Theoretical solution of transient heat conduction problem in one-dimensional double-layer composite medium

Abstract

To make heat conduction equation embody the essence of physical phenomenon under study, dimensionless factors were introduced and the transient heat conduction equation and its boundary conditions were transformed to dimensionless forms. Then, a theoretical solution model of transient heat conduction problem in one-dimensional double-layer composite medium was built utilizing the natural eigenfunction expansion method. In order to verify the validity of the model, the results of the above theoretical solution were compared with those of finite element method. The results by the two methods are in a good agreement. The maximum errors by the two methods appear when τ (τ is nondimensional time) equals 0.1 near the boundaries of ξ =1 (ξ is nondimensional space coordinate) and ξ =4. As τ increases, the error decreases gradually, and when τ =5 the results of both solutions have almost no change with the variation of coordinate ξ.

Keywords

composite medium / transient heat conduction / theoretical solution / natural eigenfunction expansion method