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Journal ArticleDOI

Analysis of Convective Heat Flow Visualization within Porous Right Angled Triangular Enclosures with a Concave/Convex Hypotenuse

25 Jul 2013-Numerical Heat Transfer Part A-applications (Taylor & Francis Group)-Vol. 64, Iss: 8, pp 621-647
TL;DR: In this article, a generalized non-Darcy model without Forchheimer term is employed for fluid flow in a porous matrix and the governing equations are solved by the Galerkin finite element method.
Abstract: Analysis of natural convection in porous right angled triangular enclosures with a concave/convex hypotenuse has been carried out using the Bejan's heatlines approach. A generalized non-Darcy model without Forchheimer term is employed for fluid flow in a porous matrix and the governing equations are solved by the Galerkin finite element method. The cavity is subjected to a thermal boundary condition of an isothermal cold left wall, isothermal hot curved right wall, and adiabatic bottom wall. Due to intense closed loop heatlines, thermal mixing is higher in convex cases compared to the concave case for all parameters. Average heat transfer rate is found to be largest in the concave hypotenuse case.
Citations
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Book ChapterDOI
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

Journal ArticleDOI
TL;DR: In this paper, a review of the studies on natural convection heat transfer in triangular, trapezoidal, parallelogrammic enclosures and enclosures with curved and wavy walls filled with fluid or porous media is presented.

168 citations

Journal ArticleDOI
TL;DR: A comprehensive review and comparison on heatline concept and field synergy principle have been made based on more than two hundreds of related publications as mentioned in this paper, where the role and function of heat line concept is to visualize the heat transfer path while that of field synergy theory is to reveal the fundamental mechanism of heat transfer enhancement and to guide the development of enhanced structures.

51 citations

Journal ArticleDOI
TL;DR: In this article, a review of existing works on heatlines involving various physical systems is presented in detail and the mathematical implications of heatfunctions based on derivations of governing equations and boundary conditions for heat functions are presented.

23 citations

Journal ArticleDOI
TL;DR: In this paper, the momentum and forced convection heat transfer characteristics of a heated equilateral triangular cylinder immersed in a Bingham plastic fluid have been studied numerically, and the governing equations (continuity, momentum, and thermal energy) are solved for both vertex-upstream and vertex-downstream orientations, over wide ranges of the pertinent parameters, such as Reynolds number: 0.1 ≤ Re ≤ 30, Prandtl number: 1 ≤ Pr ≤ 100, and Bingham number:0 ≤ Bn ≤ 200.
Abstract: The momentum and forced convection heat transfer characteristics of a heated equilateral triangular cylinder immersed in a Bingham plastic fluid have been studied numerically. The governing equations (continuity, momentum, and thermal energy) are solved for both vertex-upstream and vertex-downstream orientations, over wide ranges of the pertinent parameters, such as Reynolds number: 0.1 ≤ Re ≤30; Prandtl number: 1 ≤ Pr ≤100; and Bingham number: 0 ≤ Bn ≤200. Over the range of conditions, the flow is expected to be steady and symmetric. Detailed analysis of the flow and heat transfer phenomena in the vicinity of the cylinder is performed by a thorough inspection of the streamline and isotherm contours. Furthermore, due to the presence of the yield stress, the flow domain consists of yielded (or fluid-like) and unyielded (or solid-like) zones. The effect of Reynolds number and Bingham number on the shape and size of these zones has been thoroughly examined in terms of the detailed velocity and shear rate pro...

16 citations


Additional excerpts

  • ...Indeed, as the new numerical methodologies are being developed, it has become imperative to perform cross-comparisons to discriminate between them [16, 17]....

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References
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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

Book ChapterDOI
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


"Analysis of Convective Heat Flow Vi..." refers methods in this paper

  • ...(5), (8), and (9)) with boundary conditions are solved by using the Galerkin finite element method [47]....

    [...]

Journal ArticleDOI
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.

1,427 citations


"Analysis of Convective Heat Flow Vi..." refers methods in this paper

  • ...Under these assumptions and following the methodology of earlier works [46] with the Forchheimer inertia term being neglected, the governing equations for Figure 1....

    [...]

Journal ArticleDOI
TL;DR: Proposition d'une nouvelle methode de visualisation du transfert de chaleur dans un ecoulement de fluide. Application a la convection naturelle dans une enceinte carree chauffee lateralement
Abstract: Proposition d'une nouvelle methode de visualisation du transfert de chaleur dans un ecoulement de fluide. Application a la convection naturelle dans une enceinte carree chauffee lateralement

387 citations


"Analysis of Convective Heat Flow Vi..." refers background or methods in this paper

  • ...Kimura and Bejan [32] proposed the concept of heatline approach for the first time to visualize heat distribution during natural convection in a square cavity....

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  • ...Heat flow distribution in a fluid saturated porous medium for various fluids of different Pr within complex enclosures has been analyzed using Bejan’s heatline concept....

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  • ...Since the pioneering work of Kimura and Bejan [32], this approach is being used by many authors in various ways for an efficient visualization of convective heat transfer for both fluid and porous media [7, 11, 33–44]....

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  • ...ANALYSIS OF CONVECTIVE HEAT FLOW VISUALIZATION WITHIN POROUS RIGHT ANGLED TRIANGULAR ENCLOSURES WITH A CONCAVE/CONVEX HYPOTENUSE Tanmay Basak, R. Anandalakshmi, and Pratibha Biswal Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai, India Analysis of natural convection in porous right angled triangular enclosures with a concave/ convex hypotenuse has been carried out using the Bejan’s heatlines approach....

    [...]

  • ...Bejan’s heatlines concept is successfully employed to study the direction and intensity of heat flux in the enclosure....

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Journal ArticleDOI
01 Sep 2011-Energy
TL;DR: In this article, the effects of metal foams on heat transfer enhancement in phase change materials (PCMs) are investigated based on the two-equation non-equilibrium heat transfer model, in which the coupled heat conduction and natural convection are considered at phase transition and liquid zones.

356 citations