COMPUTER-AIDED CALCULATION OF APPROXIMATE CLOSED-FORM SOLUTIONS FOR LINEAR TRANSIENT HEAT-CONDUCTION PROBLEMS IN MULTILAYERED BODIES

A solution procedure, based on the Kantorovich method, is presented fo r the derivation of approximate closed-form solutions for linear heat conduction problems in multilayered plane and cylindrical bodies using computers. Constant or space dependent initial conditions; linear tim e dependent boundary conditions of the first, second, or third kind; c ontact resistances between the layers; and a homogeneous distributed t ime dependent volumetric heat source can be considered. The solution p rocedure is shown suitable for programming. In order to assess the app roximate solution obtained, an error criterion is stated. The accuracy of the method is investigated through a numerical and an analytical e xample.