Question

An uninsulated air conditioning duct of rectangular cross section $1m\times 0.5m$ carrying air at ${20}^{\circ }C$ with a velocity of 20 m/s is exposed to an ambient of ${30}^{\circ }C$. Neglect the effect of duct construction material. For air in range $20-{30}^{\circ }C$, properties are as follows.
Thermal conductivity $=0.025W/mk$
Viscosity $=18\mu Pa-s$
Prandtl numbber $=0.73$
Density $=1.2kg/m^3$
For laminar flow Nusselt number is 3.4 for constant wall temperature and for turbulent flow. The heat transfer in per meter length of the duct is
$\overline{Nu}=0.023R{e}^{0.8}P{r}^{0.33}$

• A. 1339 W
• B. 1240 W
• C. 769 W
• D. 5.3 W

Answer 1

The correct option is A 1339 W

Equivalent length, $L=\frac{4A}{P}=\frac{4\times 1\times 0.5}{2(1+0.5)}=0.667m$
$Re=\frac{pVL}{\mu }=\frac{1.2\times 20\times 0.667}{18\times {10}^{-6}}=8.893\times {10}^5$
Since Re > 4000
Flow is turbulent, $Nu=dfrachLk=0.023R{e}^{0.8}P{r}^{0.33}$
$\frac{h\times 0.667}{0.025}=0.023(8.893\times {10}^5{)}^{0.8}\times (0.73{)}^0.33$
$h=44.64W/m^{2}K$
$Q=h{A}_{\text{side}}\times (T-T_{\infty })$
$=44.64\times 2\times (1+0.5)\times 1\times (30-20)$
$Q=1339W$