Abstarct: In this thesis, the thermal conductivity of a mextal slab is estimated by an inverse heat transfer method. Material discussed could be an inhomogeneous matter. So the thermal conductivity can be Position-Dependent. And the Position-Dependent of the Thermal Conductivity, are considered in governing equations. The governing equations are Unsteady heat conduction equation (one dimensional - two dimensional). In the inverse method, Using temperature measurements of sensors, And calculate the sensitivity function, The objective function has been estimated. The total least squares error and root mean squares error is also included in the calculations. It has many industrial applications, including the estimation problem areas (due to manufacturing process) on the matter. It also has great importance in troubleshooting casting parts. It is assumed that, the local temperature in the mextal slab can be suitably measured by a thermal imaging process. The measured temperature data are employed to estimate the thermal conductivity of the plate as a function of position. The Conjugate Gradient Method (CGM) is used to optimize the objective function. This method is used for optimization in many engineering problems, Accuracy is acceptable. The efficiency of the presented inverse method is evaluated by selection of different conductivity functions in the mextal slab, i.e. quadratic function and triangular function. Inverse method is implemented as a computer program. The obtained results are compared with the physical values of thermal conductivity and the accuracy of the results is also studied. According to papers and reports, Estimation of thermal conductivity as a position function of non-homogeneous two-dimensional plate by inverse heat transfer method, Is the main novelty of the present study.