3. (Extra credit) In nucleate boiling heat transfer from a cylinder with surface temperature T to a pool of

saturated liquid at temperature Tsat, the convection heat transfer coefficient h is expected to depend on the

difference between the surface and saturation temperatures, AT = Tw - Tsats the body force arising from the

density difference between liquid and vapor, (pp.)g, the specific latent heat of vaporization, AH,, the air-

liquid surface tension, o, the tube diameter, D, and the thermophysical properties c, k, and of the liquid.

a. Using dimensional analysis with the repeating set (AH, k, μ, D), determine the dimensionless groups

necessary to correlate experimental data for the boiling heat transfer coefficient. Assuming a power-law

dependence of the Nusselt number on the other dimensionless parameters, write the most general expression

for the dependence of the boiling heat transfer coefficient on dimensional parameters.

b. Experiments on pool boiling of water on platinum wires show the heat flux to be independent of the

wire diameter. In addition, doubling A7 increases the heat flux by a factor of 8 while reducing surface

tension by a factor of 4 increases the heat flux by a factor of 2. How would you expect the heat transfer

coefficient to depend on the latent heat of vaporization for other liquids? Use the experimental findings in

conjunction with the results of your dimensional analysis to write a general expression for Nusselt number.