Chapter 10, Problem 10.76P

A thin-walled cylindrical container of diameter $D$ and height $L$ is filled to a height $y$ with a low boiling point liquid (A) at $T_{\text{sat,A}}$ . The container is located in a large chamber filled with the vapor of a high boiling point fluid (B). Vapor-B condenses into a laminar film on the outer surface of the cylindrical container, extending from the location of the liquid-A free surface. The condensation process sustains nucleate boiling in liquid-A along the container wall according to the relation $q^{″}=C{\left(T_s-T_{\text{sat}}\right)}^3$ , where $C$ is a known empirical constant.

(a) For the portion of the wall covered with the condensate film, derive an equation for the average temperature of the container wall, $T_s$ . Assume that the properties of fluids A and B are known.
(b) At what rate is heat supplied to liquid-A?
(c) Assuming the container is initially filled completely with liquid, that is, $y=L$ , derive an expression for the time required to evaporate all the liquid in the container.