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THeat3: Transient temperature distribution in an orthotropic metal bar
A long metal bar of rectangular cross-section is initially at a temperature T0 and is then suddenly quenched in a large volume of fluid at temperature Ti. The material conductivity is orthotropic, having different X and Y directional properties. The surface convection coefficient between the wire and the air is α.
Problem Type:
A plane-parallel problem of nonlinear heat transfer.
Geometry:
Given:
a = 2 in, b = 1 in
λx = 34.6147 W/K·m, λy = 6.2369 W/K·m;
Ti = 37.78°C, T0 = 260°C;
a = 1361.7 W/K·m2;
C = 37.688 J/kg·K, ρ = 6407.04 kg/m3.
Problem:
Determine the temperature distribution in the slab after 3 seconds at the center, corner edge and face centers of the bar.
Solution:
To set the non-zero initial temperature we have to solve an auxiliary steady state problem, whose solution is uniform distribution of the temperature T0
A time step of 0.1 sec is used.
Comparison of results
|
Temperature, °C |
Point |
QuickField |
ANSYS |
Reference |
(0,0) in |
238.7 |
239.4 |
237.2 |
(2,1) in |
66.43 |
67.78 |
66.1 |
(2,0) in |
141.2 |
140.6 |
137.2 |
(0,1) in |
93.8 |
93.3 |
94.4 |
Reference
Schneider P.J., "Conduction Heat Transfer", Addison-Wesley Publishing Co., Inc, Reading, Mass., 2nd Printing, 1957, Page 261, Example 10-7.
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