An algorithm for solving steady-state heat conduction in arbitrarily complex composite planar walls with temperature-dependent thermal conductivities

Abstract

An algorithm for solving steady-state heat conduction problems in arbitrarily complex composite walls is presented. Per se, steady-state heat conduction across a wall can easily be solved by hand. Yet, in practical applications the wall structure is often complex enough to deter such an approach if a finer yet simple analysis of the thermal bridges is of interest. Moreover, if high-temperature applications are involved, the additional complexity of including time-dependent thermal conductivity must be considered. Thus, a general methodology for solving arbitrary topology walls, involving any kind of thermal resistances in series and in parallel is discussed. While such a problem is formally simple to solve for a given wall following the theory, its algorithmic generalization is not. A method is provided, involving a program written in python language. The focus of the work is mainly on the algorithmic point of view: a simple way for the assessment of the wall topology and for the resolution of the heat conduction problem originating is sought. Temperature-dependent thermal conductivity of the materials is addressed, resulting in the need of evaluating the heat fluxes and the average temperature at each thermal resistance.