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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/Km, λy = 6.2369 W/Km;
Ti = 37.78C, T0 = 260C;
α = 1361.7 W/Km2;
C = 37.688 J/kgK, 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:
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.

See the THeat3.pbm problem in the Examples folder.