Temperature response of a suddenly cooled wire

QuickField simulation example

Determine the temperature response of a copper wire of diameter d, originally at temperature T₀, when suddenly immersed in air at temperature T_air. The convection coefficient between the wire and the air is α.

Problem Type
Plane problem of heat transfer.

Geometry

d = 0.1 cm.

Given
Copper initial temperature T₀ = 150°C,
   thermal conductivity λ = 391 W/m·K,
   specific heat C = 383 J/kg·K,
   volume mass density ρ = 8930 kg/m³;
Air temperature T_air = 40°C,
   convection coefficient α = 10 W/K-m².

Task
Determine the temperature in the wire.

Solution
A time step of 1 s is used to run numerical analysis.
Analytical solution^*: (T - T_air) / (T₀ - T_air) = exp(-0.0117·t)

Results
Temperature in a wire:

* Reference: Frank Kreith, Raj M. Manglik, Mark S. Bohn Principles of Heat Transfer, Cengage Learning, Jun 10, 2010 - Technology & Engineering - 696 pages, Page 119, Example 2-10.

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