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Unformatted text preview: in the azimuthal plane is analyzed. Figure 215.1 Hemispherical Shell Problem Sketch Material Properties ρ = 7 ohm-m K = 3 W/m-K Geometric Properties t = 0.2 m r = 10 m Θ1 = 10° Φ = 3° Loading 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: I= V ( V2 − V1) = R R Where resistance R is given by: ANSYS Verification Manual . ANSYS Release 9.0 . 002114 . © SAS IP, Inc. 1–493 VM215 R = ρ∫ = ρ∫ dL A 2π rdθ with φ in radians 2π rt cos θ φ pr 2π = 2π rt φ θ − 90 − θ1 ∫ θ =0 dθ cos θ pr 360° 1 1 + sin(90 − θ1) = ln 2π rt 3° 2 1 − sin(90 − θ1) The total heat flow is due to Joule Heating and is given by Q = I (V2 - V1) Results Comparison SHELL157 ANSYS Ratio I (Amps) Node 21 0.06140 0.06143 1.000 Q (Watts) Node 21 1–494...
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