Prandtl Number Formula |
||
|
\( Pr \;=\; \dfrac{ \nu }{ \alpha }\) (Prandtl Number) \( \nu \;=\; Pr \cdot \alpha \) \( \alpha \;=\; \dfrac{ \nu }{ Pr }\) |
||
| Symbol | English | Metric |
| \( Pr \) = Prandtl number | \( dimensionless \) | \(dimensionless\) |
| \( \nu \) (Greek symbol nu) = kinematic viscosity of the fluid | \(in^2\;/\;sec\) | \(mm^2\;/\;s\) |
| \( \alpha \) (Greek symbol alpha) = thermal diffusivity of the fluid | \(in^2\;/\;sec\) | \(mm^2\;/\;s\) |
Prandtl number, abbreviated as Pr, a dimensionless number, in fluid dynamics is used to calculate force by the ratio of momentum diffusivity (kinematic viscosity) and thermal diffusivities. This number helps characterize the relative thickness of the velocity boundary layer to the thermal boundary layer. The Prandtl number is typically used to classify fluids into different categories based on their behavior in heat transfer processes.
Prandtl Number Interpretation
- Low Prandtl Number () - Thermal diffusivity dominates over momentum diffusivity. This means heat diffuses faster than momentum. Common in liquid metals (mercury, Pr ≈ 0.01–0.03), where the thermal boundary layer is thicker than the momentum boundary layer.
- Prandtl Number () - Momentum and heat diffuse at similar rates. This is typical for gases like air (Pr ≈ 0.7–1), where the thermal and momentum boundary layers are of comparable thickness.
- High Prandtl Number () - Momentum diffusivity dominates over thermal diffusivity. Heat diffuses more slowly than momentum. This occurs in viscous fluids like oils (Pr ≈ 100–1000), where the thermal boundary layer is thinner than the momentum boundary layer.
Prandtl Number Formula |
||
|
\( Pr \;=\; \dfrac{ \mu \cdot Q }{ k }\) (Prandtl Number) \( \mu \;=\; \dfrac{ Pr \cdot k }{ Q }\) \( Q \;=\; \dfrac{ Pr \cdot k }{ \mu }\) \( k \;=\; \dfrac{ \mu \cdot Q }{ Pr }\) |
||
| Symbol | English | Metric |
| \( Pr \) = Prandtl number | \(dimensionless \) | \(dimensionless\) |
| \( \mu \) (Greek symbol mu) = dynamic viscosity of the fluid | \(lbf-sec\;/\;ft^2\) | \( Pa-s \) |
| \( Q \) = specific heat capacity of the fluid | \(Btu\;/\;lbm-F\) | \(kJ\;/\;kg-K\) |
| \( k \) = thermal conductivity of the fluid | \( F \) | \( K \) |
Prandtl Number Applications
The Prandtl Number is important in various applications, including the analysis of heat transfer in fluids, the prediction of boundary layer behavior in fluid flow around solid objects, and the design of engineering systems involving heat and fluid flow. It helps engineers and scientists understand the relative importance of conduction and convection in different fluids and design systems accordingly.
