Thermal Diffusion of a Two Layer System

TL;DR

This paper presents a theoretical analysis of heat diffusion in a two-layer system, deriving an exact expression for the effective thermal diffusivity based on the properties of individual layers.

Contribution

It introduces a novel theoretical approach to calculate the effective thermal diffusivity of a two-layer system without approximations, considering boundary heat flux conditions.

Findings

Derived an exact formula for effective thermal diffusivity

Analyzed heat flux boundary condition effects

Provided a comprehensive theoretical framework

Abstract

In this paper thermal conductivity and thermal diffusivity of a two layer system is examined from the theoretical point of view. We use the one dimensional heat diffusion equation with the appropriate solution in each layer and boundary conditions at the interfaces to calculate the heat transport in this bounded system. We also consider the heat flux at the surface of the samle as boundary condition instead of using a fixed tempertaure. From this, we obtain an expression for the efective thermal diffusivity of the composite sample in terms of the thermal diffusivity of its constituent materials whithout any approximations.