Prandtl-number

Prandtl number (Pr)

Prandtl number signifies that, how much heat is carried away by how much fluid, transferring from one point to another. Mathematically it is defined as the ratio of momentum diffusivity to the thermal diffusivity. It is dimensionless quantity.
Let's understand little bit about diffusivity.
Conduction is basically the ability to transfer the things from one place to other place. It signifies how much material or medium is supporting in transferring things.
Just opposite to this property conduction we have one more property called diffusion. It's basically a storage capacity or we can say absorbing ability of material.
For particular material diffusivity is defined as, how much conducting property is dominating over storage property. So from here we can conclude that net transfer is not represented by conduction it represented by diffusion.
Kinematic viscosity shows net transfer of molecular movement that's why it's called momentum diffusivity not Momentum conductivity.
Pr = momentum diffusivity / thermal diffusivity = υ/α
'υ' refers to momentum diffusivity or kinematic viscosity and its unit is metre square per second
'α' refers to thermal diffusivity and its unit is metre square per second
From where we can conclude that prandtl number is a dimensionless quantity.
       υ = μ/ρ     α = K/(ρ*Cp)

∴ Pr = υ/α = (μ/ρ) / (K/(ρ*Cp)) = (μ*Cp)/K
'μ' is dynamic viscosity and its unit is Pascal second
'ρ' is density and its unit is kilogram per cubic metre
'K' is thermal conductivity and its unit is watt per metre Kelvin
'Cp' is specific heat and its unit is joule per kilogram Kelvin

To increase the value of prandtl number we must increase dynamic viscosity and specific heat and we must decrease thermal conductivity.
If value of prandtl number is very less than 1 then it means thermal diffusivity is dominating over momentum diffusivity and if value of prandtl number is much higher than 1 then it means momentum diffusivity is more dominating over thermal diffusivity.

example - for liquid mercury the heat conduction is more significant compared to convection, so thermal diffusivity is dominant. Show value of prandtl number for mercury is very low that is 0.015. However, for engine oil, convection is very effective in transferring energy from an area in comparison to pure conduction, so momentum diffusivity is dominant. So value of prandtl number for engine oil is very high that is between 100 to 40000.

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