Tuesday, February 27, 2018

thermodynamics - heat generation due to viscosity in a 3D fluid flow


Consider an arbitrary 3D fluid flow:


ν=V(x,t)


where velocity at each point ν is a function V of position x and time t (non-steady). Due to the viscosity μ there is heat being generated at each point in space. I know this heat should be a function of velocity, viscosity and div/curl of velocity:



˙q=F(,ν,μ)


But I can't just find it out.


For a 2D problem with unidirectional horizontal velocity of:


νx=Vx(x,y,t)


I think I can write


˙q=μνxyνx


Where τx=μνxy is the shear force due to viscosity. But I'm not quite sure if that's correct.


I would appreciate if you could help me know what is the correct form for equation 2.


P.S. I'm not quite sure but I think it should be something like:


˙q=μ(ν×).ν





No comments:

Post a Comment

classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...