# Merit Number and Fluid Selection

Why is water the most commonly used heat pipe fluid, and ammonia used for spacecraft thermal control?  The reason is that they are the best heat pipe working fluids for their respective temperature ranges.

Heat pipes fluids are ranked by the Merit number: where
ρl                     Liquid density
σ                      Surface tension
λ                      Latent heat
μl                     Liquid viscosity

High liquid density and high latent heat reduce the fluid flow required to transport a given power, while high surface tension increase the pumping capability.  A low liquid viscosity reduces the liquid pressure drop for a given power.  The Merit number is derived below. Figure 3. Merit Number for Commonly Used Heat Pipe Working Fluids.

The Merit number as a function of temperature is shown in Figure 3 for a number of typical heat pipe working fluids.  From the figure, it is very clear why water is chosen as the heat pipe working fluid whenever possible.  Its Merit number is ~10 times higher than everything else except the liquid metals, meaning that it will carry ten times more power (in the proper temperature range) than other working fluids.

Ammonia is chosen for spacecraft heat pipes, since it has the highest Merit number (roughly 3 times less than water) in their typical operating temperature range.   Methanol is generally the working fluid of choice when ammonia and water are not suitable, since it has the third highest Merit number near ambient conditions.

## Merit Number Derivation

The amount of power that a heat pipe can carry is governed by the lowest heat pipe limit at a given temperature.  For a given heat pipe, the Merit number ranks the maximum heat pipe power when the heat pipe is capillary limited.  (The capillary limit generally controls the power in the mid-range, while other limits control at higher and lower temperatures).

The capillary limit is reached when the sum of the liquid, vapor, and gravitational pressure drops is equal to the capillary pumping capability: The Merit number neglects the vapor and gravitational pressure drops, and assumes that the capillary pumping capability is equal to liquid pressure drop. The equation for the liquid pressure drop in a heat pipe is: Where

ΔPl                 Liquid Pressure Drop, assumed equal to the wick pumping capability
LEffective          Effective Length
kwick              Wick permeability
Awick             Wick Area

The mass flow rate is the heat transfer rate divided by the latent heat: The wick pumping capability is: Where rc is the pore radius.

Combining the three equations and solving for Q, the maximum heat transfer when only the liquid pressure drop is considered becomes: Where the first term consists of heat pipe and wick properties, and the second term is the Merit Number.

Note that the Merit number only ranks fluids based on the capillary limit.  Close to the triple point, the sonic limit or viscous limit control the heat pipe power.