- #1
fahraynk
- 186
- 6
In a fluid moving at constant velocity V, a concentration will undergo diffusion and convection
$$U_t=\alpha^2 U_{xx}+VU_x$$
I understand that in this situation you can transform to a moving coordinate system and the convection term will disappear and you can solve for diffusion alone and transform back.
My question is for a situation where the fluid streamlines are moving at different velocities. In this situation doesn't the diffusion depend on the speed of the fluid... So will alpha^2 be a function of velocity?
Alpha^2 is The diffusivity, if heat it would be thermal conductivity/(heat capacity * density)
If it is a function of velocity... how do I determine it? If not... what is the other term other than diffusion and convection that I put into the PDE?
An example of this situation would be couette flow, fluid flow between 2 moving plates infinite in x direction finite in Y.
$$U_t=\alpha^2 U_{xx}+VU_x$$
I understand that in this situation you can transform to a moving coordinate system and the convection term will disappear and you can solve for diffusion alone and transform back.
My question is for a situation where the fluid streamlines are moving at different velocities. In this situation doesn't the diffusion depend on the speed of the fluid... So will alpha^2 be a function of velocity?
Alpha^2 is The diffusivity, if heat it would be thermal conductivity/(heat capacity * density)
If it is a function of velocity... how do I determine it? If not... what is the other term other than diffusion and convection that I put into the PDE?
An example of this situation would be couette flow, fluid flow between 2 moving plates infinite in x direction finite in Y.