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Convective Heat Flux

With the convective heat flux boundary condition, a linear heat transfer model is applied between the boundary entities and the external environment. This is useful to model general heat losses or gains such as those due to natural/forced convection or conduction with adjacent bodies of relatively constant temperature.

convective heat flux boundary condition panel
Figure 1: Convective heat flux boundary condition panel. Enter the desired reference temperature and heat transfer coefficient, or select the variable button to input a function or table.

The parameters of the boundary condition are:

  1. Reference temperature: Temperature of the environment, used to compute the boundary heat transfer.
  2. Heat transfer coefficient: Proportionality value used to compute the boundary heat transfer, with units of power \((W, Btu/h)\) divided by units of temperature \((K, °C, °F)\) and area \((m^2, in^2)\)
  3. Assignment: Set of faces where the convective heat flux value will be applied.

Supported Analysis Types

The following analysis types support the usage of this boundary condition:

Resultant Heat Transfer

The heat transfer on each element of the assigned surfaces will be given by the difference between the local temperature:

$$ \kappa (\nabla T \cdot \vec{n}) = h(T – T_{ref}) $$

Where:

  • \( \kappa \) is the thermal conductivity of the material,
  • \( \nabla T \) is the local temperature gradient,
  • \( \vec{n} \) is the area normal vector of the element boundary surface,
  • \( h \) is the convection heat transfer coefficient,
  • \( T \) is the local temperature.
  • \( T_{ref} \) is the external reference temperature, and

Variable Convective Heat Flux

Variable heat flux values can be specified with the use of the formula or table inputs for the reference temperature and/or the heat transfer coefficient. The allowed functions are:

  • Time-dependent: The parameters vary with respect to time (variable t) in a transient heat transfer, nonlinear static or dynamic thermomechanical simulation. This is useful, for instance, to ramp up the load from zero in nonlinear simulations, where a sudden application of load leads to numerical divergence, or to define heat transfer curves.
  • Coordinate-dependent: The parameters vary with respect to the position in space (variables X, Y, Z). This is useful to apply known heat transfer gradients on the boundary faces.

Maximum Number of Table Parameters

Due to numerical difficulties, the underlying structural solver (Code_Aster) only supports table function definitions of one or two variables. If you need to define a function of the three spatial coordinates (X, Y, Z), or even combine it with time, you must create an analytical formula for it.

convective heat flux example application
Figure 2: Temperature contour plot of an LED pack heat sink subjected to convective heat flux (see validation case below).

Last updated: November 26th, 2020

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