Nucleate Boiling Equations

Example Question (Fundamentals of Heat and Mass Transfer 7th Edition Incropea Dewitt, pg 666-667)

[Link provided at the bottom of the solution]

"The bottom of a copper pan, 0.3m in diameter, is maintained at 118°C by an electric heater. Estimate the power required to boil this pan. What is the evaporation rate?

Estimate the critical heat flux."

In this question we are asked to calculate 3 2 things:

1. Power required by electric heater to cause boiling.

2. Rate of water evaporation due to boiling.

3. Critical heat flux corresponding to the burnout point.

Solution:

Schematic:

Properties (in tables or given in question):

Cs,f = 0.0128, n = 1

(these correspond to the copper surface-water combination which are determined

experimentally and will be given)

C = 0.149

(for horizontal plates - bottom of the pan)

At saturated water, liquid (100°C):

ρl = 957.9 kg/m3, cp,l = 4.217 kJ/kgK, μl = 279x10-6 Ns/m2, Prl = 1.76, hfg = 2257 kJ/kg, σ = 58.9x10-3 N/m.

At saturated water, vapour (100°C):

ρv = 0.5956 kg/m3

1. Power required by electric heater to cause boiling.

Water boils at 100°C, therefore:

Then using the Rohsenow Correlation we can calculate the heat flux:

Hence the boiling heat transfer rate:

3. Critical heat flux corresponding to the burnout point.

Using the Critical Heat Flux of Zuber:

References

BERGMAN, T., LAVINE, A., INCROPERA, F. and DEWITT, D. (2011). Fundamentals of Heat and Mass Transfer. 7th ed. United States of America: JOHN WILEY & SONS, pp.666-667.