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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 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, 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

Reference

Schneider P.J., "Conduction Heat Transfer", Addison-Wesley Publishing Co., Inc, Reading, Mass., 2nd Printing, 1957, Page 261, Example 10-7.

Download simulation files:

Student's version	Professional version
theat3_stud.zip	theat3.zip