Improved lumped models for transient combined convective and radiative cooling of multi-layer composite slabs

Improved lumped parameter models were developed for the transient heat conduction in multi-layer composite slabs subjected to combined convective and radiative cooling. The improved lumped models were obtained through two-point Hermite approximations for integrals. Transient combined convective and radiative cooling of three-layer composite slabs was analyzed to illustrate the applicability of the proposed lumped models, with respect to different values of the Biot numbers, the radiation-conduction parameter, the dimensionless thermal contact resistances, the dimensionless thickness, and the dimensionless thermal conductivity. It was shown by comparison with numerical solution of the original distributed parameter model that the higher order lumped model yielded significant improvement of average temperature prediction over the classical lumped model. In addition, the higher order model was applied to analyze the transient heat conduction problem of steel-concrete-steel sandwich plates.