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Temperature response of a suddenly cooled wire

transient heat transfer with convection benchmark, dynamic temperature response, cooling simulation, Frank Kreith Principles of Heat Transfer

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
Copper wire heat transfer model Temperature response of a suddenly cooled wire Copper ( C, ρ, λ ) Air Ød T0 Tair , α

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.

Task
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:

DC wire thermal simulation

Temperature, °C

Time QuickField (Reference)*
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.

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