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THeat3: Transient temperature distribution in an orthotropic metal bar
A long metal bar of rectangular crosssection is initially at a temperature T_{0} and is then suddenly quenched in a large volume of fluid at temperature T_{i}. 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:
Plane problem of heat transfer.
Geometry:
Given:
a = 2 in, b = 1 in
λ_{x} = 34.6147 W/K·m, λ_{y} = 6.2369 W/K·m;
T_{i} = 37.78°C, T_{0} = 260°C;
a = 1361.7 W/K·m2;
C = 37.688 J/kg·K, ρ = 6407.04 kg/m^{3}.
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 nonzero initial temperature we have to solve an auxiliary steady state problem, whose solution is uniform distribution of the temperature T_{0}
A time step of 0.1 sec is used.
Comparison of results
Temperature distribution in an orthotropic metal bar:

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", AddisonWesley Publishing Co., Inc, Reading, Mass., 2nd Printing, 1957, Page 261, Example 107.
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