Question 10.13: KNOWN: Saturated ethylene glycol at 1 atm heated by a chromi......
KNOWN: Saturated ethylene glycol at 1 atm heated by a chromium-plated heater of 200 mm diameter and maintained at 480 K.
FIND: Heater power, rate of evaporation, and ratio of required power to maximum power for critical heat flux.
ASSUMPTIONS: (1) Nucleate pool boiling, (2) Fluid-surface, \mathrm C_{\mathrm{s,f}} = 0.010 and n = 1.
PROPERTIES: Table A-5, Saturated ethylene glycol (1 atm): \mathrm T_{\text{sat}} = 470 K, \mathrm h_{\mathrm{fg}} = 812 kJ/kg, \rho_{\mathrm f} = 1111 kg/m³, σ = 32.7 × 10^{-3} N/m; Saturated ethylene glycol (given, 470K): \rho_{\mathrm v} = 1.66 kg/m³, \mu_{\ell} = 0.38 × 10^{-3} N·s/m², \mathrm c_{\mathrm p,\ell} = 3280 J/kg·K, \mathrm{Pr}_{\ell} = 8.7, \mathrm k_{\ell} = W/m·K.
SCHEMATIC:
ANALYSIS: The power requirement for boiling and the evaporation rate are \mathrm q_{\text{boil}} = \mathrm q_{\mathrm s}^{\prime\prime} \cdot \mathrm A_{\mathrm s}~\text{and}~\dot{\mathrm m} = \mathrm q_{\text{boil}}/\mathrm h_{\mathrm{fg}}. Using the Rohsenow correlation,
q _{ s }^{\prime \prime}=\mu_{\ell} h _{ fg }\left[\frac{ g \left(\rho_{\ell}~-~\rho_{ v }\right)}{\sigma}\right]^{1 / 2}\left\lgroup \frac{ c _{ p , \ell} \Delta T _{ e }}{ C _{ s , f } h _{ fg } \operatorname{Pr}_{\ell}^{ n }}\right\rgroup^3
q _{ s }^{\prime \prime}=0.38 \times 10^{-3} \frac{ N \cdot s }{ m ^2} \times 812 \times 10^3 \frac{ J }{ kg }\left[\frac{9.8 m / s ^2(1111~ -~ 1.66) kg / m ^3}{32.7~ \times ~10^{-3} N / m }\right]^{1 / 2}\left\lgroup \frac{3280 J / kg \cdot K (480 ~- ~ 470) K }{0.01~ \times ~812~ \times ~10^3 \frac{ J }{ kg }(8.7)^1}\right\rgroup^3
q _{ s }^{\prime \prime}=1.78 \times 10^4 W / m ^2 ~~~\quad~~~ q _{\text{boil}}=1.78 \times 10^4 W / m ^2 \times \pi / 4(0.200 m )^2=559 W
\dot{ m }=559 W / 812 \times 10^3 J / kg =6.89 \times 10^{-4} kg / s.
For this fluid, the critical heat flux is estimated from Eq. 10.7,
q _{\text {max }}^{\prime \prime} = 0.149 h _{ fg } \rho_{ v }\left[\sigma g \left(\rho_{\ell} – \rho_{ v }\right) / \rho_{ v }^2\right]^{1 / 4}
q _{\max }^{\prime \prime} = 0.149 \times 812 \times 10^3 \frac{ J }{ kg } \times 1.66 \frac{ kg }{ m ^3}\left[\frac{32.7~ \times ~10^{-3} N / m ~\times~ 9.8 m / s ^2(1111~ – ~1.66) kg / m ^3}{\left(1.66 kg / m ^3\right)^2}\right]^{1 / 4}
q _{\max }^{\prime \prime} = 6.77 \times 10^5 W/m^2.
Hence, the ratio of the operating heat flux to the critical heat flux is,
\frac{ q _{ s }^{\prime \prime}}{ q _{\max }^{\prime \prime}}=\frac{1.78~ \times ~10^4 W / m ^2}{6.77 ~\times ~10^5 W / m ^2} \approx 0.026 ~~~\quad~~~ \text { or } ~~~\quad~~~ 2.6 \%.
COMMENTS: Recognize that the results are crude approximations since the values for \mathrm C_{\mathrm{s,f}} and n are just estimates. This fluid is not normally used for boiling processes since it decomposes at higher temperatures.