Fluid Mechanics Viscous Dissipation

  • #1
2
0
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!
 

Answers and Replies

  • #2
27
4
Um.. I think you need to be a bit more specific. What form are you working with?
 
  • #3
2
0
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. Im just confused ....sorry if Im confusing the matter here.
 
  • #4
20,773
4,502
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. Im just confused ....sorry if Im 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
 

Related Threads on Fluid Mechanics Viscous Dissipation

  • Last Post
Replies
9
Views
9K
  • Last Post
Replies
2
Views
3K
Replies
1
Views
2K
  • Last Post
Replies
10
Views
7K
  • Last Post
Replies
1
Views
805
Replies
7
Views
4K
  • Last Post
Replies
5
Views
7K
  • Last Post
Replies
4
Views
2K
Top