4th order tensor when deriving shear stress tensor in NS equations

TurbJet · February 5, 2018, 23:45

When deriving shear stress tensor for NS equations, it has 4th order tensor $\alpha_{ijkl}$ , which can be expanded as the following pic.

But how the expansion is done?

elones · February 7, 2018, 06:52

Quote:

Originally Posted by TurbJet

When deriving shear stress tensor for NS equations, it has 4th order tensor $\alpha_{ijkl}$ , which can be expanded as the following pic.

But how the expansion is done?

Look into Aris' Vectors, Tensors and the Basic Equations of Fluid Mechanics.

FMDenaro · February 7, 2018, 11:11

Quote:

Originally Posted by TurbJet

When deriving shear stress tensor for NS equations, it has 4th order tensor $\alpha_{ijkl}$ , which can be expanded as the following pic.

But how the expansion is done?

Could you explain in which equation you are using a 4th order tensor? It should appear somehow expressed as eiej Tijkl ekel

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