Supplementary Reading: Sections $9\mathrm{.}1,9\mathrm{.}5,$ and $9\mathrm{.}6$ in Bergman

In nucleate boiling heat transfer from a cylinder with surface temperature T$\_($w$)$ to a pool of saturated liquid at

temperature T$\_($ata $),$ the convection heat transfer coefficient h is expected to depend on the difference between

the surface and saturation temperatures, $\backslash$Delta T$=$T$\_($w$)-$T$\_($tast $),$ the body force arising from the density difference

between liquid and vapor, $(\backslash$rho $\_($i$)-\backslash$rho $\_(2))$g$,$ the specific latent heat of vaporization, $\backslash$Delta H$\_($v$),$ the air$-$liquid surface

tension, $\backslash$sigma $,$ the tube diameter, D$,$ and the thermophysical properties c$,$k$,$ and $\backslash$mu $\{$:$\backslash$Delta H$\_($v$),$k$,\backslash$mu $,$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 $\backslash$Delta T 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.