An 20 cm-diameter horizontal steam pipe carries 1.66 kg/min of dry saturated steam at 120°C. If ambient air temperature is 20°C, determine the rate of condensate flow at the end of 3 m of pipe. Use an emissivity of 0.85 for the pipe surface. If heat losses are to be kept below 1 per cent of the rate of energy transport by the steam, what thickness of fiberglass insulation is required? The rate of energy transport by the steam is the heat of condensation of the steam flow. The heat of vaporization of the steam is 2210 kJ/kg.

Question

GIVEN
• A horizontal steam pipe in air
• Pipe outside diameter (D) = 20 cm= 0.2 m
• Mass flow rate of steam (ms) = 1.66 kg/min=0.0277 kg/s
• Steam temperature (Ts) = 120°C =393 K
• Ambient air temperature (T?) = 20°C= 293 K
• Emissivity of pipe surface (?) = 0.85
• Heat of vaporization (hfg) = 2210 kJ/kg
FIND
(a) Rate of condensate flow (mc) at the end of 3 m of pipe.
(b) Thickness of fiberglass insulation (S) to keep loss below 1% of the energy transport by steam
ASSUMPTIONS
• Steady state
• Air is still
• Thermal resistance of the convection in the pipe and of the pipe wall are negligible
• The surroundings behave as an enclosure at T?
• Insulation is foil covered, its emissivity ? 0.0
PROPERTIES AND CONSTANTS
the Stephan-Boltzmann constant (?) = 5.67 × 10–8 W/(m2 K4)
Thermal conductivity of fiberglass (ki) = 0.035 W/(m K)
for dry air at the mean temperature of 70°C
Thermal expansion coefficient (?) = 0.00291 1/K
Thermal conductivity (k) = 0.0288 W/(m K)
Kinematic viscosity (?) = 17.1*10-6 m2/s
Prandtl number (Pr) = 0.71

Answer 1

(a) The Grashof number for the uninsulated pipe is



The rate of heat transfer from 3 m of the pipe( considering 1% loss in energy transport) is



This must equal the convection from the surface of the insulation (radiation is negligible) and the conduction through the insulation.



where



Rearranging to eliminate the insulation thickness



Since hc depends on the insulation surface temperature Tsi, an iterative procedure must be used. For the first iteration, let Tsi =50°C.

for dry air at the mean temperature of 35°C

Thermal expansion coefficient (?) = 0.00323 1/K

Thermal conductivity (k) = 0.0261 W/(m K)

Kinematic viscosity (?) = 17.1*10-6 m2/s

Prandtl number (Pr) = 0.71

Assuming the insulation is thin compared to the pipe radius



Checking the units then eliminating them for clarity



By trial and error: Tsi = 97.8°C

Performing further iterations



The surface temperature of the insulation is about 84°F



Thus about a 5.5 mm of insulation is required.