隔熱材料在過去四十年來一直是能源工程或熱傳工程上極為重要的研究領域。由於隔熱材料應用之廣泛，如太空工程，低溫工程，能源工程及核子工程等，因此全世界各先進國家莫不卯足全力發展。探討隔熱材料的熱交換現象的相關研究與實驗也不曾間斷。近年來由於以氟氯碳化物充當發泡劑之隔熱材料，對臭氧層造成環境破壞。因此本研究以實驗方式量測不同泡孔直徑(150350 m)的硬質PU發泡材料，以水當發泡劑，經過熱烘除濕後，置入積層薄膜袋內，在不同壓力(7600.014 Torr)下封裝製成真空保溫片，以等效熱傳係數測定儀量測其等效熱傳係數。另外，為瞭解PU發泡材料內的輻射熱傳量所佔的比例，亦利用傅利葉轉換紅外線光譜儀進行垂質穿透率的量測並推導出消散係數，再應用擴散近似法估算輻射熱傳係數，其次配合等效熱傳係數求得氣體熱傳導係數。其結果顯示，氣體熱傳在一大氣壓與室溫下佔將近70至80%，而利用抽真空方式，可有效降低氣體熱傳的影響。此外，泡孔直徑對輻射熱傳的影響亦非常劇烈。
本文為探討輻射熱傳在隔熱材料的熱傳比例，又採用更嚴謹的理論，對PU發泡材料傳導與輻射交互影響下之熱傳現象做一理論分析。假設發泡材料為具有吸收、放射及等向性散射之介質，且表面具漫射及反射特性。對輻射熱傳部份，本文採用P3近似法求解積分－微分輻射傳遞方程式。對穩態熱傳情況，採用有限差分法來處理能量方程式。其結果顯示，較低消散係數之發泡材料，在低溫狀況下，輻射熱傳係數與利用擴散近似法所得之輻射熱傳係數差異有近60%。
由於孔隙材料應用非常廣泛，本文亦探討孔隙材料中隨著位置變化的孔隙度對輻射與傳導熱傳的影響。其中討論四種不同孔隙度的模式對平均熱傳導係數與輻射熱通量的關係。事實上，每一種模式都有不同的特性：模式一代表孔隙度不隨位置變化，且為定值；模式二代表孔隙度由兩多項式所組成，且隨位置有震盪變化；模式三代表孔隙度由指數方程式所組成，且隨位置變化；模式四代表孔隙度由Bessel方程式所組成，且隨位置亦有震盪變化。其結果發現，隨位置變化的孔隙度對平均熱傳導係數與輻射熱通量的影響非常劇烈。
本文亦探討輻射與傳導熱傳的逆邊界問題。利用介質內中的兩點位置量測隨時間變化的溫度變化，再利用空間配合法反算隨著時間變化的熱通量邊界。對輻射熱傳部份，本文採用擴散近似法求解，因此僅考慮介質在光學厚度較大的情況，討論的參數有格點數、反算位置、量測誤差，輸入資料與傳導輻射比值等。其結果顯示，傳導熱傳佔優勢的情況，反算效果較佳，且反算位置較接近熱通量邊界所反算的結果越佳。此外，輸入的資料越多，反算效果也越好。
本文所探討之PU發泡材料其性能與世界先進國家相當，且對環境破壞毫無疑慮，採用水發泡方式，甚至可重複利用，可應用在低溫系統或超低溫系統的隔熱，文中所分析之結果與方式，對業界應能提供最佳化之設計理念。

Thermal insulation has long been an important subject to engineers and is indeed one of the major concerns in the development of heat transfer technology. Due to the wide application in many engineering systems, the researches for developing advanced insulation techniques are still a continuous and challenging issue. Different models and various experimental techniques have been developed to obtain a detailed description of the thermal exchange phenomena inside this material. Therefore, in this work, the thermal properties of polyurethane foams are measured from atmospheric pressure to 0.014 Torr. The effective thermal conductivity measured by Guarded-hot-plate system is carried out on six different samples with cell sizes in the range of 150 to 350 m. To identify the contribution of radiative heat transfer, a Fourier Transform Infrared Spectrometer is used to measure the transmittance of these samples in the wavelength range 2.5 to 25 m. Diffusion approximation is also used to estimate the radiative thermal conductivity. Since solid and radiative contributions are independent of gas pressure, gas conduction at higher pressure is obtained by subtracting the measured results from the total heat transfer.
Over the past thirty years, the analysis of simultaneous radiation and conduction heat transfer in a participating medium, like thermal insulation, as well as inverse conduction/radiation problems have been the subjects of numerous investigations. It is well known that the formulation of the radiative heat transfer problem combined with the conduction mode of heat transfer leads to a nonlinear integro-differential equation because of inherent complexity resulting from radiative contribution to the total heat flux for a given geometrical configuration of the system. Therefore, only approximate solutions for specific geometries are available. Next, we focuses theoretically on determining the heat transfer mode in polyurethane foams and predicting the radiative thermal conductivity. The stepwise gray or box model is applied to incorporate the effects of the non-gray characteristics. Moreover, the radiative heat transfer is calculated using the P-3 approximation, which has been demonstrated to effectively generate accurate approximate solutions to the gray problem.
Combined conduction and radiation heat transfer in packed beds has become an increasingly important research because of its wide applications in thermal insulation systems designs. Numerous studies have been reported in relation to this topic. The effects of four different porosity distributions on mean effective thermal conductivity and radiative heat flux distributions in packed beds is investigated theoretically. In fact, each model has different characteristics: model 1 represents the mean porosity in the bulk region; model 2 consists of two principal equations, an order-3 polynomial expression and a damped cosine, along with plus a constant; model 3 is an exponential function that ignores the oscillations in porosity in the near-wall region; model 4 uses the Bessel function as an oscillatory factor allowing consideration of the effects of damped oscillations. The variable porosity distribution is found that significantly affect the total effective thermal conductivity as well as the radiative heat flux near the walls.
Finally, the surface heat flux and temperature histories of a solid is determined from transient temperature measurements at one or more interior locations; this is called an inverse boundary problem. The space-marching technique is employed to analyze the inverse heat conduction-radiation problem (IHCRP). The radiative source term is calculated by diffusion approximation when the medium is treated as optically thick condition such as thermal insulation material. The present analysis considers a semitransparent gray slab bounded by infinite black walls and discusses the influence parameters such as conduction-to-radiation parameter, number of grid point, time step, measurement error, inverse position, and data input in detailed.

COVER
Abstract(in Chinese)
Abstract
Acknowledgements
Table of Contents
List of Figures
List of Tables
Nomenclature
1 Introduction
1.1 Basic Concept of thermal Insulation
1.2 Literature Survey
1.3 Objective
2 Thrmal Conductivity of Polyurethane Foams
2.1 Analysis
2.2 Experiments
2.3 Results and Discussion
2.4 Conclusions
3 Heat Transfer in Open Cell Polyurethane Foam Insulation
3.1 Analysis
3.2 Box Method
3.3 Radiative Properties
3.4 Method of Solution
3.5 Results and Discussion
3.6 Conclusions
4 Combined Conduction an Radiation Heat Transfer on Plane-Parallrl Packed Beds with Variable Porosity
4.1 Analysis
4.2 Results and Discussion
4.3 Conclusions
5 Inverse Conduction/Radiation in Plane-Parallel Media
5.1 Analysis
5.2 Test cases
5.3 Results and Discussion
5.4 Conclusions
6 Conclusions
References
List of Publications
Resume

1. Tien, C. L. and Cunnington, G. R., 1973, “Cryogenic Insulation Heat Transfer,” Advances in Heat Transfer, NY: Academic Press, Vol. 9, pp. 349-417.
2. Tye, R. P., ed., 1978, “Thermal Transmission Measurement of Insulation,” ASTM STP600.
3. Tien, C. L. and Cunnington, G. R., 1978, “Glass Microsphere Cryogenic Insulation, Cryogenics,“ Vol. 16, pp. 583-586.
4. Tong, T. W. and Tien C. L., 1983, “Radiative Heat Transfer in Fibrous Insulations－Part I: Analytic Study,” ASME J. Heat Transfer, Vol. 105, pp. 70-75.
5. Tong, T. W., Yang, Q. S. and Tien C. L., 1983, “Radiative Heat Transfer in Fibrous Insulations－Part II: Experimental Analytic Study,” ASME J. Heat Transfer, Vol. 105, pp. 76-81.
6. Ostrogorsky, A. G., Glicksman, L. R. and Reitz, D. W., 1986, “Aging of Polyurethane foams,” Int. J. Heat Mass Transfer, Vol. 29, pp. 1169-1176.
7. Glicksman, L. R., Schuetz, M. and Sinofsky, M., 1987, “Radiation Heat Transfer in Foam Insulation,” Int. J. Heat Mass Transfer, Vol. 30, pp. 187-197.
8. Kuhn, J., Ebert, H. P., Arduini-Schuster, M. C., Buttner D. and Fricke, J., 1992, “Thermal Transport in Polystyrene and Polyurethane Foam Insulations,” Int. J. Heat Mass Transfer, Vol. 35, pp. 1795-1801.
9. Doermann, D. and Sacadura, J. F., 1996, “Heat Transfer in Open Cell Foam Insulation,” ASME J. Heat Transfer, Vol. 118, pp. 88-93.
10. Caps, R. Heinemann, U., Fricke, J., and Keller, K., 1997, “Thermal Conductivity of Polyimide Foams,” Int. J. Heat Mass Transfer, Vol. 40, pp. 269-280.
11. Tseng, C. J., Yamaguch, M., and Ohmori, T., 1997, “Thermal Conductivity of Polyurethane Foams from Room Temperature to 20 K,” Cryogenics, Vol. 37, pp. 305-312.
12. Aronson, J. R., Emslie, A. G., Ruccia, F. E., Smallman, C. R., Smith, E. M., and Strong, P. F., 1979, ”Infrared Emittance of Fibrous Materials,” Applied Optics, Vol. 18, pp. 2622-2633.
13. Tong, T. W. and Tien, C. L., 1980, ”Analytical Models for Thermal Radiation in Fibrous Insulation,” J. Thermal Insulation, Vol. 4, pp. 27-43.
14. Scheuerpflug, P., Caps, R., Buttner, D. and Fricke, J., 1985, “Apparent Thermal Conductivity of Evacuated SiO2-aerogel Tiles under Variation of Radiative Boundary Condition,” Int. J. Heat Mass Transfer, Vol. 28, pp. 2299-2306.
15. Chu, H. S., Stretton, A. J. and Tien, C. L., 1988, “Radiative Heat Transfer in Ultra-Fine Powder Insulation,” Int. J. Heat Mass Transfer, Vol. 31, pp. 1627-1634.
16. Heinemann, U., Caps, R. and Fricke, J., 1996, “Radiation-Conduction Interaction: an Investigation on Silica Aerogels,” Int. J. Heat Mass Transfer, Vol. 39, pp. 2115-2130.
17. Hahn, O., Raether, F., Arduini-Schuster, M. C. and Fricke, J., 1997, “Transient Coupled Conductive/radiative Heat Transfer in Absorbing, Emitting and Scattering Media: Application to Laser-Flash Measurements on Ceramic Materials,” Int. J. Heat Mass Transfer, Vol. 40, pp. 689-698.
18. Tien, C. L., 1988, “Thermal Radiation in Packed and Fluidized Beds,” ASME J. Heat Transfer, Vol. 110, pp.1230-1242.
19. Drolen, B. L. and Tien, C. L., 1987, “Independent and Dependent Scattering in Packed-Sphere Systems,” J. Thermophysics Heat Transfer, Vol. 1, pp. 63-68.
20. Singh, B. P. and Kaviany, M., 1991, “Independent Theory versus Direct Simulation of Radiation Heat Transfer in Packed Beds,” Int. J. Heat Mass Transfer, Vol. 34, pp. 2869-2881.
21. Singh, B. P. and Kaviany, M., 1992, “Modeling Radiative Heat Transfer in Packed Beds,” Int. J. Heat Mass Transfer, Vol. 35, pp. 1397-1404.
22. Nasr, K., Viskanta, R. and Ramadhyani, S., 1994, “An Experimental Evaluation of the Effective Thermal Conductivities of Packed Beds at High Temperature,” ASME J. Heat Transfer, Vol. 116, pp. 829-837.
23. Benenati, R. F. and Brosilow, C. B., 1962, “Void Fraction Distribution in Beds of Spheres,” AIChE J. , Vol. 8, pp. 359-361.
24. Ridgway, K. and Tarbuck, K. J., 1966, “Radial Voidage Variation in Randomly-Packed Beds of Spheres of Different Sizes,” J. Pharm. Pharmacol., Vol. 18, pp. 168-175.
25. Vafai, K. and Tien, C. L., 1981, “Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media,” Int. J. Heat Mass Transfer, Vol. 24, pp. 195-203.
26. Vafai, K. and Tien, C. L., 1982, “Boundary and Inertia Effects on Convective Mass Transfer in Porous Media,” Int. J. Heat Mass Transfer, Vol. 25, pp. 1183-1190.
27. Vafai, K., Alkire, R. L. and Tien, C. L., 1985, “An Experimental Investigation of Heat Transfer in Variable Porosity Media,” ASME J. Heat Transfer, Vol. 107, pp. 642-647.
28. Lu, J. D., Flamant, G. and Variot, B., 1994, “Theoretical Study of Combined Conductive, Convective and Radiative Heat Transfer Between Plates and Packed Beds,” Int. J. Heat Mass Transfer, Vol. 37, pp. 727-736.
29. Kamiuto, K., Iwamoto, M. and Nagumo, Y., 1993, “Combined Conduction and Correlated-Radiation Heat Transfer in Packed Beds,” J. Thermophysics Heat Transfer, Vol. 7, pp. 496-501.
30. Kozdoba, L. A. and Krukovsky, P. G., 1982, “Methods for Solving Inverse Heat Transfer Problems,” Naukova Dumka, Kiev.
31. Beck, J. V., Blackwell, B. and Clair, C. R. St., 1985, Inverse Heat Conduction－Ill-Posed Problems, Wiley, New York.
32. Beck, J. V. and Arnold, K. J., 1977, Parameter Estimation in Engineering and Science, Wiley, New York.
33. Chen, H. T., Lin, J. Y., Wu, C. H., and Huang, C. H., 1996, “Numerical Algorithm for Estimating Temperature-Dependent Thermal Conductivity,” Numerical Heat Transfer, Vol. 29, pp. 509-522.
34. Chen, H. T. and Lin, J. Y., 1998, “Simultaneous Estimations of Temperature-Dependent Thermal Conductivity and Heat Capacity,” Int. J. Heat Mass Transfer, Vol. 41, pp. 2237-2244.
35. Keanini, R. G., 1998, “Inverse Estimation of Surface Heat Flux Distributions during High Speed Rolling Using Remote Thermal Measurements,” Int. J. Heat Mass Transfer, Vol. 41, pp. 275-285.
36. Beck, J. V., Blackwell, B. and Haji-Sheikh, A., 1996, “Comparison of Some Inverse Heat Conduction Methods Using Experimental Data,” Int. J. Heat Mass Transfer, Vol. 39, pp. 3649-3657.
37. Yang C. Y. and Chen C. K., 1996, “The Boundary Estimation in Two-Dimensional Inverse Heat Conduction Problems,” J. Phys. D: Appl. Phys., Vol. 29, pp. 333-339.
38. Osman, A. M., Dowding, K. J. and Beck, J. V., 1997, “Numerical Solution of the General Two-Dimensional Inverse Heat Conduction Problem (IHCP),” ASME J. Heat Transfer, Vol. 119, pp. 38-45.
39. Subramaniam, S. and Menguc, M. P., 1991, “Solution of Inverse Radiation problem for Inhomogeneous and Anisotropically Scattering Medium Using a Mote Carlo Technique,” Int. J. Heat Mass Transfer, Vol. 34, pp. 253-266.
40. McCormic, N. J., 1992, “Inverse Radiative Transfer Problems: A Review,” Nuclear Science Engineering, Vol. 112, pp. 185-198.
41. Neto, A. J. S. and Ozisik, M. N., 1992, “An Inverse Analysis of Simultaneously Estimating Phalane Function, Albedo and Optical Thickness,” the 28th National Heat Transfer Conference, San Diego, CA, August.
42. Menguc, M. P. and Manickavasagam, S., 1993, “Inverse Radiation in Axisymmetrical Scattering Media,” J. Thermophysics Heat Transfer, Vol. 7, pp. 479-486.
43. Nicolau, V. P., Raynaud, M. and Sacadura, J. F., 1994, “Spectral Radiative Properties Identification of Fiber Insulating Materials,” Int. J. Heat Mass Transfer, Vol. 37, pp. 311-324.
44. Li, Y. H. and Ozisik, M. N., 1993, “Inverse Radiation problem for Simultaneous Estimation of Temperature Profile and Surface Reflectivity,” J. Thermophysics Heat Transfer, Vol. 7, pp.88-93.
45. Li, Y. H., 1997, “Inverse Radiation Problem in Two-Dimensional Rectangular Media, “J. Thermophysics Heat Transfer, Vol. 11, pp. 556-561.
46. Manickavasagam, S. and Menguc, M. P., 1993, “Inverse Radiation/Conduction Problem in Plane-Parallel Media,” the 29th National Heat Transfer Conference, Atlanta, Georgia, August.
47. Ruperti, Jr. N. J., Raynaud, M., and Sacadura, J. F., 1995, “Influence of Radiation on the Coupled Inverse Heat Conduction-Radiation Problem,” ASME HTD-Vol.312, pp.79-86.
48. Ruperti, Jr. N. J., Raynaud, M., and Sacadura, J. F., 1996, “A Method for the Solution of the Coupled Inverse heat Conduction-Radiation Problem,” ASME J. Heat Transfer, Vol. 118, pp.10-17.
49. Li, Y. H., 1999, “Estimation of Thermal Properties in Combined Conduction and Radiation, Int. J. Heat Mass Transfer,” Vol. 42, pp. 565-572.
50. Siegel, R. and Howell, J. R., 1992, Thermal Radiation Heat Transfer, Hemisphere, Washington.
51. Rosseland, S., 1936, Theoretical Astrophysics, Oxford University Press, London.
52. Ozisik, M. N., 1973, Radiative Transfer and Interactions with Conduction and Convection, Wiley, New York.
53. Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York.
54. Brewster, M., 1992, Thermal Radiative Transfer and Properties, Wiley, New York, PP. 443-444.
55. Editorial, 1993, “Journal of Heat Transfer Policy on Reporting Uncertainties in Experimental Measurements and Results,” ASME J. Heat Transfer, Vol. 115, pp. 5-6.
56. Modest, M. F., 1993, Radiative Heat Transfer, McGraw-Hill Inc..
57. Bayazitoglu, Y. and Higenyi, J., 1979, “Higher-Order Differential Equations of Radiative Transfer: P3 Approximation,” J. Thermophysics Heat Transfer, Vol. 17, pp. 424-431.
58. Hunt, M. L. and Tien, C. L., 1988, “Non-Darcian Convection in Cylindrical Packed Beds,” ASME J. Heat Transfer, Vol. 110, pp. 378-384.
59. Mueller, G. E., 1991, “Prediction of Radial Porosity Distributions in Randomly Packed Fixed Beds of Uniformly Sized Spheres in Cylindrical Containers,” Chemical Eng. Sci., Vol. 46, pp. 706-708.
60. Raynaud, M. and Bransier, J., 1986, “A New Finite Difference Method for the Nonlinear Inverse Heat Conduction Problem,” Numer. Heat Transfer, Vol. 9, pp. 27-42.
61. Raynaud, M. and Bransier, J., 1986, “Experimental Validation of a New Space Marching Finite Difference Algorithm for the Inverse Heat Conduction problem,” Proceedings of the Eighth Int. Heat Transfer Conference, San Francisco, CA.
62. Raynaud, M. and Beck, J. V., 1988, “Methodology for Comparison of Inverse Heat Conduction Methods,” ASME J. Heat Transfer, vol. 110, pp. 30-37.
63. Ratzel, A. C. and Howell, J. R., 1982, “Heat Transfer by Conduction and Radiation in One-Dimensional Planar Media Using the Differential Approximation,” ASME J. Heat Transfer, Vol. 104, pp. 388-391.
64. Wu, J. W, Sung, W. F. and Chu, H. S., 1999, “Thermal Conductivity of Polyurethane Foams,” Int. J. Heat Mass Transfer, Vol. 42, pp. 2211-2217.