A NEW FINITE-DIFFERENCE METHOD FOR THE NONLINEAR INVERSE HEAT CONDUCTION PROBLEM

A new space-marching finite-difference algorithm is developed to solve the nonlinear inverse heat conduction problem. This algorithm uses interior temperature measurements at future times to estimate the surface heat flux. The results of this method are compared on a test case with four other numerical schemes. The method is as accurate as the method developed by Beck [ 1] and uses a smaller computational time. This scheme is also employed to estimate the effects of different types of experimental errors on the estimation of the surface heat flux. Errors due to temperature measurements, thermocouple locations, and material properties are each investigated.

[1]  G. Stolz.  Numerical Solutions to an Inverse Problem of Heat Conduction for Simple Shapes , 1960 .

[2]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[3]  R. J. Schoenhals,et al.  APPLICATION OF THE FINITE-ELEMENT METHOD TO THE INVERSE HEAT CONDUCTION PROBLEM , 1978 .

[4]  K. Miller,et al.  Calculation of the surface temperature and heat flux on one side of a wall from measurements on the opposite side , 1980 .

[5]  D. Murio.  On the estimation of the boundary temperature on a sphere from measurements at its center , 1982 .

[6]  O. Burggraf.  An Exact Solution of the Inverse Problem in Heat Conduction Theory and Applications , 1964 .

[7]  D. M. Curry,et al.  An analytical and experimental study for surface heat flux determination , 1977 .

[8]  K. Miller,et al.  On the necessity of nearly-best-possible methods for analytic continuation of scattering data , 1973 .

[9]  Norbert Dsouza,et al.  Numerical solution of one-dimensional inverse transient heat conduction by finite difference method , 1975 .

[10]  A. Haji-Sheikh,et al.  AN ITERATIVE APPROACH TO THE SOLUTION OF INVERSE HEAT CONDUCTION PROBLEMS , 1977 .

[11]  Murray Imber,et al.  Prediction of Transient Temperature Distributions with Embedded Thermocouples , 1972 .

[12]  J. Beck.  Surface heat flux determination using an integral method , 1968 .

[13]  Charles F. Weber,et al.  Analysis and solution of the ill-posed inverse heat conduction problem , 1981 .

[14]  G. P. Mulholland,et al.  The accuracy and resolving power of one dimensional transient inverse heat conduction theory as applied to discrete and inaccurate measurements , 1979 .

[15]  J. Beck.  Criteria for comparison of methods of solution of the inverse heat conduction problem , 1975 .

[16]  B. F. Blackwell,et al.  EFFICIENT TECHNIQUE FOR THE NUMERICAL SOLUTION OF THE ONE-DIMENSIONAL INVERSE PROBLEM OF HEAT CONDUCTION , 1981 .

[17]  K. Miller.  Least Squares Methods for Ill-Posed Problems with a Prescribed Bound , 1970 .

[18]  J. Beck,et al.  EFFICIENT SEQUENTIAL SOLUTION OF THE NONLINEAR INVERSE HEAT CONDUCTION PROBLEM , 1982 .

[19]  J. V. Beck,et al.  Combined function specification-regularization procedure for solution of inverse heat conduction problem , 1984 .

[20]  E. Sparrow,et al.  The Inverse Problem in Transient Heat Conduction , 1964 .

[21]  I. Frank.  An application of least squares method to the solution of the inverse problem of heat conduction. , 1963 .

[22]  L. C. Chow,et al.  Inverse Heat Conduction by Direct Inverse Laplace Transform , 1981 .

[23]  J. Beck.  Nonlinear estimation applied to the nonlinear inverse heat conduction problem , 1970 .