Page 235 - Introduction to Computational Fluid Dynamics

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7 Phase Change May 25, 2005 11:14

7.1 Introduction

There is hardly a product that, during its manufacture, does not undergo a process of
melting and solidification. Engineering processes such as casting, welding, surface
hardening or alloying, and crystallisation involve phase change. The processes of
freezing and thawing are of interest in processing of foods. Phase-change materials
(PCMs) are used in energy storage devices that enable storage and retrieval of
energy at nearly constant temperature.
The phenomenon of melting or solidification is brought about by a process
of latent heat (λ) transfer at the interface between solid and liquid phases. For a
pure substance, throughout this process, the temperature T m (melting point) of the
interface remains constant whereas in the liquid and solid phases, the temperatures
vary with time. Both λ and T m are properties of a pure substance. Within each of
the single phases, heat transfer is essentially governed by a process of unsteady heat
conduction, although, under certain circumstances, convection may also be present
in the liquid phase under the action of body (buoyancy, for example) or surface
(surface tension) forces.
There are two approaches to solving phase-change problems:

1. the variable domain formulation and
2. the fixed domain (or fixed-grid) formulation.
In the first approach, which has several variants, two energy equations are solved
in the solid and the liquid phases with temperatures T s and T l , respectively, as
dependent variables. In addition to the initial (i.e., at t = 0) and the domain bound-
ary conditions, the following interface conditions are also invoked to match the
temperatures of the two phases:
T s = T l = T m , (7.1)

∂T s ∂T l
k s − k l = ρλV i , (7.2)
∂n ∂n
i i
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