In petroleum processing plants, it is often necessary to pump highly viscous liquids such as asphalt through pipes. To keep pumping costs within reason, the pipelines are electrically heated to reduce the viscosity of the asphalt. Consider a 15-cm-OD uninsulated pipe and an ambient temperature of 20°C. How much power per meter of pipe length is necessary to maintain the pipe at 50°C? If the pipe is insulated with 5 cm of fiberglass insulation, what is the power requirement?

Question

GIVEN
• An electrically heated pipe
• Diameter (D) = 15 cm = 0.15 m
• Pipe surface temperature (Tsp) = 50°C FIND
(a) Power per meter (qe/L) required with no insulation
(b) Power per meter required with 5 cm (0.05 m) of fiberglass insulation
ASSUMPTIONS
• The pipe is horizontal and in quiescent air
• Radiative heat transfer is negligible
• No heat is transferred to the fluid in the pipe
PROPERTIES AND CONSTANTS
for dry air at the mean temperature of 35°C
Thermal expansion coefficient (?) = 0.00325 1/K
Thermal conductivity (k) = 0.0262 W/(m K)
Kinematic viscosity (?) = 17.1 × 10–6 m2/s
Prandtl number (Pr) = 0.71
the thermal conductivity of fiberglass (kfg) = 0.035 W/(m K)

Answer 1

The correlation for the average heat transfer coefficient for this geometry is

(Note that the criteria of 103 < GrD < 109 and Pr > 0.5 is satisfied.) The thermal properties needed to evaluate hc must be calculated at the mean of Tsi and T?. Therefore, an iterative process is required. For iteration #1, let Tsi = 35°C From Appendix 2, Table 28, for dry air at the mean temperature of 27.5°C

Thermal expansion coefficient (?) = 0.00333 1/K

Thermal conductivity (k) = 0.0256 W/(m K)

Kinematic viscosity (?) = 16.4 × 10–6 m2/s

gives the heat transfer coefficient

Performing further iterations using the same Procedure

Prandtl number (Pr) = 0.71



COMMENTS

The insulation has reduced the rate of heat loss by 84%.