Question

Which is the diffusion terms of the y-momentum equation?

(a) \(\frac{\partial\tau_{xy}}{\partial x}+\frac{\partial\tau_{yy}}{\partial y}+\frac{\partial\tau_{zy}}{\partial z}\)

(b) \(\frac{\partial\tau_{yx}}{\partial x}+\frac{\partial\tau_{yy}}{\partial y}+\frac{\partial\tau_{yz}}{\partial z}\)

(c) \(\frac{\partial\tau_{xx}}{\partial x}+\frac{\partial\tau_{yx}}{\partial x}+\frac{\partial\tau_{zx}}{\partial x}\)

(d) \(\frac{\partial\tau_{xy}}{\partial y}+\frac{\partial\tau_{yy}}{\partial y}+\frac{\partial\tau_{zy}}{\partial y}\)

I have been asked this question in an interview for job.

This question is from Navier Stokes Equation topic in division Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

Right answer is (a) \(\frac{\partial\tau_{xy}}{\partial x}+\frac{\partial\tau_{yy}}{\partial y}+\frac{\partial\tau_{zy}}{\partial z}\)

Easy explanation: \(\frac{\partial\tau_{xy}}{\partial x}+\frac{\partial\tau_{yy}}{\partial y}+\frac{\partial\tau_{zy}}{\partial z}\) are the diffusion terms of the y-momentum equation. It involves all the shear stress tensors which are in the y-direction.