Heat Transfer Question A 50m long section of a steam pipe wi

Heat Transfer Question:

A 50-m long section of a steam pipe, with an outer diameter of 10 cm, passes through an open space of air at T=15°C. The average temperature of the outer surface of the steam pipe is measured to be 150°C. If the heat transfer coefficient on the outer surface is 25 W/m2K, (a) determine the rate of heat loss from the steam pipe, and (b) the thickness of fiberglass insulation (k = 0.040 W/m-K) that should be added to the outside of the pipe to reduce the heat transfer rate by 90%. You can assume that the surface temperature of the steam pipe remains at 150°C. Note that you will need to use an iterative solver to find the thickness since you will get a nonlinear equation. You can use any method you prefer

Solution

a) rate of heat loss from steam pipe = h A (T_s-T_o)

= 25*3.14(d)^{2 *} (423-288)

=106.03 W

b) thickness of fibre glass insulation (k=0.40W/mK)

= heat loss by 90%= 0.90*106.03 = 95.427W

95.427= (T_s-T_o)/{1/hA +L/kA}

= t2+ 1.656t+0.0328

t= 2 cm