Influence of boiler size and location on one-dimensional two-phase vertical pipe flow

We study the evolution of flow and temperature of a fluid moving upstream in a long, thin vertical pipe when a boiler element is involved. The main goal of this work is to understand how the size and position of the boiler will affect the flow and temperature in the pipe over time, as current literature considers cases where the heater or boiler covers the whole length of the pipe, or when already boiling fluid enters a pipe without a boiler. Therefore, we shall allow for a boiling element which covers only a fraction of the pipe when devising out mathematical model. The boiling process results in a transition to different multiphase flow regimes, and we therefore consider a two-phase flow model. From this model, we obtained a simplified one-dimensional model, since we are concerned with a long, thin pipe, under reasonable assumptions and reductions which still preserve the desired physics. We performed a stability analysis for the boiling boundary denoting the phase change in this model. We then obtained numerical simulations for the steady and transient solutions. The numerical results suggest that both the size and position of the boiler strongly affect the flow regime. In particular, depending on the size of the boiler, transition to other phases might not always occur, and depending on its position along the pipe, the fluid coming out at the top of the pipe might not have the desired thermal profile. As such, one may tailor the position and size of the boiler element in order to obtain a useful thermal profile for particular applications. Such results are of possible relevance in industrial applications where heating or boiling of fluid is required.