Question 10.9: KNOWN: Fluids at 1 atm: mercury, ethanol, R-12. FIND: Critic......
KNOWN: Fluids at 1 atm: mercury, ethanol, R-12.
FIND: Critical heat flux; compare with value for water also at 1 atm.
ASSUMPTIONS: (1) Steady-state conditions, (2) Nucleate pool boiling.
PROPERTIES: Table A-5 and Table A-6 at 1 atm,
| \mathrm h_{\mathrm{fg}} | \rho_{\nu} | \rho_{\ell} | \sigma \times 10^3 | \mathrm T_{\text{sat}} | |
| (kJ/kg) | (kg/m³) | (N/m) | (K) | ||
| Mercury | 301 | 3.90 | 12,740 | 417 | 630 |
| Ethanol | 846 | 1.44 | 757 | 17.7 | 351 |
| R-12 | 165 | 6.32 | 1,488 | 15.8 | 243 |
| Water | 2257 | 0.596 | 957.9 | 58.9 | 373 |
ANALYSIS: The critical heat flux can be estimated by the modified Zuber-Kutateladze correlation, Eq. 10.7,
q _{\max }^{\prime \prime}=0.149 h _{ fg } \rho_{ v }\left[\frac{\sigma g \left(\rho_{\ell} ~ -~ \rho_{ v }\right)}{\rho_{ v }^2}\right]^{1 / 4}.
To illustrate the calculation procedure, consider numerical values for mercury.
q _{\max }^{\prime \prime}=0.149 \times 301 \times 10^3 J / kg \times 3.90 kg / m ^3 \times \left[\frac{417 ~\times ~10^{-3} N / m ~\times~ 9.8 m / s ^2(12,740 ~-~ 3.90) kg / m ^3}{\left(3.90 kg / m ^3\right)^2}\right]^{1 / 4}
q _{\max }^{\prime \prime}= 1.34 MW/m^2.
For the other fluids, the results are tabulated along with the ratio of the critical heat fluxes to that for water.
COMMENTS: Note that, despite the large difference between mercury and water properties, their critical heat fluxes are similar.
| Flluid | \mathrm q_{\max}^{\prime\prime} (MW/m²) | \mathrm q_{\max}^{\prime\prime}/\mathrm q_{\max,\text{water}}^{\prime\prime} |
| Mercury | 1.34 | 1.06 |
| Ethanol | 0.512 | 0.41 |
| R-12 | 0.241 | 0.19 |
| Water | 1.26 | 1.00 |