Question

Superheated steam flows steadily through steel tubing (k 35 W/m-K) applying a tube inner surface temperature of 575°C. The tubing has an inner diameter of 300 mm and a wall thickness of 30 mm. Insulation (k 0.10 W/m-K) is applied to the outer surface of the tube while thin aluminum sheet is applied around the insulation as a protective covering. The ambient air at 27°C provides a convection coefficient of 6 W/m2-K. Determine the minimum insulation thickness necessary (mm) to yield a aluminum cover outer surface temperature of 50°C. Assume negligible thermal conduction resistance for the thin aluminum sheet. Hint: perform an energy analysis and use trial and error to solve for the insulation thickness

Answer 1

Given data

35 W/mK

0.10 WmK

0.30.15 m 2

r20.150.03 0.18 m

T = 575 °C

T3= 50 °C

T=27 °C

$\textup{By energy analysis}$

2*ㅠ* L * (Ti -13)- h *2*ㅠ * T3 * L * (T3-14) (I() k2

$\frac{\left ( T_{1}-T_{3} \right )}{\frac{ln\left ( \frac{r_{2}}{r_{1}} \right )}{k_{1}}+\frac{ln\left ( \frac{r_{3}}{r_{2}} \right )}{k_{2}}}=h*r_{3}*\left ( T_{3}-T_{4} \right )$

575- 50 6r3 (50 27) tn( 0.1 O.18 0.15 35 rs 0.18

$3.80434=r_{3}*\left ( \frac{ln\left ( \frac{0.18}{0.15} \right )}{35}+ \frac{ln\left ( \frac{r_{3}}{0.18} \right )}{0.1} \right )$

T3 3.80434 5.209187 10* 3 10 r3*In (a1

$5.209187*10^{-3}*r_{3}+10*r_{3}*ln\left ( \frac{r_{3}}{0.18} \right )-3.80434=0$

$\textup{By trail and error method we get}$

$r_{3}=0.307933\textup{ m}$

$\textup{minimum insulation thickness of aluminium}\left (t \right )$

$t=0.307933-0.18=0.127933\textup{ m}$

$t=127.933\textup{ mm}$