Wall Heat Transfer - Boundary Condition Description
Wall Heat Transfer is the convective heat transfer boundary condition that uses the Newton’s law of cooling. The law states the rate of heat loss of a body is directly proportional to the difference between the body temperature \(T_b\) and the surrounding ambient temperature \(T_a\).
Additionally, Wall Heat Transfer may include radiation and can be extended with the concept of thermal resistance, allowing one to model combined conductive and convective effects.
Wall Heat Transfer - Boundary Condition Understanding Wall Heat Transfer
Mathematically, the boundary condition can be expressed as:
\(q_n = h(T_b - T_a) + \epsilon \sigma (T_b^4 - T_a^4)\)
where:
\(q_n\) - heat flux normal to the boundary wall \([\frac{W}{m^2}]\),
\(h\) - heat transfer coefficient \([\frac{W}{m^2K}]\),
\(T_b\) - temperature at the boundary \([K]\),
\(T_a\) - ambient temperature \([K]\),
\(\epsilon\) - emissivity \([-]\),
\(\sigma\) - Boltzmann’s constant equal to \(5.67 · 10^{-8} [\frac{W}{m^2·K^4}]\)
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 total thermal resistance includes both conductive and convective components and can be expressed as:
\(R = \frac{1}{h} + \sum \frac{\delta_i}{\kappa_i}\)
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 \([\frac{W}{mK}]\).
Graphically, the above formula can be expressed as in Figure 1:
Wall Heat Transfer - Boundary Condition Application & Physical Interpretation
The Wall Heat Transfer boundary condition physically means that the boundary 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.
Wall Heat Transfer 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 | Wall Heat Transfer |
Wall Heat Transfer - Boundary Condition Wall Heat Transfer in SimFlow
To define Wall Heat Transfer in SimFlow the proper option must be selected from the drop-down menu for the Wall boundary - Figure 2.
\(T_{\infty}\) - ambient temperature
\(h\) - heat transfer coefficient
Emissivity - surface emissivity for radiative flux to ambient (used when Radiation is on)
Relaxation - Relaxation for the wall temperature, used when outer correctors and under-relaxation is applied
Wall Heat Transfer - Boundary Condition Wall Heat Transfer - Alternatives
In this section, we propose boundary conditions that are alternative to Wall Heat Transfer. 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 Wall Heat Transfer, but power instead is defined | |
specifies heat flux at the boundary |