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.

Question

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

Answer 1

(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