analysis of transient heat conduction in different geometries - ethesis ...

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ACKNOWLEDGEMENT It is with a feeling of great pleasure that I would like to express my most sincere heartfelt gratitude to Dr. Santosh Kumar Sahu, Dept. of Mechanical Engineering, NIT, Rourkela for suggesting the topic for my thesis report and for his ready and able guidance throughout the course of my preparing the report. I am greatly indebted to him for his constructive suggestions and criticism from time to time during the course of progress of my work. I express my sincere thanks to Professor R.K.Sahoo, HOD, Department of Mechanical Engineering, NIT, Rourkela for providing me the necessary facilities in the department. I am also thankful to all my friends and the staff members of the department of Mechanical Engineering and to all my well wishers for their inspiration and help. Pritinika Behera Date Roll No 207ME314 National Institute of Technology Rourkela-769008, Orissa, India
CONTENTS Abstract i List of Figures ii List of Tables iv Nomenclatures v Chapter 1 Introduction 1-9 1.1 General Background 1 1.2 Modes of heat transfer 1 1.3 Heat conduction 2 1.4 Heat conduction problems 3 1.5 Description of analytical method and numerical method 5 1.6 Low Biot number in 1-D heat conduction problems 6 1.7 Solution of heat conduction problems 7 1.8 Objective of present work 9 1.9 Layout of the report 9 2 Literature survey 10-18 2.1 Introduction 10 2.2 Analytical solutions 10 3 Theoretical analysis of conduction problems 19-42 3.1 Introduction 19 3.2 Transient analysis on a slab with specified heat flux 19 3.3 Transient analysis on a tube with specified heat flux 23 3.4 Transient analysis on a slab with specified heat generation 26 3.5 Transient analysis on a tube with specified heat generation. 30 3.6 Transient heat conduction in slab with different profiles. 35 3.7 Transient heat conduction in cylinder with different profiles 39 3.8 Closure 42
Page 1 and 2: ANALYSIS OF TRANSIENT HEAT CONDUCTI
Page 3: National Institute of Technology Ro
Page 7 and 8: ABSTRACT Present work deals with th
Page 9 and 10: Fig4.6 Average dimensionless temper
Page 11 and 12: NOMENCLTURE B Biot Number k Thermal
Page 13 and 14: 1.1 GENERAL BACKGROUND CHAPTER 1 IN
Page 15 and 16: direction. When no single and domin
Page 17 and 18: though the atmosphere has already b
Page 19 and 20: higher. When Biot number is more th
Page 21 and 22: 1.8 OBJECTIVE OF PRESENT WORK 1. An
Page 23 and 24: 2.1 INTRODUCTION CHAPTER 2 LITERATU
Page 25 and 26: A. G. Ostrogorsky [5] has used Lapl
Page 27 and 28: linear polynomial pieces which are
Page 29 and 30: error. In this case the approximate
Page 31 and 32: systems based on the flux formulati
Page 33 and 34: CHAPTER 3 THEORTICAL ANALYSIS OF CO
Page 35 and 36: equation. This can then be converte
Page 37 and 38: Based on the analysis a closed form
Page 39 and 40: a + 2a =−Bθ 1 2 Subtracting the
Page 41 and 42: ∂T 1 ∂ ⎛ m ∂T ⎞ = α r G
Page 43 and 44: Thus, a 2 Bθ =− 2 We can also wr
Page 45 and 46: We consider the heat conduction in
Page 47 and 48: Thus, a 1 = 0 (3.86) Applying secon
Page 49 and 50: θ = − τU e + V U ⎛ 2B ⎞ U =
Page 51 and 52: Differentiating the above equation
Page 53 and 54: 3.7 TRAINSIENT HEAT CONDUCTION IN C
Page 55 and 56:
Thus a + 2a =−Bθ 1 2 a 2 Bθ =
Page 57 and 58:
CHAPTER 4 RESULT AND DISCUSSION
Page 59 and 60:
Dimensionless temperature (θ) 1000
Page 61 and 62:
4.2 HEAT GENERATION FOR BOTH SLAB A
Page 63 and 64:
Dimensionless temperature (θ) 1.1
Page 65 and 66:
Dimensionless temperature 1.0 0.8 0
Page 67 and 68:
Table 4.2 Comparison of modified Bi
Page 69 and 70:
5.1 CONCLUSIONS CHAPTER 5 CONCLUSIO
Page 71 and 72:
CHAPTER 6 REFRENCES
Page 73 and 74:
12. O¨. Ercan Ataer, “An approxi
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