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# 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 Tair. 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 Tair = 40°C,
convection coefficient α = 10 W/K-m².

Determine the temperature in the wire.

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

Results
Temperature in a wire: QuickField Reference* Temperature, °C Time 30 s 117.5 117.4 60 s 94.6 94.5 120 s 67.1 67.0

* 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. 