=10−2).,From an industrial point of view, the present study will have applications in micro-electronic devices, building systems with complex geometries, solar collectors, electric machinery and lubrication systems.,This research examines numerically the buoyancy driven heat transfer irreversibility in a quadrantal porous enclosure that is subjected to uniform temperature heating from the bottom wall, that was not investigated in the literature before.
27 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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