Power - Boundary Condition Description
Power boundary condition specifies the heat load applied to a wall by defining the total thermal power delivered through the boundary. Instead of prescribing heat flux directly, the user provides the overall power \(Q\) (in \(W\)), which is then automatically converted into uniform heat flux over the boundary surface.
This boundary condition is used whenever the heat input is known as a total power, for example for heaters, electronic components, laser sources, or any device where the total thermal output is specified rather than a flux or a heat-transfer coefficient.
The effective boundary temperature is not fixed explicitly. Instead, it is determined from the imposed power, the material thermal properties (conductivity, thickness), and any thermal resistance between the wall and its surroundings. As a result, the wall temperature adjusts to ensure that the prescribed power is transferred across the boundary.
Power - Boundary Condition Understanding Power
The formula used in the calculations is the following:
\(q_n = \vec n \cdot q = - \kappa \nabla_n T\)
where:
- \(q_n\) - heat flux normal to the boundary \([\frac{W}{m^2}]\),
- \(\kappa\) - thermal conductivity defined in material properties \([\frac{W}{mK}]\),
- \(\nabla_n T\) - temperature gradient normal to the boundary \([\frac{K}{m}]\).
When power is provided as an input, the \(q_n\) is defined as:
\(q_n = \frac{Q}{S_f}\)
where:
- \(Q\) - power \([W]\),
- \(S_f\) - patch area \([m^2]\).
Additionally, the concept of thermal resistance, which is an analogue to electrical resistance in Ohm’s Law, can be introduced. The higher the thermal resistance, the lower the heat transfer through the material.
In the thermal-resistance analogy, the heat flux is related to the temperature difference across the wall by:
\(q_n = \frac{\Delta T}{R}\)
where:
- \(R\) is thermal resistance.
The thermal resistance includes both convective and conductive heat transfer and can be expressed in the following way:
\(R = \frac{1}{h} + \sum \frac{\delta_i}{\kappa_i}\)
where:
- \(h\) - heat transfer coefficient \([\frac{W}{m^2K}]\),
- \(\delta_i\) - thickness of the wall or its part,
- \(\kappa_i\) - thermal conductivity of the wall or its part \([\frac{W}{mK}]\).
This formulation represents a simplified one-dimensional thermal resistance model commonly used to interpret wall heat transfer.
Graphically, the above formula can be expressed as in Figure 1:
Power - Boundary Condition Application & Physical Interpretation
The Power boundary condition physically means that the boundary effectively represents the external thermal environment (flux, convection, radiation) and supplies the correct temperature or gradient so that the interior solution exchanges exactly that amount of heat.
Power in Thermal Analysis applications
Example applications: heat transfer through the wall
These types of simulations can be solved using the buoyantSimpleFoam (solver). This could involve studying the effectiveness of insulation or the impact of solar radiation on external walls.
The boundary condition is used to model the heat flux through building walls due to external factors like solar radiation, internal heating or cooling, and convective heat transfer with the external environment.
| Physics | Pressure | Velocity | Temperature |
|---|---|---|---|
Building’s wall | Zero Gradient | Fixed Value | Power |
Power - Boundary Condition Power in SimFlow
To define Power in SimFlow the proper option must be selected from the drop-down menu for the Wall boundary - Figure 2.
q - heat flux at the boundary
\(\delta\) - thickness of the wall
\(\kappa\) - thermal conductivity
Power - Boundary Condition Power - Alternatives
In this section, we propose boundary conditions that are alternative to Power. While they may fulfill similar purposes, they might be better suited for a specific application and provide a better approximation of physical world conditions.
| Boundary Condition | Description |
|---|---|
fixes the temperature at the wall boundary | |
works in a similar way to Power, but heat flux instead is defined | |
works in a similar way to Power, but Wall Heat Transfer coefficient \(h\) and ambient temperature \(T_{\infty}\) are defined |