Design a stagger tube bank to heat the air flow. The conditions and requirements are listed

below:

Conditions:

The inlet temperature of air Ti is $20$ degree C with velocity $6\frac{m}{s},$ pressure $1$ATM.

The surface temperature of tube is assumed to be constant, $Ts=100$ degree $C.$

Each row has $10$ tubes.

Building a tube with hot fluid needs $$250.$ So$,$ building the tube bank costs $$250N_{L}10$

Operational cost: $$\frac{0\mathrm{.}05}{k}Wh.$ Please calculate the annual operation cost by assuming that

the pump works for $24$ hours, $365$ days. The total cost is the summation of tube bank cost

and annual operational cost.

The tube is $L=1m$ with diameter $0\mathrm{.}020m,St=0\mathrm{.}040m$

$P{r}_s=0\mathrm{.}7111$

Assume the friction factor $f={0\mathrm{.}6}^{S\frac{L}{D}}+0\mathrm{.}05S\frac{L}{D},=1.$

Requirements:

The outlet temperature of air Te should be greater than $60$ degree $C$

The air properties used in the calculation should be at the $Tm=\frac{Ti+Te}{2},$ except $P{r}_s.$ If

you cannot find the exact temperature $Tm$ on the Table, please use the closet temperature

on the Table $($Justify your choice$).$

If $N_L$ should be less than $16,$ please choose $N_L=1,2,3,4,5,7,10,13,$ in order to use Table $7-$

$3$ to obtain correction factor $F.$

The $S_L$ should be less than $0\mathrm{.}090m.$ Please use $2$ significant figures for $S_L.$

Objective: Design a stagger tube bank to achieve all requirements while the total cost should be

minimized.Report:

Please show each step of your calculation. The design should explicitly show:

$S_D,S_L,V_{\text{m}\text{a}\text{x}}(6pts)$

List the air property you use and show what temperature you use to obtain these properties. $(10$

pts$)$

Outlet temperature by calculation. $(15$ pts$)$

Number of rows $N_L($Here each row is vertically arranged as shown in slides$).$ If please

show the correction factor F$.(5$ pts$)$

Please show and justify which $$ formula to use. $(10$ pts$)$

The value of $,h,Re,m^{},T_{LM},W_{\text{p}\text{u}\text{m}\text{p}}(42$ pts$)$

Operational cost and total cost $(12$ pts$)$