Improved lumped models for asymmetric cooling of a long slab by heat convection

Unsteady cooling of a long slab by asymmetric heat convection is analyzed within the framework of lumped parameter model. As the application of classical lumped model is limited to values of Biot numbers less than 0.1075, we propose improved lumped models that can be applied in transient heat conduction with larger values of Biot numbers. The proposed lumped models are obtained through two point Hermite approximations for integrals. Closed form analytical solutions are given for the lumped models. It is shown by comparison with a reference finite difference solution of the original distributed parameter model that the proposed higher order lumped model (H1,1/H0,0 approximation) yields significant improvement of average temperature prediction over the classical lumped model.