Question

A cylindrical insulation for a steam pipe has an inside radius rt = 6 cm, outside radius r0 = 8 cm, and a thermal conductivity k = 0.5 W/(m • °C). The inside surface of the insulation is at a temperature = 430°C, and the outside surface at T0 = 30°C. Determine the heat loss per 1-m length of this insulation.

Answer 1

heat loss per 1-m length of this insulation is 4368.145 W

Step-by-step explanation:

given data

inside radius r1 = 6 cm

outside radius r2 = 8 cm

thermal conductivity k = 0.5 W/m°C

inside temperature t1 = 430°C

outside temperature t2 = 30°C

to find out

Determine the heat loss per 1-m length of this insulation

solution

we know thermal resistance formula for cylinder that is express as

Rth =
`(ln(r2)/(r1))/(2 \pi *k * L)` .................1

here r1 is inside radius and r2 is outside radius L is length and k is thermal conductivity

so

heat loss is change in temperature divide thermal resistance

Q =
`(t1- t2)/((ln(r2)/(r1))/(2 \pi *k * L))`

Q =
`((430-30)*(2 \pi * 0.5 * 1)/(ln(8)/(6) )`

Q = 4368.145 W

so heat loss per 1-m length of this insulation is 4368.145 W