Question

Steam flows through a copper pipe (kc=150Wm∙K⁄) that has an inner diameter of 19 mm and an outer diameter of 21 mm. The convection coefficient between the 200°C steam and the pipe is 200Wm2∙K⁄. The pipe is wrapped with insulation (ki=0.03Wm∙K⁄) so that the outer surface of the insulation is safe to touch. If the inner surface of the pipe is at 180°C: a) What is the temperature of the outer surface of the pipe for unit length of the pipe (or the inner surface of the insulation)? b) What is the thickness of the insulation so that the temperature is 40°C at the outer surface of the insulation? (Note: Assume negligible contact resistance)

Answer 1

Answer:

a) The temperature on the outer surface of the pipe is approximately 179.97 °C

b) The thickness of the insulation  is approximately 0.857 m

Explanation:

We have;

$\dfrac{1}{U} = \dfrac{1}{\alpha _A}$

αA = 200 W/(m²·K)

$\dot q$ =  (T₂ - T₁) × U

$\dot q$ =  (200 - 180) × 200 = 4,000

For the pipe, we have;

$\dfrac{1}{U} =\dfrac{x}{kc }$

$\dot q$/U=  (T₂ - T₁)

∴ 4000×$\dfrac{0.001}{150}$ = (180 - T₂)

T₂ ≈ 179.97 °C

The temperature on the outer surface of the pipe, T₂ ≈ 179.97 °C

b) For the insulation, we have;

$\dfrac{1}{U} = \dfrac{x}{ki } = \dfrac{x}{0.03}$

T₂ - T₃ = 179.97 °C - 40°C ≈ 139.97°C

$\dot q$/U=  (T₂ - T₃)

$x = \dfrac{\dot q \cdot kc}{T_2 - T_3} = \dfrac{4,000 \times 0.03}{139.97} \approx 0.857$

The thickness of the insulation, x ≈ 0.857 m