Here is the full question.
Saturated ethylene glycol at 1 atm is heated by a chromium-plated surface which is circular in shape and has a diameter of 200-mm and is maintained at 480 K.
At 470 K the properties of the saturated liquid are mu = 0.38 * 10-3 N. s/m^2, Cp = 3280 J/kg. K and Pr = 8.7. The saturated vapour density is p= 1.66 kg/m^3. Take the liquid to surface constants to be Cnb = 0.010 and m=4.1.
Estimate the heating power requirement and the rate of evaporation
What fraction is the power requirement of the maximum power associated with the critical heat flux
Answer:
The heating power requirement = 559.2 W
The rate of evaporation = 
The fraction of the power requirement of operating heat flux to the maximum power associated with the critical heat flux is = 0.026
Explanation:
From the thermodynamics tables; we deduced the value for enthalpy at the pressure 1 atm and
= 470 K for the saturated ethylene glycol.
Value for enthalpy of formation
= 812 kJ/kg
Density of saturated ethylene glycol
= 1111 kg/m³
Surface tension 
The heat flux can be calculated by using the formula:
![q"s = \mu___l}}}h_{fg}{[\frac{g(\rho{__l}- \rho{__v} }{\sigma} ]^{1/2} [\frac{C_p*\delta T_c}{C_{sf}*h_{fg}P_r} ]^3](https://tex.z-dn.net/?f=q%22s%20%3D%20%5Cmu___l%7D%7D%7Dh_%7Bfg%7D%7B%5B%5Cfrac%7Bg%28%5Crho%7B__l%7D-%20%5Crho%7B__v%7D%20%7D%7B%5Csigma%7D%20%5D%5E%7B1%2F2%7D%20%20%5B%5Cfrac%7BC_p%2A%5Cdelta%20T_c%7D%7BC_%7Bsf%7D%2Ah_%7Bfg%7DP_r%7D%20%5D%5E3)
![= [0.38*10^{-3}\frac{NS}{m^2} *812*10^3\frac{J}{kg} (\frac{9.81m/s^2*(1111-1.66)kg/m^3}{32.7*10^{-3}N/m} )^{1/2}*(\frac{3280J/kg.K(480-470)K}{0.01*812*10^3\frac{J}{kg}*(8.7)^1 } )]](https://tex.z-dn.net/?f=%3D%20%5B0.38%2A10%5E%7B-3%7D%5Cfrac%7BNS%7D%7Bm%5E2%7D%20%2A812%2A10%5E3%5Cfrac%7BJ%7D%7Bkg%7D%20%28%5Cfrac%7B9.81m%2Fs%5E2%2A%281111-1.66%29kg%2Fm%5E3%7D%7B32.7%2A10%5E%7B-3%7DN%2Fm%7D%20%29%5E%7B1%2F2%7D%2A%28%5Cfrac%7B3280J%2Fkg.K%28480-470%29K%7D%7B0.01%2A812%2A10%5E3%5Cfrac%7BJ%7D%7Bkg%7D%2A%288.7%29%5E1%20%7D%20%29%5D)
= 308.56 × 576.6 × 0.1
= 1.78 × 10⁴ W/m²
Now; to find the heating power requirement; we have:

= 
Thus, the heating power requirement = 559.2 W
The rate of evaporation is given as:

= 
= 
Thus, the rate of evaporation = 
To determine to what fraction in the power requirement of the maximum power is associated with the critical total flux ; we needed to first calculate the critical heat flux.
So, the calculation for the critical heat is given as:![q"max = 0.149*h_{fg}}* \rho{___l}}}}[ \frac{\sigma_g (\rho_l - \rho_v}{\rho_v^2} ]^{1/4}](https://tex.z-dn.net/?f=q%22max%20%3D%200.149%2Ah_%7Bfg%7D%7D%2A%20%5Crho%7B___l%7D%7D%7D%7D%5B%20%5Cfrac%7B%5Csigma_g%20%28%5Crho_l%20-%20%5Crho_v%7D%7B%5Crho_v%5E2%7D%20%5D%5E%7B1%2F4%7D)
= ![q"max = 0.149*812810^3* 1.66[ \frac{32.7*10^{-3}*9.8 (1111- 1.66}{1.66^2} ]^{1/4}](https://tex.z-dn.net/?f=q%22max%20%3D%200.149%2A812810%5E3%2A%201.66%5B%20%5Cfrac%7B32.7%2A10%5E%7B-3%7D%2A9.8%20%281111-%201.66%7D%7B1.66%5E2%7D%20%5D%5E%7B1%2F4%7D)
= 200840.08 × 3.37
= 6.77 × 10⁵ W/m²
Finally, the fraction of the power requirement of operating heat flux to the maximum power associated with the critical heat flux is as follows:
= 
= 
= 0.026
Thus, the fraction of the power requirement of operating heat flux to the maximum power associated with the critical heat flux is = 0.026