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- TL;DR Summary
- How to I include thermal stresses in the stress tensor
Suppose I have a mechanical stress tensor \sigma. Say I have the stress tensor for viscous flow:
\boldsymbol{\sigma}=-p\mathbf{I}+\frac{1}{2}(\nabla\mathbf{u}+(\nabla\mathbf{u})^{T})
If the thermal flux is given by \boldsymbol{\sigma}_{th}=\alpha T\mathbf{I}, so I have a total flux as:
\boldsymbol{\sigma}=-p\mathbf{I}+\frac{1}{2}(\nabla\mathbf{u}+(\nabla\mathbf{u})^{T})+\alpha T\mathbf{I}
Is this correct?
\boldsymbol{\sigma}=-p\mathbf{I}+\frac{1}{2}(\nabla\mathbf{u}+(\nabla\mathbf{u})^{T})
If the thermal flux is given by \boldsymbol{\sigma}_{th}=\alpha T\mathbf{I}, so I have a total flux as:
\boldsymbol{\sigma}=-p\mathbf{I}+\frac{1}{2}(\nabla\mathbf{u}+(\nabla\mathbf{u})^{T})+\alpha T\mathbf{I}
Is this correct?