A $2\mathrm{.}1-$m$-$long, $0\mathrm{.}2-$cm$-$diameter electrical wire extends across a room that is maintained at $20C.$ Heat

is generated in the wire as a result of resistance heating, and the surface temperature of the wire is

measured to be $180C$ in steady operation. Also, the voltage drop and electrical current through the wire

are measured to be $110V$ and $3A,$ respectively. Disregarding any heat transfer by radiation, determine

the convection heat transfer coefficient for heat transfer between the outer surface of the wire and the

air in the room.

Air at atmospheric pressure and a temperature of $300C$ flows with a velocity of $10\frac{m}{s}$ over a flat

plate $0\mathrm{.}5m$ long. Estimate the cooling rate per unit width of the plate needed to maintain it at a surface

temperature of $20C.$ The bottom surface of the plate is insulated.

Consider a staggered tube bundle arrangement which has water flowing through the tubes and air

flowing over the tubes. The tube outside diameter and length are $16\mathrm{.}4mm$ and $1\mathrm{.}0m.$ The longitudinal

and transverse pitches between the tubes are $S_L=34\mathrm{.}3mm$ and $S_T=31\mathrm{.}3mm.$ There are seven rows of

tubes in the air$-$flow direction and eight tubes per row $(N=56,N_L=7,N_T=8).$ The cylinder surface

temperature is $70C,$ while the upstream temperature and velocity of the air are $15C$ and $6\frac{m}{s}.$

Calculate the rate of heat transfer from the tube bundle. Assume that the mean temperature through the

tube bundle is $T_m=25C.$

A long rectangular plate of AISI $304$ stainless steel is initially at $1200K$ and is cooled by an array of

slot jets. The nozzle width and pitch are $W=10mm$ and $S=100mm,$ respectively, and the nozzle to$-$

plate separation is $H=200mm.$ The plate thickness and width are $t=8mm$ and $L=1m,$ respectively. If

air exits the nozzles at a temperature of $400K$ and a velocity of $30\frac{m}{s},$ what is the initial cooling rate

of the plate?

Water is to be heated from $10C$ to $80C$ as it flows through a $2-$cm$-$internal$-$diameter, $13-$m$-$long

tube. The tube is equipped with an electric resistance heater, which provides uniform heating throughout

the surface of the tube. The outer surface of the heater is well insulated, so that in steady operation all

the heat generated in the heater is transferred to the water in the tube. If the system is to provide hot

water at a rate of $5\frac{L}{m}in,$ determine the power rating of the resistance heater. Also, estimate the inner

surface temperature of the pipe at the exit.