1. Calculation of Cooling Time for an AISI 304 Steel Heating Rod Sayantan Ghosh Avinesh Ojha

2. Introduction Description of Project: This experiment is concerned with the cooling of an AISI 304 steel heating rod. We want to see how much time the rod takes to cool from an initial temperature to final temperature in the laboratory and compare it to the analytical results. The experiment mainly focuses on heat transfer between the heated cylinder and the environment in an external cross flow of air. This is an important problem in the real world because steel rods need to be moved from one place to another in factories. The final deformation processes are carried out at specific temperatures. Knowing the time taken to reach these temperatures is extremely important for the industry.

3. Materials Cylindrical heating rod. Fan. Thermocouple. Velocity anemometer. Wattmeter.

4. Experimental Setup A heating rod was taken and heated by passing electricity through it. The rod was heated until a maximum temperature of 442˚ C. The fan was operated and the rod was allowed to cool to a steady temperature of 162 ˚C. The velocity of the fan was noted to be 2830 ft/min.

5. Experimental Setup Fig: Experimental setupFig: Recording air velocity

6. Convection. Radiation.

7. Assumptions Atmospheric pressure was assumed because all the values given in the book are at atmospheric pressure. Velocity of the fan at the center is the average velocity of air. Temperature of the wall, ceiling and floor was assumed to be the same as the temperature of the air inside.

8. Convection Effects

9. Dimension of Rod Diameter of rod =.0126 m

10. Velocity of Air Calculation Velocity of air from the fan was calculated by using a velocity anemometer. Velocity of air (V) = 2830 ft/s = 14.38 m/s

11. Density: Calculation Pressure (P)= 0.85 atm T-surr (Temperature of air and walls)= 22 deg C= 295 K T-initial of rod= 442 ˚C T-final of rod= 160 ˚C T-avg (For calculation of Reynold’s number) = (160+22)/2= 91 ˚C = 364 K k of air@ 364 K= 0.0315 W/m.K

12. Reynolds Number ʋ (kinematic viscosity) of air @ 364 K= 23*10 -6 m 2 /s Re= (V*D)/ ʋ Re= (14.38 *.0126)/(23*10 -6 )= 7878

13. Nusselts Number Calculation From Table 7.2 in the book, for Re= 7878 Pr= 0.694 C= 0.193 m= 0.618 Nu= C * Re m * Pr 1/3 = 0.193*(7878) 0.618 * (0.694) 1/3 = 43.7

14. Convection-coefficient Calculation h = (Nu*k)/D= (43.7*.0315)/.0126= 109 W/m 2.K

15. Radiation Effects

16. Constants ε= 0.88 σ (Boltzmann’s constant)= 5.67*10 -8 J/K

17. h r calculation h r = σ * ε* (Ts+Tsurr)* (Ts 2 + Tsurr 2 ) = 5.67*10 -8 * 0.88 * ( 574+295) * ( 574 2 +295 2 ) = 18 W/m 2.K

18. Combined Effect h T = h+h r = 109+18 = 127 W/m 2.K h T is the combined “h” for convection and radiation.

19. Calculation of Biot Number T-avg (steel)= (442+162)/2 = 302 ˚C= 575 K k of AISI 304 steel = 18 W/m 2 *K Biot Number for Cylinder = (h*(r/2)*k) = (127*.0063)/(2*18) =.0211< 0.1 Hence, Lumped Capacitance method can be used.

20. Calculation of time Density(ρ) AISI 304 Steel = 7900 kg/m 3 Cp AISI 304 Steel = 477 J/kg.K Time (t)= (ρ * Cp * r * (Tsurr- Tinitial of rod))/(h T * 2 * (Tsurr-T final of rod)) = (7700*477* 0.0063 *420)/(127.3*2*138.2) = 283 seconds

21. Experimental time Vs Calculated time Experimental Time required for the process was recorded to be 224 seconds. %Error = (Time Calculated - Time Experimental)*100/ Time Calculated = (283-224)/283 = 20.84%

22. Conclusion There is an error of 20.84% which is considerable. The possible reasons for this are given below: 1. All the values were taken at atmospheric pressure but the atmospheric pressure of Provo is about 85% of that at sea level. 2. There are different velocities of the fan at different cross section and the assumption that the velocity is average at the center may not be correct entirely. 3. There might be error in the temperature sensor. 4. There might be some error in the radiation calculation due to the assumption that the wall temperature is the same as room temperature.

23. Recommendations Perform the experiments at standard conditions. Use devices that can measure the temperature of the walls and the heated rod correctly. Take velocity measurements of air at different points and use the mean of these velocities for Reynolds number calculations.

24. Appendices Formulas.........................1 Parameters………………….2 References…………………..3

25. Formulas Biot Number for Cylinder = (h*(r/2)*k) Time (t)= (ρ * C p * r * (Tsurr- Tinitial of rod))/(h T *2*(Tsurr-Tfinal of rod)) Re= (V*D)/ ʋ Nu= C * Re m * Pr 1/3

26. Properties k of air@ 364 K= 0.0315 W/m.K Density(ρ) AISI 304 Steel = 7900 kg/m 3 C p AISI 304 Steel = 477 J/kg.K

27. References Incorpora, F.P., Dewitt D.P., et al., Fundamentals of Heat and Mass Transfer. New Jersey: Wiley, 2007. Print.