Steam at temperature of 320oC flows in a cast iron pipe whose inner and outer di

Question

Steam at temperature of 320oC flows in a cast iron pipe whose inner and outer diameter are 5 cm and 5.5 cm, respectively. The thermal conductivity of the pipe is 80 W m-1 K-1. The pipe is covered with 3-cm-thick glass wool insulation with a thermal conductivity of 0.05 W m-1 K-1. Heat is lost to the surroundings at a temperature of 5oC by natural convection and radiation, with a combined heat transfer coefficient of 18 W m-2 K -1. Take the heat transfer coefficient inside the pipe to be 60 W m-2 K -1 .

(a) Determine the rate of heat loss from the steam per unit length of the pipe. (13)

(b) Calculate the temperature drops across the pipe shell and the insulation.

Explanation / Answer

Given : Steam temperature = 320 C

Pipe Inner Diameter = 5 cm

Pipe outer diameter = 5.5 cm

k = Themal conductivity of pipe = 80 W/mk

Insulation Thickness = 3 cm

Convectional Heat transfer Coefficient h0 = 18 W /m^2 K

1 )Find rate of heat loss per unit length of pipe ?

2) temperature drop across the pipe shell and insulation ?

r1 = Pipe inner dia /2 = 5/2 = 2.5 cm = 2.5 /100 = 0.025 m

r2 = pipe outer dia = 5.5 /2 = 2.25 cm = 0.0225m

When insulation is 3 cm thick

r0 = r2 + Thickness of insulation

2.25 +3

= 5.25 cm

= 0.0525 m

R = 1 / 2 x pie x L ( 1/k1 + Ln (r2 /r1 ) + 1 /k2 Ln (r0 /r2 ) + 1 / h0 r0 )

1 /2 x 3.14 x 1 ( 1/80 x Ln ( 0.0225 / 0.025 ) + 1 / 0..05 Ln (0.0525 /0.0225 ) + 1 / 18 x 0.0525)

R = 2.86 K/W

Rate of heat loss from the steam per unit length of thr pipe Q = Ti - T0 /R

= 320 - 50 /2.86

Q = 94 .4 W

Temperature drop across the pipe shell and insulation = Ti - To

= 320 - 50

= 270 oC

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