Question

A metal pipe of 10cm OD is covered with a 2cm thick insulation [k=0.07W/m.oC]. The heat loss from the pipe is 100W per meter of length when the pipe surface is at 100oC. What is the temperature of the outer surface of the insulation?

Answer 1

temperature of outer surface is 23.5°C

Step-by-step explanation:

given data

diameter d = 10 cm

thickness = 2 cm

heat loss Q = 100 W

temperature t1 = 100°C

k = 0.07 W/m°C

to find out

temperature t2 of outer surface

solution

we consider here r1 is outer radius and r2 is inner radius

so here r2 = 10 /2 = 5 cm

and r1 = 5 + 2 = 7 cm

now we will apply here heat loss formula that is

heat loss =
`(t1 -t2)/(ln(r1/r2)/(2\Pi KL))`

here length is 1 for unit length

so

100 =
`(100 -t2)/(ln(7/5)/(2\Pi (0.07)(1)))`

solve it and we get t2

t2 = 23.5

so temperature t2 of outer surface is 23.5°C