Conditionally Exact Closed-Form Solution for Moving Boundary Problems in Heat and Mass Transfer in the Presence of Advection

Abstract

Moving boundary problems occur in a variety of heat and mass transfer processes. While significant literature already exists on the mathematical analysis of such problems in the presence of diffusion, there is a lack of general solutions for problems in which advective transport of heat/mass due to fluid flow also occurs. This paper presents an error function based analytical solution for a one-dimensional phase change problem in the presence of advection with constant velocity. While this solution is not universally exact, however, a mathematical condition to ensure exactness of the solution is derived. Good agreement with numerical simulations, as well as with past work for special cases is shown. Even outside the condition to ensure exactness, the present method is shown to offer improved accuracy compared to other approximate analytical methods. In particular, the method offers greater accuracy at large value of the Stefan number, where other approximate analytical methods usually perform poorly. The impact of Peclet number that represents advection on the accuracy of the method is investigated. It is shown, as expected, that the t dependence of phase change front propagation is not valid in the presence of advection in general. This work improves the theoretical understanding of an important phase change problem, and may find applications in the design and optimization of engineering processes and systems involving phase change.