Identification of thermal conductivities by temperature gradient profiles: one-dimensional steady state flow

The comparison model method (CMM) is applied to the identification of spatially varying thermal conductivity in a one-dimensional domain. This method deals with the discretized steady-state heat equation written at the nodes of a lattice, a lattice which models a stack of plane parallel layers. The required data are temperature gradient and heat source (or sink) values. The unknowns of this inverse problem are not nodal values but internode thermal conductivities, which appear in the node heat balance equation. The main advantage of the CMM is its simple algebraic formulation. Its implementation in the field by means of a pocket calculator allows both a consistency check on the data being collected and estimates of the unknown values of conductivity. -from Authors