The heat loss from uninsulated hot water pipes installed in homes can be considerable and hence increases the overall energy cost of the home. Consider a 5-m-long section of such a pipe that has an outer diameter of 1.7 cm and a surface temperature of 75°C. If the room air temperature is 20°C, calculate the natural convection heat loss from the pipe section. If the radiation heat losses are to be included as well, determine its contribution as a percentage of the total pipe heat transfer rate; assume that the outer pipe surface has an emissivity of 0.7.
GIVEN
• Uninsulated hot water pipe dissipating heat to surrounding
• Emissivity (?) = 0.7
• Diameter of cylinder (D) = 1.7 cm= 0.017 m
• Surface temperature (Ts) = 75°C= 348 K
• Ambient air temperature (T?) = 20°C= 293 K
• Length of the cylinder (L)= 5 m
FIND
(a) Natural convection heat loss from pipe section.
(b) Contribution of radiation as percentage of
total pipe heat transfer rate.
SKETCH
ASSUMPTIONS
• Air is still
• Surface temperature is uniform and constant
PROPERTIES AND CONSTANTS
for dry air at the mean temperature of 47.5°C
Thermal expansion coefficient (?) = 0.00312 1/K
Thermal conductivity (k) = 0.02695 W/(m K)
Kinematic viscosity (?) = 18.27 × 10–6 m2/s
Prandtl number (Pr) = 0.71
(a) The Grashof number is
we have
Thus, heat loss by convection is given by
(b) Heat loss by radiation is given by
Thus percentage of total heat loss by radiation is
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