Simplified calculation of temperature field in heat treated cylinder using temperature measured at one point

Abstract

The calculation of the temperature field T(r) in a heat treated cylinder requires a knowledge of the heat transfer coefficient h(T_s) which may show a highly non-linear dependence on the surface temperature T_s. Since h(T_s) can very often not be explicitly determined, measurement of a temperature T_i near 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 T_s the problem can be overcome via two direct calculations. Diagrams are presented for calculation of both the surface temperature T_s and the heat transfer coefficient h(T_s). 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(T_s) is demonstrated.

MST/1497