VM215

VM215
Thermal-Electric Hemispherical Shell with Hole

Overview

Reference:	Any standard electrical engineering text
Analysis Type(s):	Coupled Thermal-Electric Shell
Element Type(s):	Thermal-Electric Shell Elements (SHELL157)
Input Listing:	vm215.dat

Test Case

A conducting hemisphere of radius, r, has a hole subtending an angle Θ₁. The edge of the hole is electrically and thermally grounded. A voltage, V₂, is applied at the equator. A Φ degree sector in the azimuthal plane is analyzed.

Figure 345: Hemispherical Shell Problem Sketch

Material Properties

Geometric Properties

ρ = 7 ohm-m

K = 3 W/m-K

t = 0.2 m

r = 10 m

Θ₁ = 10°

Φ = 3°

V₁ = 0 volts

V₂ = 100 volts

T₁ = 0°C

Analysis Assumptions and Modeling Notes

A hemispherical shell with a hole is analyzed. The symmetry of the model is utilized and only a 3 degree sector in the azimuthal direction is analyzed.

The electric current (I) in the sphere is given by:

Where resistance R is given by:

The total heat flow is due to Joule Heating and is given by Q = I (V₂ - V₁)

Results Comparison

SHELL157	Target	Mechanical APDL	Ratio
I (Amps) Node 21	0.06140	0.06143	1.000
Q (Watts) Node 21	6.14058	6.14291	1.000