Vadasz number, abbreviated as Va, a dimensionless number, is used in the study of fluid dynamics and heat transfer, particularly in the context of convection in porous media. The Vadasz number quantifies the effect of inertia in the momentum equation when a generalized Darcy model is employed. In this model, a time-derivative term is included to account for the acceleration of fluid flow through the porous medium, unlike the classical Darcy’s law, which assumes steady-state flow. The Vadasz number essentially measures the ratio of the inertial effects to the viscous effects in the porous medium.
Vadasz Number formula |
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\( Va \;=\; \dfrac{ \phi \cdot Pr }{ Da }\) (Vadasz Number) \( \phi \;=\; \dfrac{ Va \cdot Da }{ Pr }\) \( Pr \;=\; \dfrac{ Va \cdot Da }{ \phi }\) \( Da \;=\; \dfrac{ \phi \cdot Pr }{ Va }\) |
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| Symbol | English | Metric |
| \( Va \) = Vadasz Number | \( dimensionless \) | \( dimensionless \) |
| \( \phi \) (Greek symbol phi) = Porous Media | \( dimensionless \) | \( dimensionless \) |
| \( Pr \) = Prandtl Number | \( dimensionless \) | \( dimensionless \) |
| \( Da \) = Darcy Friction Factor | \( dimensionless \) | \( dimensionless \) |
Vadász Number Interpretation
- Low Vadasz Number (Va << 1) - Indicates that inertial effects are negligible compared to viscous effects. The flow adjusts almost instantly to changes, and the system behaves more like the classical Darcy flow, where the fluid motion is dominated by the porous medium’s resistance (viscosity and permeability).
- High Vadasz Number (Va >> 1) - Suggests that inertial effects become significant. The fluid takes time to accelerate or decelerate, leading to dynamic behaviors like oscillations or delayed responses to thermal or mechanical forcing. This is especially relevant in systems where rapid changes occur, such as in rotating porous media or under strong heating.
In engineering, the Vadasz number guides the design of systems involving porous media, such as filtration units, catalytic reactors, or geothermal reservoirs. If Va is high, designers must account for transient effects, possibly requiring more complex control mechanisms to manage unsteady flow or heat transfer. In geophysics, it helps model convection in Earth’s crust or mantle, where porous flow and thermal gradients drive processes like magma movement or hydrothermal circulation.
