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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:

Plane problem of heat transfer.

Geometry:

model of the orthotropic metal bar

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 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", Addison-Wesley Publishing Co., Inc, Reading, Mass., 2nd Printing, 1957, Page 261, Example 10-7.

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