An inverse problem in estimating the space-dependent thermal conductivity of a functionally graded hollow cylinder

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown space-dependent thermal conductivity of a functionally graded hollow cylinder. Two different boundary condition types are discussed. The results show that boundary condition type is very crucial to the success of the inverse method. For the case studied here, the inverse method works in conjunction with heat flux specified at the inner wall and convective heat transfer condition at the outer wall but not with constant temperatures specified at both inner and outer walls. The effect of measurement error and sensor number on the estimation accuracy is also investigated. The method can be developed into an accurate, simple, and inexpensive technique for the quality control during the manufacture of functionally graded materials.