Operator splitting approach applied to oscillatory flow and heat transfer in a tube

The method of operator splitting is applied to an advection–diffusion model as it occurs in a pulse tube. Firstly, the governing equations of the simplified model are studied and the mathematical description is derived. Then the splitting approach is used to separate the advection and the diffusion part. Now it turns out that the advective part can be solved analytically and therefore the computational cost are reduced and the accuracy is increased. It is shown that the method can model an effect called Taylor dispersion. Applying a domain decomposition strategy, the solution process can be decoupled, reducing the numerical cost even more. This procedure allows to study the relevant parameters within the model with the goal to maximize the amount of energy stored within the tube wall. As a measure of efficiency, the amount of energy transferred between the fluid phase and the wall is chosen.