Please help me to solve this problem:

$5$: A cross$-$flow plate heat exchanger is to be designed for waste heat recovery from the

exhaust streams of a metallurgical process. A flow of $5k\frac{g}{s}$ of exhaust gases enters the

exchanger at $240C$ and must be cooled to $120C$ by $5k\frac{g}{s}$ of air supplied at $20C.$ If the

overall heat transfer coefficient is estimated to be $40\frac{W}{m^2}K,$ determine the required

heat transfer area if both streams are unmixed using the NTU$-$ method. The specific

heat of the exhaust gases and air can be taken as $1200\frac{J}{k}gK$ and $1010\frac{J}{k}gK$ respectively.

$6$: Hot exhaust gases are used to preheat water

prior to being injected to a boiler using a

crossflow heat exchanger. The heat exchanger

consists of a staggered arrangement of $1\mathrm{.}6$ in

outside diameter copper tubes with a wall

thickness of $0\mathrm{.}1$ in $.$ The tubes are placed in an

array that is $5$ rows deep with a longitudinal

spacing of $3\mathrm{.}2$ in and a transverse spacing of $3\mathrm{.}2$

in as shown. The hot gases can be assumed to have similar properties as air. The hot gases

enter with a free stream velocity of $800f\frac{t}{s}$ at $1000F$ and leave at $900F.$ Pressurized

water enters the tubes at $80F$ with a total mass flow rate of $200,000lb\frac{m}{h}r$ and leaves the

heat exchanger at $220F.$ Determine:

$($a$)$ the average heat transfer coefficient on the external surface of the tubes

$($b$)$ the average heat transfer coefficient for the water in the tubes

$($c$)$ the overall conductance per unit length

$($d$)$ the heat exchanger rating per unit length

$($e$)$ the length of the pipes required to produce the proposed temperature rise on the

water.