Prandtl Number Calculator

This Prandtl number calculator can help you to find out what this dimensionless number is for various fluids. The viscosity and thermal diffusivity of a fluid determine the Prandtl number. The momentum transport is linked to the heat transport by this dimensionless entity.

The Prandtl number shows us how much faster heat diffuses through a fluid, i.e. whether heat conduction or convection is more prominent. The Prandtl number is important in heat transfer across fluids, which is a common occurrence in boundary layer flow. Continue reading to learn more about the Prandtl number and how to calculate it for air.

What is the Prandtl Number?

Consider a fluid moving over a heated flat plate, such as water. A Prandtl number is used to calculate the rate of energy or heat transfer via conduction or convection phenomena. 

Pr = Momentum Diffusivity / Thermal diffusivity

Pr = α / ν

What factors influence the Prandtl Number of a Fluid?

The following things influence Prandtl number:

  1. Fluid's dynamic viscosity
  2. Density 
  3. Thermal conductivity 
  4. Specific heat capacity (Cp)
  5. Temperarure

How do I find out the Prandtl Number?

The Prandtl number is calculated as follows:

  • Step 1: Multiply the fluid's specific heat to the dynamic viscosity.
  • Step 2: The product is divided by the fluid's thermal conductivity.

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What is the Water Prandtl Number?

Water has a Prandtl value of 6.9. The Prandtl number is calculated as Pr = 0.001002 x 4184 / 0.607 = 6.9 for a dynamic viscosity of 1.002 mPas, thermal conductivity of 0.607 W/mK, and specific heat of 4184 J/kgK.

What is the Air Prandtl Number?

Water has a Prandtl value of 0.715. The Prandtl number is calculated as Pr = 0.0000182 x1006 / 0.025596 = 0.715 for a dynamic viscosity of 0.0182 mPas, thermal conductivity of 0.025596 W/mK, and specific heat of 1006 J/kgK.

Significance of Prandtl Number 

The physical importance of the Prandtl number is that when it is smaller than 1, conductive heat transfer is a more dominating phenomenon, i.e., conduction transfers a greater proportion of heat than convection. When the Prandtl number is greater than 1, convective heat transfer takes precedence over conduction. Conduction and convection heat transfer rates are about the same for fluids with a Prandtl value near 1.

FAQs on Prandtl Number Calculator

1. What exactly is a Prandtl number?

The Prandtl number is the ratio of convection and conduction heat transfer rates. The ratio of momentum and thermal boundary layer thicknesses is a term used to describe the boundary layer phenomenon.

2. How do I calculate the Prandtl Number?

To find the Prandtl number, do the following: Multiply dynamic viscosity by the fluid's specific heat. Divide the result by the fluid's thermal conductivity.

3. What is the water number of Prandtl?

The Prandtl number is a fluid-specific property. Pr is 0.71 for air at ambient temperature, and most other gases have similar values. Water has a Prandtl value of 7.56 at 17°C.