Consider a heat treatment process in which steel rods with a 10 cm diameter at an initial temperature of 600°C are inserted into an oil bath at 25°C. Assuming a convection coefficient of 400 W/(m2 K) between the oil and the rod, estimate how long it takes for the centerline of the rod to cool to 60°C. If the steel rod, which is 1 m long, is withdrawn from the bath at this point in the process, i.e., when the centerline temperature has reached 60°C, estimate the rate at which heat must be extracted from the oil to maintain its temperature constant during the process of treating 25 rods per hour.

GIVEN

• Heat treatment of steel rod inserted in oil bath

• Rod outside diameter = 0.1 m

• Initial temperature (T0) = 600°C

• Oil bath temperature (T?) = 25°C

• The average heat transfer coefficient ch = 400 W/(m2 K)

FIND

• Time it takes for centerline of the rod to cool to 600C.

• Rate at which heat must be extracted from oil to maintain its temperature constant during the process of treating 25 rods per hour.

ASSUMPTIONS

• Radial conduction only in billet

• Uniform and constant properties

SKETCH


(a) The Biot number for the steel rod based on r0 is





Using approximate solutions, for r=0 we have



For Bi=0.466 for infinite cylinder we have



Solving for the time



The surface temperature is needed to find the surface heat flux. Thus using approximate solution

for r=r0 we have T (0, T 0



J 0(0.915) =0.8012



can be used to calculate the heat transferred from one ball during the cooling time



J,(0.915) =0.41103



the rate of heat that must be extracted to maintain oil temperature constant during treatment of 25 rods per hour is

Physics & Space Science

You might also like to view...

By what factor is the total pressure greater at a depth of 650 m in water than at the surface where the pressure is one atmosphere? (water density = 1.0 × 10^3 kg/m3, 1 atmosphere pressure = 1.01 × 10^5 N/m2, and g = 9.8 m/s2)

a. 100 c. 64 b. 83 d. 19

Physics & Space Science

A mercury-in-glass thermometer at 40°C (OD = 1 cm) is inserted through duct wall into a 3 m/s air stream at 66°C. This can be modelled as cylinder in cross-flow, as shown in figure. Estimate the heat transfer coefficient between the air and the thermometer.

GIVEN
• Thermometer in an air stream
• Thermometer temperature (Ts) = 40°C
• Thermometer outside diameter (D) = 1 cm = 0.01 m
• Air velocity (V) = 3 m/s
• Air temperature (Tb) = 66°C
FIND
• The heat transfer coefficient ch
ASSUMPTIONS
• Steady state
• Turbulence in the free stream approaching the thermometer is low
• Effect of the duct walls in negligible
SKETCH

PROPERTIES AND CONSTANTS
From Appendix 2, Table 28, for dry air at the bulk temperature of 66°C
Thermal conductivity (k) = 0.0282 W/(m K) Kinematic viscosity (?) = 20*10-6 m2/s Prandtl number (Pr) = 0.71 At the thermometer surface temperature of 40°C, the Prandtl number (Prs) = 0.71

Physics & Space Science

After correcting for detection limitations, what do astronomers believe is the most common type of exoplanet?

A. Ice giants B. Super-Earths C. Terrestrial D. Gas giants E. None of these choices are correct.

Physics & Space Science

Compared to optical telescopes, radio telescopes are built large because:

A) they're less expensive to make than optical telescopes. B) radio photons don't carry much energy. C) atmospheric turbulence is more of a problem. D) radio sources are harder to find. E) radio waves are absorbed by the atmosphere.

Physics & Space Science