Improved lumped models for transient heat conduction in a slab with temperature-dependent thermal conductivity

This work reports improved lumped-parameter models for transient heat conduction in a slab with temperature-dependent thermal conductivity. The improved lumped models are obtained through two point Hermite approximations for integrals. For linearly temperature-dependent thermal conductivity, it is shown by comparison with numerical solution of the original distributed parameter model that the higher order lumped model (H1,1/H0,0H1,1/H0,0 approximation) yields significant improvement of average temperature prediction over the classical lumped model. A unified Biot number limit depending on a single dimensionless parameter ββ is given both for cooling and heating processes.