Question $1$

A CPU chip of a computer is being cooled by circulating water under vacuum through a cooling plate attached to the chip. The water boils on the chip and the vapor generated is fed to a condenser, where the vapour is condensed on a vertical plate heat exchanger. The condensed water is then fed back to the CPU chip.

The system is operated at a system saturation temperature of $\backslash (50^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

The surface roughness of the CPU is approximately $\backslash ($ R$\_\{$p$,$ o l d$\}\backslash )$ of $\backslash (0\mathrm{.}2\backslash$mu $\backslash$mathrm$\{$~m$\}\backslash ).$

The CPU chip should not operate at a temperature of above $\backslash (75^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and it has a maximum power output of $\backslash (100\backslash$mathrm$\{$~kW$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash ),$ and this set of conditions is thus the worstcase design condition for the boiling surface. The cooling plate attached to the chip is $\backslash ($ t$=2\backslash$mathrm$\{$~mm$\}\backslash )$ thick and is a square with sides of $30$ mm and is made of pure aluminium.

a$)$ What is heat transfer coefficient expected on the boiling surface within the cooling chip under these worst$-$case design conditions?

$(3$ marks$)$

b$)$ How close to the critical heat flux is the boiling surface operating at$?($i$.$e$.,$ Express this operating condition as a percentage of the critical heat flux$)$

$(8$ marks$)$

c$)$ What is the vapour generation rate as a result of boiling under these worstcase design conditions?

$(2$ marks$)$

d$)$ What is the average condensation heat transfer coefficient on each of the condensation plates?

$(8$ marks$)$

e$)$ How many vertical plates would be needed in the condenser to condense all the vapour generated by the CPUs, if there are $10$ CPUs and they are all connected to the same condenser $?($The plates are illustrated in Figure $2).$

$(4$ marks$)$

f$)$ The design engineer is considering using a zeotropic fluid in this system. What is zeotropic fluid, and how would it effect the boiling process?

$(4$ marks$)$

The condenser has a series of vertical plates $\backslash ($ H $\backslash )$ that are $5$ mm high and $10$ mm long and maintained at a temperature $\backslash ($ T$\_\{$c$\}\backslash )$ of $\backslash (10^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ by an internal coolant, as shown in Figure $2.$