In laminar flow, the Prandtl number is the ratio of the viscous diffusion rate to the thermal diffusion rate expressed as the ratio of kinematic viscosity to the thermal diffusivity. Both of these quantities are physical parameters of the fluid and are therefore positive quantities.  In boundary layer theory the magnitude of the Prandtl number determines whether the thermal boundary layer is larger  ( Pr1) than the momentum boundary layer. In laminar natural convection flows, the situation is a bit more complicated. Pr1 viscous and buoyancy forces are in balance in the thermal boundary layer and viscous and inertia are in balance in the larger viscous boundary layer.  In turbulent flow the Prandtl number can be related to the eddy diffusivities but this is not my area of expertise- others can comment on Prandtl effects in turbulent flows. 

In laminar flow, the Prandtl number is the ratio of the viscous diffusion rate to the thermal diffusion rate expressed as the ratio of kinematic viscosity to the thermal diffusivity. Both of these quantities are physical parameters of the fluid and are therefore positive quantities.  In boundary layer theory the magnitude of the Prandtl number determines whether the thermal boundary layer is larger  ( Pr1) than the momentum boundary layer. In laminar natural convection flows, the situation is a bit more complicated. Pr1 viscous and buoyancy forces are in balance in the thermal boundary layer and viscous and inertia are in balance in the larger viscous boundary layer.  In turbulent flow the Prandtl number can be related to the eddy diffusivities but this is not my area of expertise- others can comment on Prandtl effects in turbulent flows. 

Dear Sir,

Prandtl number is relation between momentum diffusivity and thermal diffusivity of the fluid. Hence Pr is dependant only on the fluid and not on the surface on which the fluid flows. You will aslo be able to find that it is easy to find the thermal conductivity of gases at higher temperature, as Pr is mostly constant for gases. But Pr varies for liquids while they are in convection. Again the Pr is independant on the type of Convection - Free or Forced. And that is why Re and Pr helps in determining Forced Convection and Gr and Pr helps in finding Free Convection.

The value of Pr can't be negative, but it can be between 0 and 1 and also can be nearly 10 power 25. If you can have either negative thermal conductivity, negative viscosity or negative specific heat for fluids, then you can have negative Pr. As they are impossible, so negative Pr is also seemingly impossible, as from studies we have.

I think you have spelled De number wrongly. It is Deborah number.

If De > 1.0, then there is dominant elastic effects

If De < 0.5, then there is possibility of viscous effects.  

For any values other than these two extremes, the material would be showing the nature of viscoelasticity

You kindly read the following article to know about De.

http://scitation.aip.org/content/aip/magazine/physicstoday/article/17/1/10.1063/1.3051374

 @Kashif, You have two very good answers above that must have fulfilled your quest. What I would like to comment on is the need to formulate questions carefully when posting on RG. This is a common failing in the case of many others. You ask: "In fluid dynamics what is the importance and physical significance of Prandtl number?"

Pr no. does not arise in Fluid Mechanics but rather in convective heat flow. Further, if you made clear how you encountered negative Pr no. /Deborah no., respondents can give answers more useful to you.

 Dear Kashif,

You have already comprehensive answers for the question. I can add the reference to very useful book where the stucture of Pr in turbulent flow is investigated:

T. Cebeci, P. Bradshaw "Physical and computational aspects of convective heat transfer", Springer-Verlag, New York, Berlin, Heidelberg Tokyo, 1984.

Pr is the ration of momentum diffusion to thermal diffusion. Since, all the involved quantities in the definition are positive, so we can't have negative pr.

It gives us the information about momentum and thermal boundary layer

You have two very good answers above that must have fulfilled your quest. What I would like to comment on is the need to formulate questions carefully when posting on RG. This is a common failing in the case of many others. You ask: "In fluid dynamics what is the importance and physical significance of Prandtl number?"

Pr no. does not arise in Fluid Mechanics but rather in convective heat flow. Further, if you made clear how you encountered negative Pr no. /Deborah no., respondents can give answers more useful to you.

Yes, I agree with Dr. Saleem.

My answer is also the same, It can't be negative as it is a fluid property.

you can refer for its effectiveness.

• White, F. M. (2006). Viscous Fluid Flow (3rd. ed.). New York: McGraw-Hill. ISBN 0-07-240231-8.

Dear All;

I have a case with a low Pr number 0.026.

I want to know the state of the fluid is it laminar or turbulent.

I beg to disagree with Dr. Saleem, I believe fluid mechanics encompass the area heat transfer. Thermodynamics and Fluid Mechanics gave birth to heat transfer. So i believe the question was properly asked. It now depend on the researcher to give salient point on his opinion. Thank you

Suseel Jai Krishnan

You have a good answer but i would to insist that Prandtl number cant be negative and its specific for each fluid unlike other numbers.