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

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4.3 TRAINSIENT HEAT CONDUCTION IN SLAB WITH DIFFERENT PROFILES We have considered a variety of temperature profiles to see their effect on the solution. Based on the analysis a modified Biot number has been proposed, which is independent of geometry of the problem. Fig (4.9-4.10) shows the variety of temperature with time for different values of modified Biot number, P. It is seen that, for higher values of P represent higher values of Biot number. Therefore the heat removed from the solid to surrounding is higher at higher Biot number. This leads to sudden change in temperature for higher value of P. This trend is observed in the present prediction and is shown in fig (4.9). dimensionless temperature θ 1.0 0.8 0.6 0.4 0.2 0.0 p=1 p=2 p=3 p=4 p=5 p=10 p=20 p=30 1 2 3 49 p=40 dimensionless time τ p=1 p=2 p=3 p=4 p=5 p=10 p=20 p=30 p=40 Fig 4.9 Variation of average temperature with dimensionless time, for P=1 to 40 for a slab.
Dimensionless temperature 1.0 0.8 0.6 0.4 0.2 0.0 B=4 B=5 B=3 B=2 1 2 3 50 B=1 Dimensionless time B=1 B=2 B=3 B=4 B=5 Fig 4.10 Variation of average temperature with dimensionless time, for B=1 to 5 for a slab Fig (4.11) shows the comparison of present analysis with the other available results. These include classified lumped system analysis and exact solution by E.J. Correa and R.M. Cotta [4] of a slab. It is observed that the present prediction shows a better result compared to CLSA. The present prediction agrees well with the exact solution of E.J. Correa and R.M. Cotta [4] at higher time. However at shorter time, the present analysis under predicts the temperature in solid compared to the exact solution. This may be due to the consideration of lumped model for the analysis.
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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
Page 7 and 8:
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
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: Dimensionless temperature (θ) 1.1
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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