A long 0.6-m-OD 347 stainless steel (k = 14 W/(m K)) cylindrical billet at 16°C room temperature is placed in an oven where the temperature is 260°C. If the average heat transfer coefficient is 170 W/(m2 K), (a) estimate the time required for the center temperature to increase to 232°C by using the appropriate chart and (b) determine the instantaneous surface heat flux when the center temperature is 232°C. but assume that the billet is only 1.2-m-long and the average heat transfer coefficient at both ends is 136 W/(m2 K).

Question

GIVEN

• A cylindrical billet placed in an over

• Billet outside diameter = 0.6 m

• Thermal conductivity (k) = 14 W/(m K)

• Initial temperature (To) = 16°C

• Oven temperature (T?) = 260°C

• The average heat transfer coefficient h cs = 170 W/(m2 K)

• Increase of the center temperature is 232°C

• Billet length (2L) = 1.2 m

• Heat transfer coefficient at the ends h ce = 136 W/(m2 K)

FIND

• The time required using the appropriate charts

ASSUMPTIONS

• Two dimensional conduction within the billet

• Constant and uniform thermal properties

• Constant oven temperature

SKETCH

Answer 1

the solution for this geometry is



where





For the infinite plate solution



For the infinite plate solution



For the long cylinder solution



The time required to reach a product solution of 0.115 is found through trial and error.



The time required is approximately 208 min or 3.4 hours.