Hi$,$ please could you answer the below question, during which explaing and expanding all working so that it is clearly visable in step by step format and the steps explained where necessary for further clarification.

Thankyou in advance for your help.

$($a$)$ Dry saturated steam at a temperature of $180C$ is to be produced in a

fire tube boiler from the cooling of $50000kg{h}^{-1}$ of flue gases from a

pressurised combustion process. The gases enter the tubes of the boiler

at $1600C$ and leave at $200C.$ The feed water is externally preheated

to $180C$ before entering the boiler.

The mean specific heat capacity of the flue gases is $1\mathrm{.}15kJk{g}^{-1}{K}^{-1}.$

The latent heat of vaporisation of the water at $180C$ is $2015kJk{g}^{-1}.$

Feed water temperature $=180C.$

Determine the amount of steam produced per hour, if the total heat loss

is $10\%$ of the heat available for steam raising.

$($b$)$ The overall heat transfer coefficient based on the outside area of the

tubes is given as $54W{m}^{-2}{K}^{-1}.$ Determine the area of heat transfer

required to perform this duty.

$($c$)$ The tubes within the boiler are to be $25mm$ inside diameter with a

wall thickness of $3mm.$ The average flue gas velocity through the

tubes to maintain the overall heat transfer coefficient value and to

minimise pressure losses is to be more than $22m{s}^{-1}$ and less than $28$

$m{s}^{-1}.$

Assuming that the average density of the flue gases is $1\mathrm{.}108kg{m}^{-3},$

calculate:

$($i$)$ the minimum and maximum number of tubes in each pass

$($ii$)$ the overall length of tubes at each of these numbers of tubes

$($iii$)$ the minimum number of tube passes in each case, if the lengthof

a boiler tube is to be less than $5$ metres.