VM118

VM118
Centerline Temperature of a Heat-generating 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):

Thermal Analysis (CIRCU124 = 0)

Element Type(s):

2D Thermal Solid Elements (PLANE55)

3D Thermal Solid Elements (SOLID70)

Input Listing:

vm118.dat

Test Case

Determine the centerline temperature and the surface temperature T_s of a bare steel wire generating heat at the rate . The surface convection coefficient between the wire and the air (at temperature T_a) is h. Also determine the heat dissipation rate q.

Figure 168: Heat-generating Wire Problem Sketch

Material Properties

Geometric Properties

k = 13 Btu/hr-ft-°F

h = 5 Btu/hr-ft²-°F

r_o = 0.375 in = 0.03125 ft

T_a = 70°F

= 111311.7 Btu/hr-ft³

Analysis Assumptions and Modeling Notes

The problem is solved first using conducting area elements (PLANE55) and then using conducting solid elements (SOLID70). 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. Nodal coupling is used to ensure circumferential symmetry. The solution is based on a wire 1 foot long (Z-direction). POST1 is used to extract results from the solution phase. Total heat dissipation is computed parametrically at the outer surface as HRATE using q = h.area.(T_s - T_a).

Results Comparison

		Target	Mechanical APDL	Ratio
PLANE55	Centerline Temperature, °F	419.9	418.6	0.997
	T_s, °F	417.9	416.5	0.997
	q, Btu/hr	341.5	339.8	0.995
SOLID70	Centerline Temperature, °F	419.9	418.6	0.997
	T_s, °F	417.9	416.5	0.997
	q, Btu/hr	341.5	339.8	0.995