Calculate the rate of heat transfer between a pair of concentric horizontal cylinders 20 mm and 126 mm in diameter. The inner cylinder is maintained at 37°C and the outer cylinder is maintained at 17°C.
GIVEN
• Concentric cylinders
• Smaller diameter (Di) = 20 mm = 0.02 m
• Larger diameter (Do) = 126 mm = 0.126 m
• Inner cylinder temperature (Ti) = 37°C
• Outer cylinder temperature (To) = 17°C
FIND
The rate of heat transfer (q)
ASSUMPTIONS
• Steady state
• The space between the cylinders is filled with air
• Radiative heat transfer is negligible
PROPERTIES AND CONSTANTS
for dry air at the mean temperature of 27°C
The Grashof number based on the space between the cylinders is
The Rayleigh number is
To use the correlation given in Equation (8.33), the following criteria must be satisfied
The effective thermal conductivity of the air in the gap between the cylinders is
The rate of heat transfer is
where Rth is given by substituting keff for k
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