Thermal Step Response of N-Layer Composite Walls—Accurate Approximative Formulas

Abstract

For many industrial applications, heat flow through composites relates directly to energy usage and thus is of highest interest. For multilayer composites, the heat flow is a result of multiple variables, such as the temperature gradient over the surface boundaries and each material's thermal conductivity, specific heat, and thickness. In addition, the transient heat flux also depends on how the materials are aligned together. The heat flow through composites can be estimated using advanced computer simulations for applied heat transfer. Although these tools are powerful, they are also time consuming. Therefore, approximations that allow the estimation of heat flow through composites can be very useful. This paper presents approximations to solve transient heat transfer in multilayer composites, with and without an interior surface resistance. Since the energy use for various applications relates to the heat transferred at the surface boundary, the main focus of this paper is to define approximate solutions for interior heat flow. In other words, these approximations are found by applying a unit step change in temperature on one side of a composite and then in real-time emulating the surface heat flux on the opposite side from which the step change occurs. The approximations are presented based on lumped analyses and Laplace network solutions and are validated against analytical and numerical solutions.