1. Minimum Cooling Time for Metallurgy Applications
Satyän Chandra
Jordan Walser

2. Introduction: Description
Problem Focus: Cooling of Heated Metals.
Heated Aluminum cylinder left to cool experiences:
Conduction
Free Convection
Forced Convection
Radiation
Experimental and Analytical results compared.

3. Introduction: Motivation
Our goal in doing this project is:
To Validate Heat Transfer Principles and Theories learnt in this class by comparing experimental results to those obtained analytically using equations and correlations of Heat Transfer.
To Support Safety and Safety Precautions by identifying the minimum time needed for Aluminum heated to its annealing temperature to cool down to a level safe for direct contact. (This objective is derived from several months of working in the Materials Lab and observing students burn their hands by touching Aluminum that is very hot)

4. Problem Set Up Tsur = 22 C = 295 K T∞ = 20 C = 293 K
Surrounding Room Wall
At t = 0 s:
Tcylinder = 250 C = 523 K
Cylinder
Air
qconvection
Safe to Operate Temperature for Humans: 50 C = 323 K = T
qradiation
qconduction
Resting Table of Fire Clay Brick (K = < 1 W/m. K)). Flux consists of Conductive, Convective and Radiative components.
Cylinder on Table

5. Experimental Results
Used K Type Digital Thermometer for measurement of Cylinder Surface Temperature
Initial Cylinder Temperature = 250 C
Desired Cylinder Temperature = 50 C
Time (250 C C) = 1Hr. 40 Min

6. Analytical Results: I
Dimensions:
Aluminum:
Air (359 K):

7. Analytical Results: II
Find htot :

8. Analytical Results: III
Check Lumped Capacitance:
Lumped Capacitance Satisfied
Solve for time to cool from 250 ℃ to 50

9. Conclusion of Experiment
Experimental Result
Analytical Result
% Difference
1:40:00
2:45:21
40 %
1 Hour and 40 Minutes and 0 Seconds
2 Hours and 45 Minutes and 21 Seconds
It takes almost 1 hour more theoretically for an Aluminum Cylinder to cool that it does experimentally.
The Experimental and Analytical methods compare closely. Although the difference is 40%, the results are in the same range.

10. Analysis of Results
The Experimental and Analytical Results vary considerably. The following are reasons for the disparity :
Cylinder approximated as uniform. Actual Cylinder was not uniform in Diameter.
Thermal Conduction through resting table ignored due to << thermal conductivity of Fire Brick.
The extent of Forced Convection was higher in reality during heating of the room (Air gushing into the room from vents).
Approximate Properties used at average temperature (250 C C)/2
The Emissivity co-efficient did not consider surface smoothness/ roughness of Al sample cylinder.

11. Appendix: Cylinder Pictures