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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.

Results:
Temperature distribution in an orthotropic metal bar:

orthotropic metal bar thermal simulation

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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