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THeat3: Transient temperature distribution in an orthotropic metal bar

A very long 4 cm square iron rod at Ti=100°C is suddenly immersed in a coolant at T1=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:
model of the orthotropic metal bar
a = 2 cm, b = 1 cm

Given:


Iron thermal conductivity λx = 76 W/K·m
Initial temperature Ti = 100°C Coolant temperature T0 = 20°C;
Convection coefficient α = 800 W/K·m2;
C = 37.688 J/kg·K, ρ = 7800 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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