Compare the axial heat flux achievable by a heat pipe using water as the working fluid with that of a solid silver rod. Assume that both are 20-cm-long, that the temperature difference for the rod from end to end is 100°C and that the heat pipe operates at atmospheric pressure. State your other assumptions.

Question

GIVEN
? Silver rod and a heat pipe, both 20-cm-long
? End-to-end temperature difference of 100°C
? Heat pipe operates at atmospheric pressure
FIND
(a) Axial heat flux for both rods
ASSUMPTIONS
? Neglect heat pipe vapor pressure drop
? Horizontal operation for the heat pipe
? Perfect wetting of the heat pipe fluid, ? ?= 0
PROPERTIES AND CONSTANTS
From Appendix 2, Table 12, the conductivity for silver at 63°C is ksilver = 424 W/(mK)

Answer 1

The axial heat flux for the silver rod is



With the above assumptions, Equation (9.40) simplifies to



At the operating conditions, water is a satisfactory working fluid. From Figure 9.24, for an operating temperature near 100°C, we have for the figure of merit, M



Rearranging Equation (9.40) to find the heat transport



We have to make some assumptions about the wick material and thickness. Let’s try 120 mesh nickel, with thickness t = 0.01 cm. Table 38 gives for the wick pore radius rc = 0.019 cm and for the wick permeability,



We must also assume a length for the condenser and evaporator sections. Since the total length is 20 cm, a reasonable length for the condenser and evaporator is 8 cm.

Then L = 20 – 8 – 8 = 4 cm and



We can now calculate the heat transport



The heat flux for the heat pipe is therefore





This is slightly more than the heat flux for the silver rod so the performance of the two methods of heat transport seems similar. However, the heat pipe provides two advantages: (i) it will undoubtedly cost much less, and (ii) it is isothermal, that is, the temperature difference from one end to the other will be very small. This means that we can afford some temperature drop at either end of the heat pipe to get the heat from the heat source into the evaporator section and out of the condenser section to the heat

sink.