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

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obtain the solution. The temperature field for laminar flow in a circular tube for the zero Peclet number is presented. Cheroto et al. [28] modeled the simultaneous heat and mass transfer during drying of moist capillary porous media within by employing lumped-differential formulations They are obtained from spatial integration of the original set of Luikov's equations for temperature and moisture potential. The classical lumped system analysis is used and temperature and moisture gradients are evaluated. They compared the results with analytical solutions for the full partial differential system over a wide range of the governing parameters. Kooodziej and Strezk [29] analyzed the heat flux in steady heat conduction through cylinders having cross-section in an inner or an outer contour in the form of a regular polygon or a circle. They have determined the temperature to calculate the shape factor. They have considered three cases namely hollow prismatic cylinders bounded by isothermal inner circles and outer regular polygons, hollow prismatic cylinders bounded by isothermal inner regular polygons and outer circles, hollow prismatic cylinders bounded by isothermal inner and outer regular polygons. The boundary collocation method in the least squares sense is used. Through non-linear approximation the simple analytical formulas have been determined for the three geometries. Tan et al. [30] developed a improved lumped models for the transient heat conduction of a wall having combined convective and radiative cooling by employing a two point hermite type for integrals. The result is validated by with a numerical solution of the original distributed parameter model. Significant improvement of average temperature over the classical lumped model is obtained. Teixeira et al. [31] studied the behavior of metallic materials. They have considered the nonlinear temperature-dependence neglecting the thermal–mechanical coupling of deformation. They have presented formulation of heat conduction problem. They estimated the error using the finite element method for the continuous-time case with temperature dependent material properties. Frankel el at. [32] presented a general one-dimensional temperature and heat flux formulation for hyperbolic heat conduction in a composite medium and the standard three orthogonal coordinate 17
systems based on the flux formulation. Basing on Fourier’s law, non-separable field equations for both the temperature and heat flux is manipulated. A generalized finite integral transform technique is used to obtain the solution. They have applied the theory on a two-region slab with a pulsed volumetric source and insulated exterior surfaces. This displays the unusual and controversial nature associated with heat conduction based on the modified Fourier’s law in composite regions. 18
Page 1 and 2: ANALYSIS OF TRANSIENT HEAT CONDUCTI
Page 3 and 4: 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
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: error. In this case the approximate
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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