Please answer it with your best $,$ i want to learn it$,$ please do your best i will upvote$13608kg{h}^{-1}$ of superheated butane gas at $94C$ from a gas reactor needs to be cooled to a

saturated liquid at $54\mathrm{.}4C$ in a counter current double pipe heat exchanger. River water at $18C$

is available on site to be used to cool the butane. Using the data provided below:

$($a$)$ Draw the temperature profile as a function of the length of the heat exchanger and label

clearly the known and unknown information.

$($b$)$ Calculate the heat duty of the heat exchanger. Give your answer in $kW.$

$($c$)$ If the river water exiting the heat exchanger is to be discharged back into the river and the

maximum temperature permitted for discharge is $38C,$ determine and comment on the

river water flowrate restriction to prevent the river water from exceeding the discharge

temperature limit$.$ Give you answer in $kg{h}^{-1}.$

$($d$)$ What is the total surface area required for the heat exchanger to cool the butane gas to a

saturated liquid?

$($e$)$ Describe in words the different heat transfer mechanisms involved in the transfer of heat

between the butane and the liquid water assuming the liquid water is in the tube side and

express the overall heat transfer coefficient in terms of the resistances associated with each

of the heat transfer mechanisms. Make sure you define each parameters.

$($f$)$ For the section of the heat exchanger where condensation is taking place, assuming there

is no heat loss to the surroundings, show that the expression relating the temperature of the

river water as a function of time is the following:

$\frac{U_c{A}_c}{m_c^{}{C}_{pw}}t=ln(\frac{36\mathrm{.}4}{54\mathrm{.}4-T_c})$

where $U_c$ is the overall heat transfer coefficient during condensation of butane, $A_c$ is the

surface area available for heat transfer in the condensation section, $m_c^{}$ is the river water

flowrate, $C_{pw}$ is the specific heat capacity for liquid water, $t$ is time and $T_e$ is the river water

temperature as a function of time.

Data

CpBL liquid butane: $2427Jk{g}^{-1}{K}^{-1}$

$C_{pBg}$ gas butane: $1841Jk{g}^{-1}{K}^{-1}$

Latent heat of butane: $316kJk{g}^{-1}$

$C_{PW}$ river water: $4184Jk{g}^{-1}{K}^{-1}$

Overall heat transfer coefficient $(U_d)$ during desuperheating of butane: $238W{m}^{-2}{K}^{-1}$

Overall heat transfer coefficient $(U_e)$ during condensation of butane: $897W{m}^{-2}{K}^{-1}$