How to analyze heat transfer effects of viscoelastic fluids

[Idrees Afridi]

n the heat transfer analysis of boundary layer flow of viscoelastic fluids many researchers see the variation of temperature of fluid inside the boundary layer with Prandtl number, for which they use prandtl number 0.7, 2 , 3, 4 ..
This is what generally the researchers do..
Currently i am thinking that , such a analysis is wrong because the Prandtl number they use are of air and water and both fluids are not viscoelastic ..
Secondly , i need some examples of viscoelastic fluids with the correspoding values of Prandtl number.

 

[boneh3ad]

Different fluids can have the same Prandtl number. It is only one of many properties used to characterize a fluid. It's not only air that is around 0.7, for example, but many gases.

 

[Idrees Afridi]

But gasses are also not viscoelastic fluids then why they are using Prandtl number of gasses .

 

[Idrees Afridi]

boneh3ad.. kindly give me some examples of viscoelastic fuids with Prandtl numbers..

 

[boneh3ad]

I'm not much of a viscoelastic fluid expert, I'm afraid. I'm simply trying to point out that just because air has a Prandtl number of 0.7 doesn't mean that another fluid can't.

 

[Chestermiller]

Before you start looking at complicated situations like boundary layer flow, I suggest you first look at heat transfer in steady state flow of viscoelastic fluid in a simple situation like a circular pipe. Assume that a certain location along the pipe, the pipe wall temperature suddenly changes from $T_0$ to $T_1$. Before even considering the development of a temperature profile, do you know how to determine the velocity profile of a viscoelastic fluid in the pipe as a function of radial position.? If you can't work this problem, you will not be able to get a handle on what viscosity to use in calculating the Prantdl number, or what the Prantdl number should be.

 

[Idrees Afridi]

Before you start looking at complicated situations like boundary layer flow, I suggest you first look at heat transfer in steady state flow of viscoelastic fluid in a simple situation like a circular pipe. Assume that a certain location along the pipe, the pipe wall temperature suddenly changes from $T_0$ to $T_1$. Before even considering the development of a temperature profile, do you know how to determine the velocity profile of a viscoelastic fluid in the pipe as a function of radial position.? If you can't work this problem, you will not be able to get a handle on what viscosity to use in calculating the Prantdl number, or what the Prantdl number should be.

Greetings:
the heat transfer analysis of viscoelastic fluid in a circular duct or curved circular duct has been investigated by many researchers and they are taking different Prandtl number without any justification. kindly check the link below and specially see the fig 3 in which the author mention that Pr=0.85
https://link.springer.com/article/10.1007/s00231-010-0641-3

 

[Idrees Afridi]

why the researchers are taking Prandtl number of gases and water during the heat transfer analysis of viscoelastic fluids ?

 

[Chestermiller]

why the researchers are taking Prandtl number of gases and water during the heat transfer analysis of viscoelastic fluids ?

The Oldroyd B fluid does not describe the behavior of any real viscoelastic fluids. It is a "viscoelastic fluid model" which exhibits certain qualitative features of real viscoelastic fluids, but can not describe the mechanical behavior of these fluids quantitatively. One of the qualitative features it does not describe correctly is the variation of the shear viscosity with shear rate. So, rather than the shear viscosity being a function of the radial velocity gradient, the Oldroyd B fluid predicts a constant value for the viscosity. In this case, it is possible to define a Prantdl number for the fluid based on a single unique viscosity parameter. The value this has in describing real-world heat transfer behavior of real viscoelastic fluid is, to say the least, highly questionable.