An inverse analysis is provided to determine the spatial-and temperature-dependent thermal conductivities in several one-dimensional heat conduction problems. A nite difference method is used to discretize the governing equations, and then a linear inverse model is constructed to identify the undetermined thermal conductivities. The present approach is to rearrange the matrix forms of the differential governing equations so that the unknown thermal conductivity can be represented explicitly. Then, the linear least-squares-error method is adopted to nd the solutions. The results show that only a few measuring points at discrete grid points are needed to estimate the unknown quantities of the thermal conductivities, even when measurement errors are considered. In contrast to the traditional approach, the advantages of this method are that no prior information is needed on the functional form of the unknown quantities, no initial guesses are required, and no iterations in the calculating process are necessary and that the inverse problem can be solved in a linear domain. Furthermore, the existence and uniqueness of the solutions can be easily identi ed.
NomenclatureA = coef cient matrix of vector T B = coef cient matrix of vector C C = vector constructed from the unknown thermal conductivities D = vector constructed from the functions of the unknown thermal conductivities E = product of A ¡1 and B F = error function g = heat generation, W/m 3 k = thermal conductivity, W/m ¢ ± C q = heat ux, W/m 2 R = reverse matrix T = temperature, ± C T = temperature vector t = time, s x = spatial coordinate, m 1t = increment of time domain, s 1x = increment of spatial coordinate, m ¾ = standard deviation ! = random variable Subscripts esti = estimated data exact = exact data i = index of spatial coordinate j = index of time domain meas = measured data n = index at the boundary when x is equal to 1, m