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

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4 Results and discussion 43-52 4.1 Heat flux for both slab and tube 43 4.2 Heat generation for both slab and Tube 46 4.3 Transient heat conduction in slab with different profiles 49 4.4 Tabulation 51 5 Conclusions 53-54 5.1 Conclusions 53 5.2 Scope of Future work 54 6 References 55-57
ABSTRACT Present work deals with the analytical solution of unsteady state one-dimensional heat conduction problems. An improved lumped parameter model has been adopted to predict the variation of temperature field in a long slab and cylinder. Polynomial approximation method is used to solve the transient conduction equations for both the slab and tube geometry. A variety of models including boundary heat flux for both slabs and tube and, heat generation in both slab and tube has been analyzed. Furthermore, for both slab and cylindrical geometry, a number of guess temperature profiles have been assumed to obtain a generalized solution. Based on the analysis, a modified Biot number has been proposed that predicts the temperature variation irrespective the geometry of the problem. In all the cases, a closed form solution is obtained between temperature, Biot number, heat source parameter and time. The result of the present analysis has been compared with earlier numerical and analytical results. A good agreement has been obtained between the present prediction and the available results. Key words: lumped model, polynomial approximation method, transient, conduction, modified Biot number i
Page 1 and 2: ANALYSIS OF TRANSIENT HEAT CONDUCTI
Page 3 and 4: National Institute of Technology Ro
Page 5: CONTENTS Abstract i List of Figures
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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