VM109

VM109
Temperature Response of a Suddenly Cooled Wire

Overview

Reference:

F. Kreith, Principles of Heat Transfer, 2nd Printing, International Textbook Co., Scranton, PA, 1959, pg. 120, ex. 4-1.

Analysis Type(s):

Thermal Analysis (ANTYPE = 4)

Element Type(s):

Convection Link Elements (LINK34)

Thermal Mass Elements (MASS71)

Input Listing:

vm109.dat

Test Case

Determine the temperature response of a copper wire of diameter d, originally at temperature T_o, when suddenly immersed in air at temperature T_air. The convection coefficient between the wire and the air is h.

Figure 155: Cooled Copper Wire Problem Sketch

Material Properties

Geometric Properties

ρ = 558 lb/ft³

c = 0.091 Btu/lb-°F

h = 2 Btu/hr-ft²-°F

d = 1/32 in

T_air = 100°F

T_o = 300°F (at t=0)

Analysis Assumptions and Modeling Notes

The node locations are arbitrary (coincident). The final time of 0.05 hr (180 sec) is sufficient for the theoretical response comparison. An initial integration time step of 0.05/40 = 0.00125 hr is used. Automatic time stepping is used. The thermal capacitance C, and the surface area of the wire A_s, are calculated based on a unit length as follows:

Results Comparison

	Target	Mechanical APDL	Ratio
T, °F @ 0.0125hr	193.89	196.48	1.013
T, °F @ 0.0325hr	128.00	130.05	1.016
T, °F @ 0.05hr	109.71	110.83	1.010

POST26, Node 1 temperature history

Figure 156: Temperature vs. Time Display