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"Phase-Change Problems"
Abstracts:
1. SUFFICIENTS CONDITIONS TO OBTAIN A PHASE CHANGE IN A
HEAT CONDUCTION PROBLEM WITH A CONVECTIVE BOUNDARY CONDITION
María Cristina Sanziel
Universidad Nacional de Rosario - Argentina
e-mail: sanziel@fceia.unr.edu.ar
We consider a one-dimensional heat conduction problem in a slab of length L,
with initial temperature greater than the phase-change temperature. There is
a heat flux condition on one of the edges and a convective condition on the
other. Through a finite difference method we obtain a discrete problem and we
show that the solution of this discrete problem converges to the solution of
the discrete problem with temperature condition, when the heat transfer coefficient
tends to infinity. We also obtain sufficient conditions in order to have a phase
change in the discrete problem.
2. Phase change in metal alloys solidification.
Mabel Azucena Medina
Universidad Nacional de Rosario - Argentina
e-mail: mmedina@fceia.unr.edu.ar
A two-dimensional solidification model which calculates the velocity field
of the liquid phase, the temperature, the alloy solute composition and the volume
liquid fraction, is presented. The influence of convection on the metal alloy
solidification is studied, in particular, on the solute segregation and on the
solid-liquid boundary. Electromagnetic body forces are implemented. The equations
for conservation of energy with phase change, momentum, and solute are solved
by the finite element technique.
It is showed that the action of an electromagnetic field, by controlling the
flow, changes the distribution of the solute concentration field and modifies
the location of the solid liquid boundary. The prediction of the model is sensitive
to mesh sizes.
3. NON-ESSENTIAL BLOW-UP FOR THE SUPERCOOLED STEFAN PROBLEM
WITH CYLINDRICAL SYMMETRY
Pedro Roberto Marangunic
Instituto de Matemática “Beppo Levi”
Facultad de Ciencias Exactas, Ingeniería y Agrimensura
Universidad Nacional de Rosario
Av. Pellegrini 250 - (2000) Rosario
E-mail: pmarangu@fceia.unr.edu.ar
By means of the well-known relationship between the one-phase supercooled Stefan
problem and that one describing the oxygen diffusion-consumption in living tissues,
it is possible to analyze more deeply the solution’s behaviour in cases
in which blow-up occurs. This task, either for the one-dimensional case or for
plane symmetry, was performed by other authors [1]. Here we do an analogous
analysis considering cylindrical symmetry, a more realistic assumption for the
blood vessels surrounds. We prove that non-essential blow-up cases are possible,
i.e. cases in which the free boundary can actually have isolated singularities
although they do not prevent the continuation (with a proper redefinition) of
the solution, in order to describe phase change to completion.
For the sake of definiteness, if we have a cylindrical domain given by 
,
and h is
a given non-positive function in
(and there it does not vanish identically), we
consider the one-phase supercooled Stefan problem in conditions of isolated
fixed boundary, i. e. the problem which consists of finding a triple 
satisfying
the following conditions:
in 
(1.1)
(1.2)
(1.3)
(1.4)
(1.5)
(1.6)
in (1.7)
(1.8)
(1.9)
(1.10)
(1.11)
.
On the other hand, the
change 
takes the second problem into the
first one.
Physically, as its analogous version for plane symmetry, the system (1.1)-(1.5)
modelizes the solidification of a supercooled liquid (one-phase case). Besides
its intrinsic interest as a metaestable phenomenon, this subject is related
to a variety of problems, for instance the above cited oxygen diffusion-consumption
problem (1.7)-(1.11), or even that corresponding to the filtration of a liquid
in a partially saturated porous medium [2].
When problem (1.1)-(1.5) has a solution, it is
worth asking about the possibility of continuing the solution to arbitrarily
large time intervals. It is well-known that one of the following three cases
occurs:
(A) Global existence: the problem has a solution with arbitrarily large T ;
(B) Finite time extinction of the liquid phase: there is a constant 
such that 
;
(C) Blow-up: there is a constant 
such that 
and 
.
Several papers (see [3]) are devoted to study the relationship between
these 3 cases and the problem’s data. There it was obtained that an integral,
which involves the initial datum and represents an energy, allows predicting
the solution’s type.
Let us notice that in the case
(C) the solution is suddenly interrupted because of a singularity of the free
boundary. However, in [1] it is considered an idea for the possible continuation
of solutions beyond the blow-up time 
. They put the limit of the temperature (when 
) as a new initial temperature, and then they analyze whether the “new”
problem (for 
) admits a solution or not. In negative (affirmative) case they refer the
situation as a proper or essential blow-up (resp. non-essential
blow-up). In the affirmative case the solution can be continued beyond , and they explicitly construct a specific example in which the solution
exists for all times, but the free boundary has an isolated singularity.
In the present communication we adapt those ideas
to our conditions of cylindrical symmetry. First, we prove that if 
is nonvoid, necessarily 
will
“touch” the free boundary after a finite time. Then, we characterize the essential
blow-up points as such points in which meets
the free boundary.
By controlling the so-called critical isotherms,
we finally provide a specific example of non-essential blow-up. In other words,
we prove the existence of data for which we have a blow-up in the problem (1.1)-(1.5)
but not in the problem (1.7)-(1.11). Indeed, the last one admits global solution
(and obviously the function
is non-negative).
4. NUMERICAL SIMULATION OF A STEFAN PROBLEM FOR PACKAGING
SUBSTANCES
Mariela Carina Olguín
Universidad Nacional de Rosario - Argentina
e-mail: mcolguin@fceia.unr.edu.ar
There are a lot of situations, for example the transport of foods products,
environment's conditioning, etc, where it is necessary to guarantee temperature
and humidity conditions. The use, in the packaging, of substances that present
a change of phase in an appropriate range of temperature for a particular
problem, could be considered with the object to keep those conditions.
For this reason, in the present work, we analyze the behavior of different substances in order to estimate how long does the substance take to melt it completely. The numeric simulation of the problem is based upon the use of finite difference method of implicit type.
5. The use of phase change materials in thermal building conditioning
Angélica Boucíguez
Universidad Nacional de Salta - Argentina
e-mail: bouciga@unsa.edu.ar
The thermal building conditioning consumes a lot of energy, which is generated
by traditional forms. There are several alternatives to reduce this consume,
one of them is the use of no conventional energy. Among these the solar energy
plays an important role in the thermal conditioning.
The use of phase change materials as an integral part of storage collector
walls, provides an interesting alternative in passive solar conditioning of
building. They can be used in collector - storage wall, as an adaptation of
the classic Trombe wall panels.
The phase change materials can be used together with traditional building
materials such as gypsum and concrete, as part of plaster of covering of walls
and/or ceiling. Besides, they also can be used in pure state, in storage collector
walls.
The substitution of classical walls by phase change materials allows to storage
the same or a bigger quantity of energy with smaller weight and volume than
those of traditional walls.
These materials will have their melting point at an adequate temperature,
into the confort range design.
In the selection of phase change materials it is necessary to consider the
following properties:
