The purpose of this study is to estimate the unknown heat flux boundary conditions on the irregular shape fins for expanding the application of the inverse method. An inverse algorithm based on the sequential method and the concept of future time combined with the finite element package is used to determine the 2-D irregular shape heat conduction problems. Special features about the proposed method are that the stiffness matrix of the irregular shape can be solved from the finite element package. The estimated results are considered under the different kinds of fin types, the future time, the sensor's location, the sensor's number, the measured errors and the function of heat flux boundary. These estimated results are agreed with the exact solution even in the irregular shape fin. The results of this study show that this proposed method is an accurate, stable, and efficient method for solving the realistic engineering heat conduction problems. (C) 2011 Elsevier Ltd. All rights reserved.