Lumped-parameter model for the retorting of a large block of oil shale with an internal temperature gradient

A lumped-parameter model which combines the internal and external heat transfer resistances was proposed for the retorting of a large block of oil shale. In this model the temperature of oil-shale block is obtained by solving the ordinary differential equation of energy balance using an overall heat transfer coefficient U, where U is equal to h/(1 + Bi/5). The results of this model were compared with those of the uniform-temperature model which uses the external heat transfer coefficient h, instead of U, in the energy balance equation and of the rigorous model which calculates the block temperature profile more rigorously by a partial differential equation. The comparison showed that the lumped-parameter model is much better than the uniform-temperature model and is a useful alternative to the rigorous model for modelling the retorting of a large block of oil shale with an internal temperature gradient.