AbstractThe calculation of the temperature field T(r) in a heat treated cylinder requires a knowledge of the heat transfer coefficient h(Ts) which may show a highly non-linear dependence on the surface temperature Ts. Since h(Ts) can very often not be explicitly determined, measurement of a temperature Tinear the surface is employed. As a result the analysis becomes an inverse (‘ill posed’) problem which cannot be handled using standard finite element codes that are applicable only to direct problems. By implementing a procedure for an explicit estimation of the surface temperature Tsthe problem can be overcome via two direct calculations. Diagrams are presented for calculation of both the surface temperature Tsand the heat transfer coefficient h(Ts). The method is applied to the investigation of a duplex steel cylinder which is quenched in cold water. The accuracy of the method is discussed and the complex nature of h(Ts) is demonstrated.MST/1497