VM-WB-MECH-071

VM-WB-MECH-071
Centerline Temperature of a Heat Generating Wire

Overview

Reference:	Rohsenow, W. M., & Choi, H. Y. (1963). Heat, Mass and Momentum Transfer (2nd Printing) (p. 106, ex. 6.5). Englewood Cliffs, NJ: Prentice-Hall, Inc.
Solver(s):	Ansys Mechanical
Analysis Type(s):	Thermal Analysis
Element Type(s):	2-D Thermal Solid Elements

Test Case

Determine the centerline temperature T_cL and the surface temperature T_s of a bare steel wire generating heat at the rate Q. The surface convection coefficient between the wire and the air (at temperature T_a) is h. Also, determine the heat-dissipation rate q. Use a global mesh size of 0.02 ft along with a mapped face meshing.

Figure 94: Schematic

Material Properties

Geometric Properties

k = 3.6111 x 10^-3 Btu/s-ft-°F

r_o = 0.03125 ft

h = 1.3889 x 10^-3 Btu/s-ft²-°F

T_a = 70°F

Q = 30.92 Btu/s-ft³

Analysis Assumptions and Modeling Notes for Ansys Mechanical

Because of the symmetry in loading conditions and in the geometry, the problem is solved as an axisymmetric problem in Ansys Mechanical. The solution is based on a wire with a length of one foot.

Figure 95: Schematic for Ansys Mechanical

Results Comparison for Ansys Mechanical

Results	Target	Mechanical	Error (%)
Centerline Temperature (°F)	419.90	419.94	0.010
Surface Temperature (°F)	417.90	417.85	-0.012
Heat-dissipation rate (BTU/s)	-0.094861	-0.094861	0.000