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

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Dimensionless time θ 1.0 0.8 0.6 0.4 0.2 Exact solution PAM CLSA Exact solution Polynomial approximation method classical lumped system Dimensionless temperature τ 51 B=10 Fig 4.11 Comparison of solutions of PAM, CLSA and Exact solution for a slab having internal heat generation 4.4 TABULATION Table 4.1 Comparison of solutions of average temperature obtained from different heat conduction problems Average temperature θ Slab with heat flux Slab with heat generation −Uτ ⎛e + V ⎞ θ = ⎜ ⎟ ⎝ U ⎠ B U = 1+ B Where 3 , Q V = 1+ B 3 − τU e + V θ = Where U U = B 1+ B 3 V = ( ) G ( 1 ) B + 3 , Tube with heat flux −Uτ ⎛e + V ⎞ θ = ⎜ ⎟ ⎝ U ⎠ Where B U = ( 4+ B) 8 , Q V = 4+ B 8 ( ) 1 Tube with heat generation − τU e + V θ = U Where ⎛ 2B ⎞ U = ⎜ ⎟ ⎜1+ B ⎟ ⎝ 4 ⎠ , G V = ( 1+ B 4)
Table 4.2 Comparison of modified Biot number against various temperature profiles for a slab Si No Profile Value of P 2 1 θ = ( τ) + ( τ) + ( τ) p a0 a1 x a2 x 2 3 2 2 θ = a0 + a1( x − x) + a2( x −x ) 4 2 3 3 θ = a0 + a1( x − x ) + a2( x −x) 4 2 2 4 θ = a0 + a1( x − x ) + a2( x −x) 4 5 3 5 θ = a0 + a1( x − x) + a2( x −x ) 4 3 4 6 θ = a0 + a1( x − x ) + a2( x −x) 52 3B P = B + 3 13B P = 13+ 12B 30B P = 30 + 17B 30B P = 30 + 13B 24B P = 24 + 13B 20B P = 20 + 21B Table 4.3 Comparison of modified Biot number against various temperature profiles for a cylinder Si No. Profile Value of P 2 1 θ = ( τ) + ( τ) + ( τ) p a0 a1 x a2 x 2 ( ) θ = a + a x − x + a x 2 2 0 1 2 3 ( ) θ = a + a x − x + a x 3 3 0 1 2 4 3 2 4 θ = a0 + a1( x − x) + a2( x −x ) 8B P = B + 4 4B P = B + 2 30B P = 3B+ 15 10B P = 4B+ 5
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ANALYSIS OF TRANSIENT HEAT CONDUCTI
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National Institute of Technology Ro
Page 5 and 6:
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
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: Dimensionless temperature 1.0 0.8 0
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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