Question $10(24$ points$)$

Combustion air at $20C$ in a manufacturing facility is preheated by passing it over a tube bank that is maintained at $100.$ The tubes are $1$ m long. $1\mathrm{.}6$ cm in diameter, and are arranged in$-$line with $S_L-S_T=6cm.$ Air enters the tube bank at a mean velocity of $7\mathrm{.}2\frac{m}{s}.$ There are $20$ rows in the flow direction with $10$ tubes in each row. The properties of air at mean temperature and at other key points are as below:

$=6cm.$ Air enters the tube

with $10$ tubes $in$ each row. The properties $of$ air $at$ mean

below:

$k=0\mathrm{.}02625\frac{W}{m}-K,=1\mathrm{.}145k\frac{g}{m^3},C_P=1007\frac{J}{k}g-K,Pr=0\mathrm{.}7268,=1\mathrm{.}895{10}^{-5}k\frac{g}{m}-s,$

$P{r}_s=0\mathrm{.}7111,{}_i=1\mathrm{.}204k\frac{g}{m^3}.$

Show step by step calculations and;

a$.$ Determine the maximum flow velocity through the tube bank, $V_{\text{m}\text{a}\text{x}}$

b$.$ Determine the maximum flow Reynolds number, $Re$

c$.$ Determine the Nusselt number, Nu

d$.$ Determine the heat transfer coefficient, $h$

e$.$ Determine the exit temperature of air, $T_e$

f$.$ Determine the logarithmic mean temperature difference, LMTD

g$.$ Determine the rate of heat transfer, $Q$