VM58

VM58
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 (ANTYPE = 0)

Element Type(s):

2D 6-Node Triangular Thermal Solid Element (PLANE35)

2D Thermal Surface Effect Element (SURF151)

Input Listing:

vm58.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 82: 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

Since the problem is axisymmetric, only a small sector is needed. An angle Θ= 30° is used for modeling the circular sector. Four mesh divisions are chosen radially for accuracy considerations. Temperatures of the outer nodes are coupled to ensure symmetry. The solution is based on a wire 1 foot long (Z direction). Postprocessing is used to determine , T_s, and q.

Results Comparison

	Target	Mechanical APDL	Ratio
Centerline Temperature, °F	419.9	419.9	1.000
Surface Temperature, °F	417.9	417.8	1.000
q, BTU/hr	341.5	341.5[1]	1.000

Calculated from heat flow rate per 30° sector x 12 sectors