Question 10.21: KNOWN: Boiling water at 1 atm pressure on moon where the gra......
KNOWN: Boiling water at 1 atm pressure on moon where the gravitational field is 1/6 that of the earth.
FIND: Critical heat flux.
ASSUMPTIONS: Nucleate pool boiling conditions.
PROPERTIES: Table A-6, Water (1 atm): \mathrm T_{\text{sat}} = 100°C, ρ_{\ell} = 957.9 kg/m³, ρ_{\mathrm v} = 0.5955 kg/m³, \mathrm h_{\mathrm{fg}} = 2257 kJ/kg, σ = 58.9 × 10^{-3} N/m.
ANALYSIS: The modified Zuber-Kutateladze correlation for the critical heat flux is Eq. 10.7.
q _{\max }^{\prime \prime} = 0.149 \rho_{ v }^{1 / 2} h _{ fg }\left[\sigma g \left(\rho_{\ell}-\rho_{ v }\right)\right]^{1 / 4}.
The relation predicts the critical flux dependency on the gravitational acceleration as
q _{\max }^{\prime \prime} ∼ g^{1/4}.
It follows that if \mathrm g_{\text{moon}} = (1/6) \mathrm g_{\text{earth}} and recognizing \mathrm q_{\max,\mathrm e}^{\prime\prime} = 1.26 MW/m² for earth acceleration (see Example 10.1),
q _{\max , \operatorname{moon}}^{\prime \prime}= q _{\max ,\text{earth }}^{\prime \prime}\left( g _{\operatorname{moon}} / g _{\text {earth }}\right)^{1 / 4}
q _{\max ,\operatorname{moon}}^{\prime \prime}=1.26 \frac{ MW }{ m ^2}\left\lgroup \frac{1}{6}\right\rgroup^{1 / 4}=0.81 MW / m ^2.
COMMENTS: Note from the discussion in Section 10.4.5 that the g1/4 dependence on the critical heat flux has been experimentally confirmed. In the nucleate pool boiling regime, the heat flux is nearly independent of the gravitational field.