A three-dimensional inverse analysis utilizes a different perspective to estimate the surface thermal behavior of the working roll in rolling process. The inverse analysis is based on the temperature reading taken inside the roll at several different locations. At the beginning of the study, finite-difference methods are employed to discretize the problem domain and then a linear inverse model is constructed to identify the boundary conditions. The present approach is to rearrange the matrix forms of the differential governing equations and estimate the surface unknown conditions of the working roll. Then, the linear least-squares method is adopted to find the solution. The advantages of this proposed inverse analysis method are that no prior information is needed regarding the functional form of the unknown quantities, no initial guess need be used and the numbers of iterations for calculation process is limited to one. The results show that only few measuring points are sufficient to estimate the boundary conditions when measurement errors are neglected. When measurement errors are considered, more measuring points are needed in order to increase the congruence of the estimated results to exact solutions. *[S1087-1357(00)70201-2]*

*The Temperature and Thermal Stress in Rolling of Metal Strip*, Ph.D. thesis, Carnegie-Mellon Univ., Pittsburgh, PA.

*Temperature Distributions in Rolling of Metal Strip*, Ph.D. thesis, Carnegie-Mellon Univ., Pittsburgh, PA.

**3**, HTD-Vol. 96, H. R. Jacobs, ed., Houston, pp. 47–53.

*6th Natl. Congress on Heat Transfer*, Bari, pp. 481–494.

*Numerical Analysis of Forming Processes*, Wiley, New York, pp. 269–283.

*The Finite Element Method in Engineering Science*, McGraw-Hill, London.

*Inverse Heat Conduction-III Posed Problem*, Wiley, New York.

*Inverse Theory and Applications for Engineers*, Prentice-Hall, Englewood Cliffs, NJ.