Accuracy of lumped-parameter representations for heat conduction modeling in multilayer slabs

Abstract

Heat conduction in homogeneous solids can be studied by resorting to one-dimensional schemes, as is often done, e.g., for building construction elements. In such situations, a simple model often employed makes use of an electrical analogy between temperature and heat flux, on one side, and voltage and electrical current on the other side. Within this framework, a few lumped-parameter representations have been described in literature to describe the thermal behavior of a single homogeneous slab or of multilayer slabs. Such models have the advantage of providing some physical insight into the phenomenon of one-dimensional heat conduction, by conveying the concepts of thermal resistance and thermal capacitance, the latter related to heat storage ability. There is, however, a certain degree of approximation in such models. The simplifying assumptions and approximations underlying these approaches will be reviewed and discussed in this contribution.The accuracy of some lumped-parameter model will be analyzed in order to show under which circumstances the approximate solutions can be satisfactorily employed. In particular, the focus will be on the comparison of the predictions that approximate and accurate methods provide when studying the influence of layer order and distribution on the thermal performance of multilayer structures.