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  • Surface heat flux

    With the surface heat flux boundary condition, a prescribed constant or variable heat flux per unit area can be applied to the assigned boundary faces. This is useful to model heat sources or heat sinks, where the power per unit area is known.

    surface heat flux boundary condition setup panel
    Figure 1: Surface heat flux boundary condition panel. Enter the desired heat flux and units, or select the variable button to input a function or table.

    The parameters of the boundary condition are:

    1. Heat flux value: The value of the surface heat flux variable to be applied, in units of power \((W, Btu/s)\) per units of area \((m^2, in^2)\).
    2. Assignment: Set of faces where the heat flux value will be applied.

    Application Hints

    For positive flux values, the heat enters the body (heat source), and for negative values the heat leaves the body (heat sink).

    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:

    $$ \kappa (\nabla T \cdot \vec{n}) = Q_s $$


    • \( \kappa \) 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, and
    • \( Q_s \) is the specified surface heat flux.

    Variable Heat Flux

    Variable heat flux values can be specified with the use of the formula or table inputs. The allowed functions are:

    • Time-dependent: The heat flux varies 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 power loading curves.
    • Coordinate-dependent: The heat flux varies with respect to the position in space (variables X, Y, Z). This is useful to apply known power gradients on faces.
    • Temperature-dependent: Available in nonlinear simulations, the local heat flux at each point is a function of the surface temperature. This type of function can be used to model radiation heat transfer using the Boltzmann equation, as exemplified in the validation case ‘Hollow sphere, convection and radiation‘, linked below.

    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.

    surface heat flux example application
    Figure 2: Temperature contour plot of a hollow sphere subject to surface heat flux (see validation case below).

    Last updated: August 30th, 2022