Question 10.18: KNOWN: Zuber-Kutateladze correlation for critical heat flux,......
KNOWN: Zuber-Kutateladze correlation for critical heat flux, \mathrm q_{\max}^{\prime\prime}.
FIND: Pressure dependence of \mathrm q_{\max}^{\prime\prime} for water; demonstrate maximum value occurs at approximately 1/3 \mathrm p_{\text{crit}}; suggest coordinates for a universal curve to represent other fluids.
ASSUMPTIONS: Nucleate pool boiling conditions.
PROPERTIES: Table A-6, Water, saturated at various pressures; see below.
ANALYSIS: The Z-K correlation for estimating the critical heat flux, has the form
q _{\max }^{\prime \prime}=0.149 \rho_{ v } h _{ fg }\left[\frac{ g \sigma\left(\rho_{\ell} ~ – ~ \rho_{ v }\right)}{\rho_{ v }^2}\right]^{1 / 4}where the properties for saturation conditions are a function of pressure. The properties (Table A-6) and the values for \mathrm q_{\max}^{\prime\prime} are as follows:
The \mathrm q_{\max}^{\prime\prime} values are plotted as a function of \mathrm p/\mathrm p_{\mathrm c}, where \mathrm p_{\mathrm c} is the critical pressure. Note the rapid decrease of hfg and σ with increasing pressure. The universal curve coordinates would be
\mathrm q_{\max}^{\prime\prime}/\mathrm q_{\max}^{\prime\prime} (1/3 \mathrm p_{\text{crit}})~\text{vs.}~\mathrm p/\mathrm p_{\mathrm c}.
| p | \mathrm p/\mathrm p_{\mathrm c} | \rho_{\ell} | \rho_{\mathrm v} | h | σ × 10³ | \mathrm q_{\max}^{\prime\prime} |
| (bar) | (kg/m³) | (kJ/kg) | (N/m) | |||
| (MW/m²) | ||||||
| 1.01 | 0.0045 | 957.9 | 0.5955 | 2257 | 58.9 | 1.258 |
| 11.71 | 0.053 | 879.5 | 5.988 | 1989 | 40.7 | 3.138 |
| 26.40 | 0.120 | 831.3 | 13.05 | 1825 | 31.6 | 3.935 |
| 44.58 | 0.202 | 788.1 | 22.47 | 1679 | 24.5 | 4.398 |
| 61.19 | 0.277 | 755.9 | 31.55 | 1564 | 19.7 | 4.549 |
| 82.16 | 0.372 | 718.4 | 43.86 | 1429 | 15.0 | 4.52 |
| 123.5 | 0.557 | 648.9 | 72.99 | 1176 | 8.4 | 4.047 |
| 169.1 | 0.765 | 562.4 | 117.6 | 858 | 3.5 | 2.905 |
| 221.2 | 1.000 | 315.5 | 315.5 | 0 | 0 | 0 |
