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Transient temperature distribution in an orthotropic metal bar
THeat3: Transient temperature distribution in an orthotropic metal bar
A very long 4 cm square iron rod at T_{i}=100°C is suddenly immersed in
a coolant at T_{1}=100°C. What is the temperature
on a line 1 cm from one side and 2 cm from the adjoining side, after
10 s?
Problem Type:
Plane problem of heat transfer.
Geometry:
a = 2 cm, b = 1 cm
Given:
Iron thermal conductivity λ_{x} = 76 W/K·m
Initial temperature T_{i} = 100°C
Coolant temperature T_{0} = 20°C;
Convection coefficient α = 800 W/K·m2;
C = 37.688 J/kg·K, ρ = 7800 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.
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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