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Calculations
and Examples
The following is an example of the equations and process
followed for a complete cycle of the working fluid within a
heat pipe.Step 1:
Working fluid sits in liquid form in the ground, which is warmer than the air at the top of the heat pipe. Heat is transferred via conduction (direct contact of particles) from the ground, to the metal surrounding the heat pipe, and then into the working fluid also via conduction.
Thermodynamics by Cengle and Boles, 8th Edition
The above diagram shows an example of convection similar to what would happen in a heat pipe. Except instead of air transferring through metal to soda, the ground transfers through metal to the working fluid.
Step 2:
As the fluid heats, it will eventually boil and evaporate. In doing so, it has removed heat (energy) from the ground surrounding it.
Q=n*Cv*T
Where Q= heat (in joules), n = number of moles of working fluid, Cv = the molar specific heat at constant volume for the working fluid (this is a constant specific to the fluid) and T= the change in temperature of the fluid.
So, for example, lets say we wish to reduce the temperature of surrounding ground by 1 degree Celsius. For examples sake, we will say we have 25 moles of ground we wish to cool. (In reality the ground is contentious, and so more is involved in the heat transfer, but for this examples sake we will simplify the problem, as the idea stays the same.) We will also say that the specific heat at constant volume for this ground is 50J/(n*k) = Cv. For the working fluid, lets say we have 1 mole, and the Cv(ammonia)= 28J/(n*k). The heat transfer from the dirt must equal the heat transfer into the working fluid.
n(ground)*Cv(ground) *T(ground) = n(fluid)*Cv(fluid)*T(fluid)
Plugging in,
(25n)(50 J/(n*k))(1K)=(1n)(28J/(n*k)(T(ammonia)
T(ammonia)= 44.6 Kelvin = 44.6 Celsius
So, we can see that to cool this amount of ground, the ammonia increases in temperature greatly. In doing such it evaporates and rises up within the heat pipe, just like boiling water on a stove.
Step 3:
Now that the ammonia is in a gaseous state and has risen to the top, it is in contact with the cooling fins. These cooling fins are also in contact with the surrounding air, which is much colder than the ammonia, as well as the ground. Energy is now transferred from the warm ammonia, into the metal, and into the cold air in the exact same way it was transferred from the ground into the ammonia at the start of the process. As the ammonia cools and energy is removed from it, it will condense back into liquid form due to its lower energy level. At this point it now falls back to the bottom of the heat pipe from the force of gravity now acting on the much larger droplets of liquid water as compared to the gaseous ammonia. When the liquid ammonia reaches the bottom, the cycle repeats and the ground continues to be cooled until there is a temperature equilibrium between the ground and air, or until the air is of higher temperature than the ground, which will prevent the ammonia from being able to cool, should it be evaporated by heat from the ground.
As we can see, temperature difference is the driving force in this cycle, and no outside energy or work is needed to aid or control the process. Further cooling could take place with the use of an electric refrigeration unit, but for a system requiring no additional energy, heat pipes are very effective.