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=μ∂νx∂yνx
Where τx=μ∂νx∂y 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
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