Question 10.16: KNOWN: Nickel wire passing current while submerged in water ......
KNOWN: Nickel wire passing current while submerged in water at atmospheric pressure.
FIND: Current at which wire burns out.
ASSUMPTIONS: (1) Steady-state conditions, (2) Pool boiling.
SCHEMATIC:
ANALYSIS: The burnout condition will occur when electrical power dissipation creates a surface heat flux exceeding the critical heat flux, \mathrm q_{\max}^{\prime\prime}. This burn out condition is illustrated on the boiling curve to the right and in Figure 10.6.
The criterion for burnout can be Expressed as
\mathrm q _{\max }^{\prime \prime} \cdot \pi \mathrm D = \mathrm q _{\text {elec }}^{\prime} ~~~~\quad~~~~\mathrm q _{\text {elec}}^{\prime}= \mathrm I ^2 \mathrm R _{\mathrm e}^{\prime}. (1,2)
That is,
\mathrm I =\left[\mathrm q _{\max }^{\prime \prime} \pi \mathrm D / \mathrm R _{\mathrm e}^{\prime}\right]^{1 / 2}. (3)
For pool boiling of water at 1 atm, we found in Example 10.1 that
\mathrm q _{\max}^{\prime \prime} = 1.26 MW/m^2.
Substituting numerical values into Eq. (3), find
\mathrm I =\left[1.26 \times 10^6 W / m ^2(\pi \times 0.001 m ) / 0.129 \Omega / m \right]^{1 / 2}=175 A.
COMMENTS: The magnitude of the current required to burn out the 1 mm diameter wire is very large. What current would burn out the wire in air?
