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.

Question

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

Answer 1

(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