modelFreeAeraulicConvection

Information

This components allows to model the air movement induced by natural convection over a vertical wall. It assumes that the prerequisites presented in the information tab of the FreeConvection of the HeatTransfer component are known.

To quantify the convective flow of gas an analogy between heat and mass transfer is made. The natural convection heat transfer coefficient encompasses the balance between the buoyancy force and the viscous force. This is a globalisation of the local resolution of momentum and energy conservation. Therefore, it is supposed that all the heat dissipated by the wall creates the work to make the gas move. To computed the mass flow rate inducted bu natural convection, it is necessary to make closure hypotheses. Indeed, the mathematical model under the analogy presented above gives:

Where:

• m_flow is the mass flow rate induced by convection
• cp is the specific heat capacity at constant pressure of the mixture
• T_outlet is the mean outlet Temperature of the boundary layer
• T_inlet is the mean inlet Temperature of the boundary layer
• h_cv is the convective heat transfer coefficient
• S is exchange surface area
• T_wall is the wall Temperature
• T_∞ is fluid Temperature outside the boundary layer

The unknown variables are m_flow, T_outlet and T_inlet. With this tree unknowns and one equation, two closure equations are required.

The obvious comes with the inlet temperature which is equal to the T_∞ because there is there is not yet a boundary layer.
The second is to assume that T_outlet = T_wall. In pratical is never true. A Computationnal Fluid Dynamic (CFD) study performed on a flat plate in a rest atmosphere gives roughly a flow rate twice that calculated from the method above.

The final expression for the mass flow rate derives:

All the flowports have to be connected to components of type control volume (lump volume, boundaries...).

Parameters

Connectors

Components

Contents

Name	Description
Medium