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 () - This corresponds to fluids with a high thermal conductivity compared to their viscosity. Common examples include metals and molten salts. In these cases, thermal diffusion is very effective compared to momentum diffusion.
- High Prandtl Number () - This represents fluids where momentum diffuses more rapidly than heat. Common examples include oils and liquid metals. In these cases, heat transfer is relatively slower compared to momentum transfer.
- Intermediate Prandtl Number () - For fluids like water and air, which are commonly encountered in many engineering applications, the Prandtl number is around 1. In these cases, momentum and heat transfer are of comparable importance.
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.
Prandtl Number Formula |
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\( Pr \;=\; \dfrac{ \nu }{ \alpha }\) (Prandtl Number) \( \nu \;=\; Pr \cdot \alpha \) \( \alpha \;=\; \dfrac{ \nu }{ Pr }\) |
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| 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 Formula |
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\( Pr \;=\; \dfrac{ \mu \cdot Q }{ k }\) (Prandtl Number) \( \mu \;=\; \dfrac{ Pr \cdot k }{ Q }\) \( Q \;=\; \dfrac{ Pr \cdot k }{ \mu }\) \( k \;=\; \dfrac{ \mu \cdot Q }{ Pr }\) |
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| 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 | \( F \) | \( K \) |
