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Carbon steel (AISI 1010) shafts of 0.1 m diameter are heat treated in a gas-fired furnace whose gases are at 1200 K and provide a convection coefficient of 100 W/(m2*K). The shafts enter the furnace at 300 K. A.  Determine Bi and state whether the lumped capacitance approximation is valid. Estimate the carbon steel’s properties at an intermediate stage’s temperature at 550 K. Show the equations of linear interpolation. B. Express the temperature equation of the shaft. Use the solution form of the lumped capacitance method, attached below. Evaluate the thermal time constant and substitute all available values in the equation. Then, estimate the time it takes for the shaft to be heated to 800 K. C.  How long does it take a shaft to accumulate 95% of the maximum possible thermal energy?

Carbon steel (AISI 1010) shafts of 0.1 m diameter are heat treated in a gas-fired furnace whose gases are at 1200 K and provide a convection coefficient of 100 W/(m2*K). The shafts enter the furnace at 300 K. A.  Determine Bi and state whether the lumped capacitance approximation is valid. Estimate the carbon steel’s properties at an intermediate stage’s temperature at 550 K. Show the equations of linear interpolation. B. Express the temperature equation of the shaft. Use the solution form of the lumped capacitance method, attached below. Evaluate the thermal time constant and substitute all available values in the equation. Then, estimate the time it takes for the shaft to be heated to 800 K. C.  How long does it take a shaft to accumulate 95% of the maximum possible thermal energy?

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter6: Forced Convection Over Exterior Surfaces
Section: Chapter Questions
Problem 6.14P
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Carbon steel (AISI 1010) shafts of 0.1 m diameter are heat treated in a gas-fired furnace whose gases are at 1200 K and provide a convection coefficient of 100 W/(m2*K). The shafts enter the furnace at 300 K.

A.  Determine Bi and state whether the lumped capacitance approximation is valid. Estimate the carbon steel’s properties at an intermediate stage’s temperature at 550 K. Show the equations of linear interpolation.
B. Express the temperature equation of the shaft. Use the solution form of the lumped capacitance method, attached below. Evaluate the thermal time constant and substitute all available values in the equation. Then, estimate the time it takes for the shaft to be heated to 800 K.
C.  How long does it take a shaft to accumulate 95% of the maximum possible
thermal energy?

T(0,+)=800K- -r=0.05m T(r,0)=T;=300K T-1200K h=100W/m².K
Transcribed Image Text:T(0,+)=800K- -r=0.05m T(r,0)=T;=300K T-1200K h=100W/m².K
Ө 0₁ T-T = = exp[-(m.),] T₁-T (5.6)
Transcribed Image Text:Ө 0₁ T-T = = exp[-(m.),] T₁-T (5.6)
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