Inverse determination of thermal conductivity for one-dimensional problems

An LGSM to identify nonhomogeneous heat conductivity functions by an extra measurement of temperature

“…(44), (45) and (38), it can be seen that G is fully determined by T 0 and T f , and is independent on the vector field f in Eq. (11). Notice that the above G is different from the one in Eq.…”

“…Then, Chen and Zou [10] extended that method to a non-smooth case in the steady-state elliptic system. Lam and Yeung [11] have employed a first-order finite difference method to determine the heat conductivity in a one-dimensional heat conduction equation. Yeung and Lam [1] extended that result by using a second-order finite difference technique.…”

Inverse determination of temperature dependent thermal conductivity using network simulation method

“…(1)-(4) and the set of temperatures T(x f , t j , ε j ) gives by Eq. (5). With this information available, the aim now is to estimate the dependence of k(T) of the solid in the approximate form of a piece-wise function, for any kind of function that specifies k in the DHCP.…”

“…Tervola [4] investigated homogenous materials, using the Davidon-Fletcher-Powell method and finite element techniques based on measured temperature profiles; Lam and Yeung [5] used two finite difference techniques; Scarpa et al [6] used the Monte Carlo method; Huang et al [7] used the conjugate gradient method of minimization with an adjoint equation in both homogeneous and nonhomogeneous materials, while Yang [8] developed a direct procedure (noniterative) by means of a linear inverse model and, subsequently, Yang [9] presented an iterative approach starting with temperature measurements taken on one side of the surface. In Yang's technique linearization method was necessary to solve the set of nonlinear equations.…”

Inverse determination of thermal conductivity using semi-discretization method

“…To avoid the iteration process in calculation of IHCP, the direct or non-iteration method has been proposed in recent years. Lam and Yeung [12] used a first order finite difference and Yeung and Lam [13] further applied a second-order finite difference technique to estimate the thermal conductivity by solving the discretized linear equations. Lin et al [14] employed finite difference method to discretize the heat conduction equation and then the linear least-squares-error was adopted to solve IHCP.…”