Modelling and Simulation Investigation of Transient Heat Conduction in Composite Two-Material Rods

Abstract

This study investigated the modeling and simulation of transient heat conduction in composite two-material rods. Since many real-world systems are made of two or more materials with different thermal properties, transient heat conduction in composite materials is a significant issue in thermal engineering. These issues are very challenging to solve analytically and practically. The numerical solutions are therefore unavoidable. Transient heat conduction, in contrast to steady-state conduction, explains how a material’s temperature changes over time in response to changes in its initial or boundary thermal conditions. For the purpose of evaluating thermal stresses, material integrity, energy transfer, and the service performance of engineering systems, it is crucial to accurately predict this temperature evolution. The Crank–Nicolson method and a second-order finite-difference discretization in space were used to systematically formulate the problem. For a composite rod, the standard nondimensional transient conduction model is as follows: ∂Tₐ/∂t = ∂²Tₐ/∂x², 0 ≤ x ≤ 1/2 and ∂Tᵦ/∂t = ∂²Tᵦ/∂x², 1/2 ≤ x ≤ 1. The second material’s relatively high thermal conductivity helps it stay near the normalized temperature of unity. All the results illustrate the gradual transition from the initial non-equilibrium state to the steady thermal state and validate the anticipated physical behavior of transient conduction in a composite rod.