VM173

VM173
Centerline Temperature of an Electrical Wire

Overview

Reference:	W. M. Rohsenow, H. Y. Choi, Heat, Mass and Momentum Transfer, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1963, pg. 106, ex. 6.5.
Analysis Type(s):	Static, Coupled-Field Analysis (ANTYPE = 0)
Element Type(s):	3D Coupled-Field Solid Elements (SOLID5)
Input Listing:	vm173.dat

Test Case

Determine the centerline temperature and the surface temperature T_s of a bare steel wire carrying a current I and having a resistance R/I. The surface convection coefficient between the wire and the air (at temperature T_a) is h. Also determine the heat dissipation rate q.

Figure 251: Electrical Wire Problem Sketch

Material Properties

Geometric Properties

R = .0001 ohm/ft

k = 13 Btu/hr-ft-°F

h = 5 Btu/hr-ft²-°F

ρ = 8.983782 x 10^-8 ohm-ft

= 1 in = (1/12) ft

r_o = 0.375 in = 0.03125 ft

Θ = 10°

I = 1000 A

T_a = 70°F

Analysis Assumptions and Modeling Notes

A 1 inch axial (Z) length is chosen for convenience. Since the problem is axisymmetric, only a one-element sector is needed. A small angle Θ = 10° is used for approximating the circular boundary with a straight-sided element.

The calculated resistivity, rho = RA/I, in units of [ohms-ft] was converted to units of [(Btu/hr)/watt] using the conversion factor [3.415 (ohm-ft)] / [(Btu/hr)/watt]. With this conversion, the Joule heat units match the thermal units. The voltage drop per foot, IR/ , is calculated as 0.1 volt/ft. Nodes 1 though 16 are assumed to be ground nodes for reference. The steady-state convergence procedures are used. The heat dissipation rate, q, is calculated as q = hA(T-T_a) where A = exterior surface area of the wire (parameter AREA).

Results Comparison

	Target[1]	Mechanical APDL	Ratio
Centerline Temperature, °F	419.9	418.6	0.997
T_s , °F	417.9	416.5	0.997
q, Btu/hr/ft	341.5	339.8	0.995

Solution recalculated