Question

Water flows at 112°C through a steel pipe (k=90 W/m °C) which has a 6 cm inside diameter and 8cm outside diameter. Such that, hi =346 W/m2 °C and ho =6.0 W/m2 °C. Surrounding air temperature is 20°C. To reduce heat loss to the surroundings the pipe is covered with an insulation insulation having the thickness of 4.0 mm and k=0,5W/m°C . Calculate;
a.    The heat loss by convection per unit length from the bare pipe (before insulation).
b.    The heat loss from the insulated pipe,
c. The critical radius. And discuss the result.

Answer 1

a.    The heat loss by convection per unit length from the bare pipe (before insulation) = 135.5 W
b.    The heat loss from the insulated pipe = 141.8 W
c. The critical radius = 0.0833 m

results discussion

We know that adding more insulation to a wall always decreases heat transfer. The thicker the insulation, the lower the heat transfer rate. This is expected, since the heat transfer area A is constant, and adding insulation always increases the thermal resistance of the wall without increasing the convection resistance.

Adding insulation to a cylindrical pipe, however, is a different matter. The additional insulation increases the conduction resistance of the insulation layer but decreases the convection resistance of the surface. The heat
transfer from the pipe may increase or decrease, depending on which effect
dominates. It can be predicted by using critical radius of insulation which depends on the thermal conductivity of the insulation k and the external convection heat transfer coefficient h. The rate of heat transfer is increased when adding the insulation up to critical radius of insulation and it reaches maximum value at critical radius of insulation after increasing insulation decreases the rate of heat transfer

In this problem radius of insulation is less than the critical radius of insulation that's why when we add 4 mm thick insulation heat loss by Convection per unit length is greater than without insulation pipe