Heat Transfer and Temperature Distribution in a Fin

This Demonstration calculates temperature distributions and heat transfer for a fin (a.k.a. extended surface) of uniform cross-sectional area. Two possible tip conditions are considered: (1) there is no heat transfer through the tip surface (adiabatic case); (2) the tip loses heat through convection, implying that the size of the tip surface is large enough for heat loss to be taken into account. The fin is attached to a base of equal cross-sectional area that is at a constant temperature of 100 Down the length of the fin, heat is lost through natural convection to the ambient air. The temperature decreases down the fin due to conduction down the fin and to heat being lost by convection. The conduction is assumed to be one-dimensional along the length of the fin. Maximum heat transfer is achieved when the temperature of the fin is uniform, and heat is also lost through the tip. You can vary the dimensions and shape of the fin, as well as the thermal conductivity. A three-dimensional representation of the fin is also shown.
  • Contributed by: Benjamin L. Kee
  • (University of Colorado Boulder, Department of Chemical and Biological Engineering)


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Heat Transfer Constants
tempBase = 100 °C, temperature of the base
tempInf = 100 °C, temperature of the ambient air
, convection heat transfer coefficient
, thermal conductivity of copper
, thermal conductivity of platinum
, thermal conductivity of carbon steel
Fin Dimensions
len, fin length (m)
, position down the fin (m)
Axial Temperature Distribution
Total Heat Transfer
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