Viscous Stress Tensor for a Newtonian Fluid

Using the Newton’s Law of Viscosity, the equation for Shear Stress can be written as

$${\tau }_{ij}=2v{S}_{ij}=v\left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i}\right)$$

Where,

• $v\to$ Kinematic Molecular Viscosity
• $S_{ij}\to$ Strain Rate Tensor