Fin-Shape Thermal Optimization Using Bejan's Constuctal Theory

Book description

The book contains research results obtained by applying Bejan's Constructal Theory to the study and therefore the optimization of fins, focusing on T-shaped and Y-shaped ones. Heat transfer from finned surfaces is an example of combined heat transfer natural or forced convection on the external parts of the fin, and conducting along the fin. Fin's heat exchange is rather complex, because of variation of both temperature along the fin and convective heat transfer coefficient. Furthermore possible presence of more fins invested by the same fluid flow has to be considered.

Classical fin theory tried to reduce the coupled heat transfer problem to a one-dimensional problem by defining an average temperature of the fin and writing equations using this parameter. However, it was shown that this approach cannot be used because of the effects of two-dimensional heat transfer, especially in the presence of short fins. CFD codes offer the possibility to consider bi-dimensional (and more generally, three-dimensional) effects and then a more real approach to the physic phenomena of finned surface's heat exchange.

A commercial CFD code was used to analyse the case of heat exchange in presence of T-shaped fins, following an approach suggested by Bejan's Constructal Theory. The comparative results showed a significant agreement with previous research taken as a reference, and this result allows for the application of this approach to a wider range of systems. T-shaped optimized fin geometry is the starting point for further research.

Starting from the optimal results (T-shape optimized fins), we show the trend of the assessment parameter (the dimensionless conductance) in function of the angle α between the two horizontal arms of the fin. A value for α, 90° < α < 180° capable of a higher value of the dimensionless conductance, has not been found. The thermal efficiency showed a significant increase of this parameter, especially for values of α smaller than 100°. Thus, a new definition of optimisation is achieved by introducing the fundamental "space factor." The present work unifies the "classic" definitions of optimisation and efficiency in a new general performance criterion, opening a new perspective on multi-fin systems.

The last chapter deals with a brief overview on Bejan's Constructal Theory. It explains either tree-shape natural flows or other geometric form in nature and engineering, applying the principle of performance maximization. The Constructal principle also recognizes that a new good form comes to another previous good form which serve the same objective and have the same constraints. Changes in configuration are dynamic, thus a time arrow is then associated to the evolution in system's configuration.

Table of Contents: General Introduction / General Overview on Heat Transfer / Conservation Equations / Dimensionless group / Units and conversion factors / Overview of heat transfer on extended surfaces / State of the art in the T-Shaped Fins / Thermal exchange basis / T-Shaped fins / Y-Shaped fins / Modular systems of Y-Shaped fins / Heat removal vs Pressure drops / Conclusions

Table of contents

  1. Preface
  2. Introduction
    1. General Introduction
    2. General Overview on Heat Transfer
      1. Conduction
      2. Radiation
      3. Convection (1/2)
      4. Convection (2/2)
        1. Heat transfer coefficient
        2. Boundary Layer Concept
        3. Laminar and turbulent flows
        4. Non-newtonian Fluids
      5. Combined heat transfer mechanisms
    3. Conservation Equations
      1. The equation of continuity
      2. The equation of motion
      3. The energy equation
      4. The conservation equation for species
      5. Use of conservation equations to solve physical problems
    4. Dimensionless group (1/2)
    5. Dimensionless group (2/2)
    6. Units and conversion factors (1/2)
    7. Units and conversion factors (2/2)
    8. Overview of heat transfer on extended surfaces
      1. Fin's energetic balance
      2. Extended surface assemblies
      3. Current design methodology
      4. Fin efficiency
      5. Mathematical representation of heat flow through an isolated fin
      6. Discussion of the validity of the design methodology and of the classical assumptions
      7. Conclusions
    9. State of the art in the T-Shaped Fins
      1. Other studies on the T-shapes
      2. Conclusions
  3. Methods of analysis
    1. Thermal exchange basis
      1. Analytical models
  4. Models
    1. T-Shaped fins
      1. Introduction
      2. Model definition
      3. Method and tests
      4. Results and comments
      5. Conclusions
    2. Y-Shaped fins
      1. Introduction
      2. Model definition
      3. Results and comments
      4. Conclusions
    3. Modular systems of Y-Shaped fins
      1. Introduction
      2. Model definition
      3. Methods and tests
      4. Results and comments
      5. Conclusions
    4. Heat removal vs Pressure drops
      1. Introduction
      2. Systems and conditions investigated (1/2)
      3. Systems and conditions investigated (2/2)
      4. Method and tests performed
      5. Results and preliminary discussion
      6. The overall optimisation (1/3)
      7. The overall optimisation (2/3)
      8. The overall optimisation (3/3)
      9. Conclusions
    5. Conclusions
  5. Constructal Theory
    1. Constructal Law: A New Sight on Engineering and Nature
    2. The Concepts of Objective, Constraints and ``Better''
    3. The Volume-To-Point Flow Problem
    4. Elemental Volume
      1. Heat Trees
      2. Fluid Trees
    5. First Construct
      1. Heat Trees
      2. Fluid Trees
    6. Second and Higher Order Constructs
      1. Heat Trees
      2. Fluid Trees
    7. Three Dimensional Trees in Fluid flows
    8. Rivers and Ducts
      1. Rivers
      2. Fluid Flow for River Basin
      3. Ducts
    9. Turbulence
      1. The First and Smallest Eddy
      2. Growth of Mixing Regions
    10. Dendritic Crystals
    11. Tree-Shaped Living Systems
    12. Fluid Layers Heated from Below: The Case of Benard Convection
    13. Optimized Flow Paths in Fluid Layers Heated from Below
    14. Parallel-Plate Channels (1/2)
    15. Parallel-Plate Channels (2/2)
    16. Flow Spacing in Forced and Natural Convection
      1. Forced Convection Flow
      2. Natural Convection Flow
      3. Improvement of Design
    17. Multiobjective Architectures
      1. Plate Fins with Variable Thickness and Height
      2. Pin-Fins
    18. Duct with Wrinkled Entrances
    19. Thermodynamics of Flow Structures
      1. Equilibrium and Non-Equilibrium Flow Structures
      2. Constructal Law and Thermodynamics
  6. Bibliography for the Appendix
  7. Bibliography
  8. Authors' Biographies

Product information

  • Title: Fin-Shape Thermal Optimization Using Bejan's Constuctal Theory
  • Author(s): Giulio Lorenzini, Simone Moretti, Alessandra Conti
  • Release date: January 2011
  • Publisher(s): Morgan & Claypool Publishers
  • ISBN: 9781608456086