Discuss the below:
Q: A long, hollow cylinder is constructed from a material whose thermal conductivity is a function of temperature according to k = 0.060 + 0.00060 T, where T is in °F and k is in Btu/h °F. The inner and outer radii of the cylinder are 5 and 10 in., respectively. Under steady-state conditions, the temperature at the interior surface of the cylinder is 800°F and the temperature at the exterior surface is 200°F.
(a) Calculate the rate of heat transfer per foot length, taking into account the variation in thermal conductivity with temperature.
(b) If the heat transfer coefficient on the exterior surface of the cylinder is 3 Btu/(h ft2 °F), calculate the temperature of the air on the outside of the cylinder.
GIVEN
A long hollow cylinder
Thermal conductivity (k) = 0.060 + 0.00060 T [T in °F, k in Btu/(h ft °F)]
Inner radius (ri) = 5 in.
Outer radius (ro) = 10 in.
Interior surface temperature (Twi) = 800°F
Exterior surface temperature (Two) = 200°F
Exterior heat transfer coefficient ( ho ) = 3 Btu/(h ft2 °F)
Steady-state conditions
ASSUMPTIONS
Steady state heat transfer
Conduction occurs in the radial directiononly
