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.
GIVEN
• A long cylindrical billet placed in an oven
• Billet outside diameter = 0.6 m
• Thermal conductivity (k) = 14 W/(m K)
• Initial temperature (Ti) = 16°C
• Oven temperature (T?) = 260°C
• The average heat transfer coefficient h c= 170 W/(m2 K)
• Center temperature increases to 232°C
FIND
(a) The time required using the appropriate chart (b) The instantaneous surface heat fluxes when the center temperature is 232°C
ASSUMPTIONS
• Radial conduction only in billet
• Uniform and constant properties
SKETCH
(a) The Biot number for the billet is
for r=0 we have
For Bi=3.643 for Infinite cylinder, we have
43 J 0(0) =1
(b) The surface temperature is needed to find the surface heat flux. For r = ro, from approximate solution
using Equation (3.44a) we have
J 0(1.865) =0.30217
The instantenous surface flux is
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