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, $).$

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 $0\mathrm{.}020m,St=0\mathrm{.}040m$

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

Requirements:

The outlet temperature of air Te should be greater than ${)}_{{?}_{?}}$

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.