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

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CHAPTER 5 CONCLUSION & SCOPE FOR FUTURE WORK
5.1 CONCLUSIONS CHAPTER 5 CONCLUSIONS & SCOPE FOR FUTURE WORK An improved lumped parameter model is applied to the transient heat conduction in a long slab and long cylinder. Polynomial approximation method is used to predict the transient distribution temperature of the slab and tube geometry. Four different cases namely, boundary heat flux for both slab and tube and, heat generation in both slab and tube has been analyzed. Additionally different temperature profiles have been used to obtain solutions for a slab. A unique number, known as modified Biot number is, obtained from the analysis. It is seen that the modified Biot number, which is a function of Biot number, plays important role in the transfer of heat in the solid. Based on the analysis the following conclusions have been obtained. 1. Initially a slab subjected to heat flux on one side and convective heat transfer on the other side is considered for the analysis. Based on the analysis, a closed form solution has been obtained. −Uτ ⎛e + V ⎞ θ = ⎜ ⎟ ⎝ U ⎠ B Q U = V = 1+ B 1+ B Where 3 , 3 2. A long cylinder subjected to heat flux on one side and convective heat transfer on the other side is considered for the analysis. Based on the analysis, a solution has been obtained. U = Where ( + B) −Uτ ⎛e + V ⎞ θ = ⎜ ⎟ ⎝ U ⎠ B 4 8 53 V = Q 4 8 , ( + B) 3. A slab subjected to heat generation at one side and convective heat transfer on the other side is considered for the analysis. Based on the analysis, a closed form solution has been obtained.
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ANALYSIS OF TRANSIENT HEAT CONDUCTI
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National Institute of Technology Ro
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CONTENTS Abstract i List of Figures
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ABSTRACT Present work deals with th
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Fig4.6 Average dimensionless temper
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NOMENCLTURE B Biot Number k Thermal
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1.1 GENERAL BACKGROUND CHAPTER 1 IN
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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: Table 4.2 Comparison of modified Bi
Page 71 and 72: CHAPTER 6 REFRENCES
Page 73 and 74: 12. O¨. Ercan Ataer, “An approxi
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