Improved Lumped Models for a One-Dimensional Nonlinear Heat Conduction Problem

This work reports improved lumped-parameter models for a class of one-dimensional nonlinear heat conduction problems in a slab, cylinder or sphere with linearly temperature-dependent thermal conductivity and subject to combined convective and radiative boundary condition. The improved lumped models are obtained through two point Hermite approximations for integrals. It is shown by comparison with numerical solution of the original distributed parameter models that the higher order lumped models (H_{1, 1}/H_{0, 0} approximation for slab and cylinder, H_{2, 1}/H_{0, 0} for sphere) yield significant improvement of average temperature predictions over the classical lumped model.