P$2\mathrm{.}1.$

The fin shown in below figure has a base maintained at $300-C$ and is exposed to the convection environment indicated. If $k=1\mathrm{.}0$

W$/$ mK $,$ write the energy balance equations and calculate

a$)$ the steady$-$state temperatures of the nodes $5,6,7$ and $8$

b$)$ the steady$-$state temperatures of nodes $1,2,3,$ and $4,$

c$)$ the heat loss from the fin.

P$2\mathrm{.}2.$

In a large cold$-$storage facility the refrigeration is supplied by an ammonia system. The ammonia condenser operates at $30-C$ as a

shell$-$and$-$tube heat exchanger with one shell pass for the condensing ammonia and two tube passes for a water coolant. The total

energy that must be removed from the ammonia is $457$ kW $.$ The value of hrg for ammonia at $30-C$ is $1145k\frac{J}{k}g.$ Cooling water is

available for the condenser at $16C.$ Using an approximate value of $U=1050\frac{W}{m^2}K$ and an exit water temperature of $25C,$

determine the heat exchanger area required. Then devise two designs for the exchanger, one with $2$ water tubes and one with $4$

water tubes, specifying the exchanger length if the pipe diameter must be $\frac{1}{20}$ the exchanger length. Comment on the design.

Correction factor for a shell$-$and$-$tuhe heat exchanger

with one shell and any multiple of two tube passes $($two$,$ four, etc. tube

passes$).$