Heat Transfer

The primary methods of heat transfer within a heat pipe are conduction and convection. Inside of the pipe, the evaporation and condensation of water in different regions causes the build up of a pressure gradient. This gradient forces water vapor to move toward the condenser end of the pipe before recycling through capillary action back to the evaporator end. This thereby creates a constant cycle of heat transfer via rapidly moving steam. As the water vapor condenses on the copper wick and the walls of the condenser region, the latent heat held by the vapor is released into the copper where it then is transferred to the exterior of the pipe and the heat sink via conduction. Upon reaching the exterior of the pipe, the convection of air around the pipe takes heat from the pipe and disperses it in the surrounding atmosphere.

Modeling Maximum Power Output

The thermal power output of the heat pipe design can be modeled as a combination of heat transfer mechanisms using the equation below. In this equation, q is the heat flow in watts, ΔT is the overall difference in temperature between the interior and exterior of the pipe, and ΣR is the sum of the all the thermal resistances of each heat transfer mechanism in the pipe. In the case of this heat pipe, thermal resistances will need to be calculated for the internal convection, the copper pipe conduction, the aluminum heatsink conduction, anCad the external, atmospheric convection.

The thermal resistance of the copper pipe is found by R=ln(ro/ri)/2πkL where ro is the outer diameter of the pipe, ri is the inner diameter of the pipe, k is the thermal conductivity of copper, and L is the length of the condensing region of the pipe (the location where most heat is released). The thermal resistance of the internal and external convections are found by R=1/hA where h is the heat transfer coefficient of the convecting fluid and A is the surface area of the pipe that is in contact with the source of convection. [4]

The thermal resistance of the heat sink is more difficult to calculate due to its unusual shape. At the moment, we are unable how to account for the heat sink and can only complete the power output calculation by assuming its resistance is negligible and only acts to increase the surface area for external convection.

Heat Pipe Performance Limitations

Capillary Limit

The most common limiting factor in low temperature heat pipes, like the one being designed for this project, it the capillary limit of the wicking material. When the wicking material cannot return condensed working fluid to the evaporator fast enough, the evaporator can dry out. If this limit is reached, the evaporator will rapidly begin to heat up as heat cannot be quickly transferred to the condenser. [7]

Sonic Limit

The velocity of the vapor flowing inside of the pipe cannot exceed the local speed of sound of the inside of the pipe. This limit is not usually encountered within low temperature heat pipes unless the condenser is transferring extremely large amounts of heat. [7]

Boiling Limit

If the evaporator is heated too much, the water in contact with the walls and wick can boil and create bubbles of vapor around the walls. These bubbles can prevent the internal liquid from getting to the walls of the pipe, thereby decreasing the rate of vaporization of the working fluid. This limit is characterized by hot spots in the evaporator section of the pipe. [7]

Condenser Heat Transfer Limit

The condenser can only remove heat from the pipe at a certain rate. If the maximum heat transfer rate between the evaporator and condenser exceeds the rate of dissipation at the condenser, the overall heat transfer rate will be limited to the rate of the condenser. [7]

Entrainment Limit

In heat pipes with small diameters operating at low temperatures, the convecting vapor can launch droplets from the wick back up toward the condenser. This limits the flow of fluid back to the evaporator and can cause the evaporator to dry out. [7]