本文主要是以混合拉氏轉換法(Laplace transform technique)和有限差分法(Finite difference method)的數值方法，並配合最小平方法(Least-squares scheme)和溫度量測值來預測以噴霧冷卻(Spray cooling)熱表面時之表面溫度(Surface temperature)及表面熱通量(Surface heat flux)。首先利用拉氏轉換法處理統制微分方程式及邊界條件之時間域，而後再以有限差分法處理轉換後之統制微分方程式及邊界條件，最後再以數值逆拉氏轉換法求取測試件之表面溫度值和表面熱通量。本文在進行逆算過程時，估算值(Estimates)的函數型態先前是未知的。為了欲求得較精確的估算值，整個時間域被分割成數個小時間區間(Sub-time interval)，而後再利用本文之混合逆算法求出每一小時間區間的估算值。本文數值方法的優點是可以求得在某一特定時間的溫度值，而不需要由初始時間慢慢地求解。本文列舉各種不同的實例來驗證本文反算法之精確性。計算結果顯示本文之預測值與前人的預測值差異不大。為了更進一步證實本文之預測值的可靠性，利用已獲得之預測值所求得於其他量測位置之溫度值與實驗值也甚吻合。預測結果顯示本文之數值方法能夠有效地預測出較精確的估算值，且所求得於表面溫度也頗吻合實驗值。

The present study applies the Laplace transform technique and finite difference method in conjunction with least-squares scheme and the experiment data to predict the variation of the surface temperature and surface heat flux during spray cooling on a hot surface. First, time-dependent terms in the governing differential equation and the boundary conditions are removed by using the Laplace transform technique, and then the resulting differential governing equation and boundary conditions are solved by using the finite-difference method. The functional form of the unknowable estimates is not given a prior before performing the inverse calculation. To obtain more accurate estimates, the whole time domain is divided into several sub-time domains. The hybrid inverse scheme is applied to obtain the present estimates for each sub-time domain. The advantage of the present numerical scheme is that, the temperature can be calculated at a specific time without step-by-step computation from the initial time. In this thesis, various examples are illustrated to show the accuracy of the present hybrid inverse numerical method. The results show that the present numerical method can accurately and efficiently obtain the present estimates. Also, the estimated the surface temperature is coincided with the experimental data.

1.L.C. Chow, D.E. Tilton, M.R. Pais, “High power density spray cooling,” WRDC-TR-89-2082, Wright Laboratory, OH, 1989.

2.M.S. Sehmbey, M.R. Pais, L.C. Chow, “Effect of surface material properties and surface characteristics in evaporative spray cooling,” AIAA J. Thermophysics and Heat Transfer, vol. 6, no. 3, pp.505-512, 1992.

3.Y.M. Qiao, S. Chandra, “Spray cooling enhancement by addition of a surfactant,” ASME J. Heat Transfer, vol. 120, pp. 92-98. 1998.

4.W. Jia, H.H. Qiu, “Experimental investigation of droplet dynamics and heat transfer in spray cooling,” Proceedings of ASME NHTC’01 35th National Heat Transfer Conference, Paper NHTC2001-20109, 2001.

5.W. Jia, H.H. Qiu, “Experimental investigation of droplet dynamics and heat transfer in spray cooling,” Experimental Thermal and Fluid Science 27, pp. 829-838, 2003.

6.Q. Cui, S. Chandra, S. McCahan, “The effect of dissolving salts in water sprays used for quenching a hot surface: Part 2－spray cooling,” ASME J. Heat Transfer, Volume 125, pp. 333-338, 2003.

7.S.S. Hsieh, T.C. Fan, H.H. Tsai, “Spray cooling characteristics of water and R-134a. Part II: transient cooling,” Int. J. Heat Mass Transfer 47, pp. 5713-5724, 2004.

8.王安邦, 陳仕昇, 宋佩芳, 林怡君, 陳家智和費德全, “液滴與介面交互作用之十年研究回顧,” 國立台灣大學「台大工程」學刊, 第九十一期, 第103-115頁, 民國九十三年六月.

9.N.V. Shumakoy, “A method for the experimental study of the process of heating a solid body,” Soviet Physics-Technical Physics (Translated by Institute of Physics), Vol. 2, pp. 771, 1957.

10.H.T. Chen, J.Y. Lin, “Hybrid Laplace transform technique for non-linear transient thermal problems,” Int. J. Heat Mass Transfer, Vol. 34, pp. 1301-1308, 1991.

11.H.T. Chen, J.Y. Lin, “Numerical analysis for hyperbolic heat conduction,” Int. J. Mass Transfer, Vol. 36, pp. 2891-2898, 1993.

12.H.T. Chen, and J.Y. Lin, “Analysis of two-dimensional hyperbolic heat conduction problems,” Int. J. Heat Mass Transfer, Vol. 37, pp. 153-164, 1994.

13.H.T. Chen, S.M. Chang, “Application of the hybrid method to inverse heat conduction problems,” Int. J. Heat Mass Transfer, Vol. 33, pp. 621-628, 1990.

14.H.T. Chen, S.Y. Lin, L.C. Fang, “Estimation of surface temperature in two-dimensional inverse heat conduction problems,” Int. J. Heat Mass Transfer, Vol. 44, pp. 1455-1463, 2001.

15.H.T. Chen, S.Y. Lin, L.C. Fang, “Estimation of two-sided boundary conditions for two-dimensional inverse heat conduction problems,” Int. J. Heat Mass Transfer, Vol. 45, pp. 15-23, 2002.

16.H.T. Chen, X.Y. Wu, “Application of the hybrid method to the estimation of surface conductions from experimental data,” in: Trends in Heat, Mass and Momentum Transfer, India, 2003, submitted for publication.

17.H.T. Chen, X.Y. Wu, Y. S. Hsiao, “Estimation of surface condition from the theory of dynamic thermal stresses,” Int. J. Thermal Sciences, Vol. 43, pp. 95-104, 2004.

18.G. Honig, U. Hirdes, “A method for the numerical inversion of Laplace transforms,” J. Comp. Appl. Math., Vol. 9, pp. 113-132, 1984.

19.M. NECATI ÖZISIK, “HEAT CONDUCTION -2nd Edition,” John Wiley & Sons, Inc., Canada, 1993

20.A.F. MILLS, “HEAT TRANSFER -2nd Edition,” Prentice Hall, Inc., Upper Saddle River, New Jersey, 1999