Fluid Mechanics Viscous Dissipation

AI Thread Summary
The discussion centers on finding the correct expression for viscous dissipation in the context of Burgers' vortex, specifically in cylindrical coordinates with a velocity component in the V theta direction. There is confusion regarding the appropriate equations, with references to different forms such as τ:S and τ:∇V. Clarification is provided that the rate of deformation tensor S is defined as (∇V + ∇VT)/2, leading to the conclusion that τ equals 2μS. Ultimately, all mentioned relations are consistent and should yield the same results for viscous dissipation. Understanding these equations is crucial for accurate analysis in fluid mechanics.
Jade Sola
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I am trying to find an expression for viscous dissipation for burger's vortex Velocity field which only has velocity component in the V theta direction. I'm confused as to which equation for viscosity dissipation is correct. I am seeing a lot of different things tau:S, tau:delV..which one is correct?

Thanks!
 
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Um.. I think you need to be a bit more specific. What form are you working with?
 
a_potato said:
Um.. I think you need to be a bit more specific. What form are you working with?
cylindrical coordintates...so this is what the velocity field is
upload_2014-11-26_18-20-1.png

what I am confused about is what exactly is the equation for viscous dissipation ... My professor said in class that it is 2muS:S (from Navierstokes eq.3) but I am seeing differen things online and I also heard from another classmate of mine that it has something to do with Sxtau components. I am just confused ...sorry if I am confusing the matter here.
 
Jade Sola said:
cylindrical coordintates...so this is what the velocity field is
View attachment 75868
what I am confused about is what exactly is the equation for viscous dissipation ... My professor said in class that it is 2muS:S (from Navierstokes eq.3) but I am seeing differen things online and I also heard from another classmate of mine that it has something to do with Sxtau components. I am just confused ...sorry if I am confusing the matter here.
If S is the rate of deformation tensor (which it certainly appears to be), then:
S = (∇V+∇VT)/2
and
τ = 2μS
So, the rate of viscous dissipation is τ:∇V = τ:S = 2μS:S. All the relations you wrote are the same, and should give the same results.

Chet
 

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