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Transient temperature distribution in an orthotropic metal bar

transient temperature response, heat transfer benchmark simulation, orthotropic bar temperature distribution, Schneider 'Conduction Heat Transfer'

A very long square iron rod at Ti=260°C is suddenly immersed in a coolant at T0=37.78°C.

Problem Type
Plane-parallel problem of heat transfer.

Geometry
Transient temperature distribution in an orthotropic metal bar A very long square iron rod at is suddenly immersed in a coolant Model T0 , α Ti X Y a b

a = 2", b = 1"

Given
Iron thermal conductivity λx = 34.6 W/K-m, λy = 6.24 W/K-m
Initial temperature Ti = 260°C;
Coolant temperature T0 = 37.8°C;
Convection coefficient α = 1363 W/K-m²;
Specific heat C = 38 J/kg·K, ρ = 6400 kg/m³.

Task
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 (Reference)*
(0,0) in 239 237
(2,1) in 66.7 66.1
(2,0) in 142 137
(0,1) in 94.1 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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