This study addresses the conjugate heat transfer problem of thermally developing, hydrodynamically developed turbulent flow in a circular pipe. An inverse method is used to estimate the unknown heat flux on the external surface of the circular pipe based on temperature measurements taken at several different locations within the fluid. The present approach rearranges the matrix forms of the governing differential equations, and then applies the linear least-squares-error method to determine the unknown boundary conditions of the pipe flow. The results confirm that the proposed method is capable of yielding accurate results even when errors in the temperature measurements are present, and that the accuracy of the estimated results is improved by taking temperature measurements in locations close to the innerwall. (c) 2005 Elsevier Ltd. All rights reserved.