Case Studies in Computational Heat Transfer / Panagiotis (Takis) Sismanis.

Format:

Book

Author/Creator:

Sismanis, Panagiotis G., 1959- author.

Series:

Mechanical engineering theory and applications.

Mechanical Engineering Theory and Applications Series

Language:

English

Subjects (All):

Heat--Transmission.

Heat.

Physical Description:

1 online resource (190 pages)

Edition:

First edition.

Place of Publication:

New York : Nova Science Publishers, Inc., [2024]

Summary:

Mathematicians, scientists, and engineers often look for simple and robust computer programs in order to solve the Fourier differential equation for heat transfer in a numerical way. Specifically, the 2D differential equation may take various initial and boundary conditions applicable in many practical applications. Simplifications to 1D differential equations may also be applied to the numerical solution of various practical problems in heat and mass transfer. The implicit scheme for the finite difference solution of the heat transfer equation, as formulated by Patankar, is mostly deployed throughout the book. It is worth noting that the method is proven to be stable and fast for most time scales. In fact, fast convergence is attained for steady state problems that have searched for solutions within a time span of more than the universe age. Furthermore, mathematical problems that finalized phenomena within a period of a few milliseconds have proven the remarkable stability of the numerical solution. A practitioner has thirty selected cases in order to grasp the salient and advanced features of the implicit scheme. A program core developed in C++ allows the introduction of the relevant initial and boundary conditions and solves various problems with only minor changes. About two-thirds of the selected cases were based on mathematical problems for which analytical solutions exist. In this way, analytical and numerical solution programs are given in order for the practitioner to compile, run the code, and plot the desired results. Orthogonal and cylindrical coordinates are deployed according to border geometry; Python programs were developed for the analytical solutions in cylindrical symmetry. Induction heating of billets and slabs, rebar production by quench and tempering, and steel billet solidification are some of the most practical examined cases.

Contents:

Intro

Contents

List of Figures

Preface

Acknowledgments

Chapter 1

Introduction

1.1. The Implicit Finite-Difference Scheme

1.2. Derivation of the Implicit-Scheme for the 1D Differential Equation

1.3. Deployed Solution Procedure

1.4. Computer Code for the Solution of the Case Studies

Chapter 2

Case Study 1

2.1. Steady-State in a Rectangular Plate (Isothermal Borders)

Chapter 3

Case Study 2

3.1. Steady-State in a Rectangular Plate (Mixed BC-I)

Chapter 4

Case Study 3

4.1. Steady-State in a Rectangular Plate (Mixed BC-II)

Chapter 5

Case Study 4

5.1. Unsteady State in a Rectangular Plate (Isothermal BC)

Chapter 6

Case Study 5

6.1. Unsteady State in a Rectangular Plate (Mixed BC-I)

Chapter 7

Case Study 6

7.1. Unsteady State in a Rectangular Plate (Mixed BC-II)

Chapter 8

Case Study 7

8.1. Unsteady State in a Rectangular Plate (Heat Generation)

Chapter 9

Case Study 8

9.1. Unsteady State in a Rectangular Plate (Mixed BC-III)

Chapter 10

2D Geometry in Polar Coordinates

Chapter 11

Case Study 9

11.1. Unsteady State in a Long Cylinder (Zero Surface Temperature)

Chapter 12

Case Study 10

12.1. Unsteady State in a Long Cylinder (Parabolic Temperature Distribution)

Chapter 13

Case Study 11

13.1. Unsteady State in a Long Cylinder (Surface Temperature Proportional to Time)

Chapter 14

Case Study 12

14.1. Unsteady State in a Long Cylinder (Constant Heat Flux at the Surface)

Chapter 15

Case Study 13

15.1. Unsteady State in a Long Cylinder (Convection at the Surface)

Chapter 16

Case Study 14 - Induction Heating of Steel Billets

16.1. Cylindrical Billets with Sections Equivalent to Square Ones

Chapter 17

Case Study 15 - Slab Reheating

17.1. Thin Slab Reheating

Chapter 18.

Case Study 16 - Heavy Slab Reheating

18.1. Thick Slab Reheating

Chapter 19

Case Study 17

19.1. Quenched and Tempered (Q&amp

T) Reinforced Concrete Steels

Chapter 20

Case Study 18

20.1. A Cylindrical Billet in a Soaking Pit

Chapter 21

Case Study 19

21.1. A Spherical Specimen in a Soaking Pit

Chapter 22

Case Study 20

22.1. A Refractory Wall under Preheating

Chapter 23

Case Study 21

23.1. Heat Conduction in a Slab

Chapter 24

Case Study 22

24.1. Temperature of a Bar (1D Case-I: Mixed IC and BC)

Chapter 25

Case Study 23

25.1. Temperature of a Bar (1D Case-II: Mixed IC and BC)

Chapter 26

Case Study 24

26.1. Temperature of a Bar (1D Case-III: Mixed IC and BC)

Chapter 27

Case Study 25

27.1. Temperature of a Bar (1D Case-IV: Mixed IC and BC)

Chapter 28

Case Study 26

28.1. Temperature of a Bar (1D Case-V: Mixed IC and BC)

Chapter 29

Case Study 27

29.1. Temperature of a Bar (1D Case-VI: Mixed IC and BC)

Chapter 30

Case Study 28

30.1. Temperature of a Bar (1D Case-VII: Mixed IC and BC)

Chapter 31

Case Study 29

31.1. Temperature of a Bar (1D Case-VIII: Mixed IC and BC)

Chapter 32

Case Study 30

32.1. Solidification of a Billet in a Continuous Casting Machine

Chapter 33

Some Published Works on the Topic

33.1. Special Reinforced NSC-Columns under Fire

33.2. Continuous Casting of Carbon Steels

Conclusion

Appendix 1

A1.1. Routines Used for Plotting

Appendix 2

Case Studies Borrowed from the Literature

A2.1. Steady State in a Rectangle (Case Study 1)

A2.2. Steady State in a Rectangle (Case Study 2)

A2.3. Steady State in a Rectangle (Case Study 3)

A2.4. Unsteady State in a Rectangle (Case Study 4)

A2.5. Transient State in a Cylinder (Case Study 9).

A2.6. Transient State in a Cylinder (Case Study 10)

A2.7. Transient State in a Cylinder (Case Study 11)

A2.8. Unsteady State in an Infinite Cylinder (Case Study 12)

A2.9. Unsteady State in an Infinite Cylinder (Case Study 13)

A2.10. A Refractory Wall (Case Study 20)

A2.11. Heat Conduction in a Slab (Case Study 21)

A2.12. Temperature of a Bar (1D Case-I: Mixed IC and BC) (Case Study 22)

A2.13. Temperature of a Bar (1D Case-II: Mixed IC and BC) (Case Study 23)

A2.14. Temperature of a Bar (1D Case-III: Mixed IC and BC) (Case Study 24)

A2.15. Temperature of a Bar (1D Case-IV: Mixed IC and BC) (Case Study 25)

A2.16. Temperature of a Bar (1D Case-V: Mixed IC and BC) (Case Study 26)

A2.17. Temperature of a Bar (1D Case-VI: Mixed IC and BC) (Case Study 27)

A2.18. Temperature of a Bar (1D Case-VII: Mixed IC and BC) (Case Study 28)

A2.19. Temperature of a Bar (1D Case-VIII: Mixed IC and BC) (Case Study 29)

Appendix 3

A3.1. Induction Heating of Steel Billets/Slabs

Acronyms

References

About the Author

Index

Blank Page.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Other Format:

Print version: Sismanis, Panagiotis (Takis) Case Studies in Computational Heat Transfer

ISBN:

979-88-911-3300-6