Chapter 10, Problem 10.63P

A technique for cooling a multichip module involves submerging the module in a saturated fluorocarbon liquid. Vapor generated due to boiling at the module surface is condensed on the outer surface of copper tubing suspended in the vapor space above the liquid. The thin-walled tubing is of diameter $D=10$ mm and is coiled in a horizontal plane. It is cooled by water that enters at 285 K and leaves at 315 K. All the heat dissipated by the chips within the module is transferred from a $100\text{-mm}\times 100\text{-mm}$ boiling surface, at which the flux is ${10}^5{\text{W/m}}^2$ to the fluorocarbon liquid, which is at $T_{\text{sat}}=57°\text{C}$ . Liquid properties are $k_l=0.0537\text{W/m}\cdot \text{K}$ , $c_{p,J}=1100\text{J/kg}\cdot \text{K}$ , ${h^{\prime }}_{fg}\approx h_{fg}=84,400\text{J/kg}$ , ${\rho }_l=1619.2{\text{kg/m}}^3$ , ${\rho }_{\upsilon }=13.4{\text{kg/m}}^3$ , $\sigma =8.1\times {10}^{-3}\text{N/m}$ , ${\mu }_l=440\times {10}^{-6}\text{kg/m}\cdot \text{s}$ , and $P_{rl}=9$ .

(a) For the prescribed heat dissipation, what is the required condensation rate (kg/s) and water flow rate (kg/s)?

(b) Assuming fully developed flow throughout the tube, determine the tube surface temperature at the coil inlet and outlet.

(c) Assuming a uniform tube surface temperature of $T_s=53.0°\text{C}$ , determine the required length of the coil.