In this Section, we were introduced to transient thermal analysis and learned about additional
material properties related to these analyses (analy-seez) such as specific heat, thermal
capacitance etc. We also looked at a few practical applications of transient thermal analysis.
Now, suppose you take a solid block of butter and heat it in a pan. After about a minute of heating,
the temperature of the butter and the pan increases, as dictated by the principles of
transient thermal analysis. But there is something else that we observe which hasn’t been discussed
until now. We see that the solid block of butter has turned to liquid and is flowing freely in
the pan. This transition of matter from one phase to another is known as phase change.
Matter exists primarily in three phases – solid, liquid or gas and the transitions from one phase
to another have different names. In the example we saw, the butter went from a solid phase to a
liquid phase. This process is known as melting. If the liquid butter is kept in the fridge, it will
turn into a solid again. This process is known as solidification. We also see the melting process
when a wax candle is lit, and when the candle is blown the liquid wax solidifies again.
The transition from liquid phase to gas is known as boiling. The most common example of boiling we
come across is when we see steam rising from a vessel in which water is being heated. The
steam is water in gaseous form. The reverse process is known as condensation. When we walk
on a lawn in the early morning, we find that the grass is wet. This happens because water vapor
from the atmosphere condenses during the cold night, and deposits dew drops on the grass.
The transformation of a substance from solid phase to gaseous phase, without passing through
the liquid phase, is known as sublimation and the reverse process is known as deposition. You
might have noticed that the naphthalene balls or mothballs that are used in cupboards reduce in
size over time. This is because naphthalene sublimes and turns into gaseous state,
thereby disappearing slowly. Phase change generally occurs at a
constant temperature when the pressure is constant. This constant temperature
has different names based on the process, e.g. boiling point, melting point etc.
So how exactly does phase change occur? To answer this, let’s get to the atomic scale and look at
the arrangement of molecules in various phases. The molecules vibrate about their mean positions
in solids, slide over one another in case of liquids and move about freely in case of gases.
Thus, gases have the most energy, while solids have the least amount of energy. When a material
is heated, the energy of its molecules increases. As more heat energy is added to a solid material,
at a certain temperature, the molecules have enough energy to overcome intermolecular forces,
and transition to a liquid. This process is known as melting and the temperature at which
this process occurs is called the melting point. Further, if we keep adding heat, at a certain
temperature, the molecules in the liquid will have enough energy to transition to a gas. This
process is called boiling, and the transition temperature is called the boiling point.
The amount of energy required to change the phase of a material is known as the enthalpy,
or latent heat for that phase change. Its SI unit is joule. Heating a solid causes its
molecules to vibrate more, thereby increasing the temperature of the solid (as predicted by
its specific heat). When temperature of the solid reaches its melting point, adding more
heat does not change the temperature because all the energy goes into melting the solid. Thus,
phase generally occurs at a constant temperature. Once the solid has completely transitioned to the
liquid phase, adding more heat will increase the temperature of the liquid. A few exceptions exist,
for example amorphous solids do not have ordered internal structures, and hence do not have a
sharp melting point. But in most practical cases, phase change occurs at a constant temperature.
The amount of heat required to melt the solid completely in known as the enthalpy of melting
or latent heat of melting. The enthalpy of solidification is numerically equal to the
enthalpy of melting. But enthalpy of melting is positive since heat is added to the system,
while enthalpy of solidification is negative since heat is removed from the
system to cool the liquid. The temperature at which phase change occurs in a given material,
depends on the pressure. For example, water boils at 100 C at atmospheric pressure, but boils at 120
C in a pressure cooker due to the higher pressure. Since the water reaches higher temperatures in a
pressure cooker, the food cooks faster. Now that we understand phase change and the
physical meaning of enthalpy, let us simulate a phase change in ANSYS Mechanical. When modeling a
phase change, enthalpy is an additional material property that we need to define. Up until now,
and in most textbooks, enthalpy is defined as the energy absorbed or released by a body to
undergo phase change i.e. its SI unit is joule. But in simulations, this definition is modified
to be the energy absorbed by a “unit volume” of a body. So it has dimensions of energy/volume and
its SI unit is joule/m^3. In theory, enthalpy can be calculated from the specific heat, c,
and the density of the material, by calculating the this integral. However, for accuracy,
we define an enthalpy curve which specifies the enthalpy at different temperatures.
Now we will simulate the freezing of water into ice in a freezer. This is the geometry
that we have. It consists of a plastic ice tray filled with water. Let’s say the water
is initially at 10 C. The freezer is maintained at a constant temperature
of -5 C. The freezing point of water is 0 C. We have certain information about water and ice.
We know that its melting or freezing point is 0 C and its density is 997 kg/m^3. The specific heat
for ice is about 2100 J/kg-C and that for water is about 4200 J/kg-C. The enthalpy of melting is
334,000 J/kg. Based on this information we first need to define an enthalpy-temperature curve.
Let’s say the enthalpy is 0 at -100C. Instead of a distinct melting point at 00C, let’s assume
melting starts at -10C and ends at 10C to avoid abrupt, steep changes in enthalpy. The enthalpy at
-1 C is the sum of the enthalpy at -10 C and the product of density, specific heat of ice and the
temperature difference. Further, the enthalpy at 1 C is equal to the sum of enthalpy at -1 C plus
the product of density and enthalpy of melting. Finally enthalpy at 20 C is the sum of enthalpy
at 1 C and the product of density, specific heat of water and the temperature difference. The
figure here shows the enthalpy-temperature curve that we will be defining in ANSYS Mechanical.
So now that we have an enthalpy-temperature curve, let’s see how to apply the boundary conditions.
The initial temperature of the water and the ice tray is defined to be 10 C. We define a step
which 10000 s or about 2 hr 47 minutes long. Now we need to simulate the fact that heat is
being lost from the water and the ice tray to the cold air in the freezer. So we apply a convection
boundary condition on the surfaces of the ice-tray and the surfaces of the water, that are in contact
with the cold freezer air. We assume a film coefficient of 30 W/m^2-C. The ambient temperature
of the freezer is assumed to be –5 C. After solving the system, we use contour
plots with customized levels to observe the progress of solidification. The red color
indicates liquid phase, green color indicates transition while blue color indicates solid phase.
We see that water starts freezing from the outer surfaces and the freezing progresses inwards. At
about 6620s, I.e. after about 1 hour 50 minutes, the water solidifies completely into ice.
In addition, if we plot the variation of the average temperature of water with time,
we find that the temperature remains almost constant at 00C when the water
undergoes freezing. Thus, heat removed from water during this time does not reduce the
temperature of the water but is in fact spent in transforming the water to ice.
In addition to the examples we saw previously, melting and solidification processes have
important industrial applications. For example, solder is melted and solidified quickly to connect
various electronics parts. Casting is a process in which molten metal in liquid phase is poured into
a mold and cooled down, to get a solid body with desired shape. 3D printing is a type of additive
manufacturing method which involves depositing material in liquid phase layer-by-layer,
and allowing it to cool down to form complex solid shapes. Thus, it is essential to
understand phase change in order to simulate such industrial processes accurately.