Please Help me to solve this problem.

Hot oil is used in a shell and tube heat exchanger with one shell pass and eight tube passes to

heat pressurized water from $85F$ to $150F.$ The hot oil enters at $250F$ and for safety reasons

should exit at a temperature not greater than $200F.$ The total external surface area of the heat

exchanger tubes is $225f{t}^2.$ The manufacturer declares that the expected overall heat transfer

coefficient is $45Bt\frac{u}{h}r*f{t}^2*F.$ The water runs through the shell side and the oil runs through the

tube.

Determine: $$

$($a$)$ rate of heat transfer in the heat exchanger.

$($b$)$ water exit temperature if a fouling resistance of $0\mathrm{.}002hr*f{t}^2*\frac{F}{B}tu$ occurs on the outer surface

of the tubes due to service time and lack of maintenance.

It is desired to heat $230k\frac{g}{h}r$ of water from $35$ to $95C$ with oil $(c_p=2\mathrm{.}1\frac{kJ}{k}g*K)$ having an

initial temperature of $175C.$ The mass flow rate of oil is also $230k\frac{g}{h}r.$ Two concentric pipe

counterflow heat exchanger designs are available:

Heat exchanger $1$:

$U=570\frac{W}{m^2}*K$

$A=0\mathrm{.}47m^2$

Heat exchanger $2$:

$U=370\frac{W}{m^2}*K$

$A=0\mathrm{.}94m^2$

Select which heat exchanger should be used. Justify your answer.

Hint: There are two possible ways to determine the solution. One alternative is easier than the other

and will result in the least amount of work. Before you start working consider the two methods

discussed in class and think about which one will be provide you the answer you need with the least

amount of work.