Numerical Solution of Transient Heat Conduction Equation for Heat-Treatable Alloys Whose Thermal Properties Change With Time and Temperature

Changes in microstructure occur in as-received aluminum alloy (Al-2024-T351) when it is subjected to elevated temperatures (150–260°C). These changes, which are called precipitation hardening, in turn influence the thermal properties, making them time as well as temperature dependent. A computer-assisted transient experimental procedure has been developed to determine the values of thermal conductivity of as-received Al-2024-T351 under the influence of precipitation-hardening. Based on isothermal experimental data and related algebraic modeling of the thermal conductivity, a mathematical model in the form of two differential equations is proposed. Instantaneous values of volume fraction of precipitate and thermal conductivity can be predicted using this model. A method for the simultaneous numerical solution of the partial differential equation of conduction and the proposed differential equations of precipitation are also given. The influence of precipitation—hardening on temperature distribution and on values of thermal conductivity is shown graphically for several cases involving the Al-2024-T351 material.