Thermophysical continuous profiles and their discretization

• Published in: International journal of thermal sciences 2011-11, Vol.50 (11), p.2078-2083
• Main Authors: Grossel, Ph, Depasse, F.
• Format: Article
• Language: English
• Subjects: Condensed matter: structure, mechanical and thermal properties; Continuous profiles; Discretization; Exact sciences and technology; Exact solutions; Iterative methods; Mathematical analysis; Mathematical models; Multilayers; Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves; Physics; Riccati equation; Solvents; Thermal quadrupoles; Thermal waves; Thermophysical; Transport properties of condensed matter (nonelectronic)
• ISSN: 1290-0729; 1778-4166
• DOI: 10.1016/j.ijthermalsci.2011.03.031

Most of the time the surface of materials presents profiles of physical properties that are variable along the depth. The heat diffusion equation of current thermophysical profiles rarely accepts analytical solutions that can be introduced in a rapid minimization scheme. A thermal Riccati equation is defined in case of any continuous profiles, the solutions of which are shown to be the limit of the exact solutions for simple staircase multilayer modellings when the layers are taken thinner and thinner. Thanks to the use of iterative methods based on the thermal wave or the quadrupole descriptions, it is shown that the choice of the multilayer approach to describe continuous depth profiles of materials leads to exact solutions of the problem. ► The Riccati and the heat equations for thermophysical continuous profiles. ► Solutions of the Riccati equation reveals an iterative structure within depth. ► A numerous thin multilayer can be used with great confidence for the continuous case.