Can we solve convection diffusion equation using pdetoolbox given a is constant vector?

Hi!

We would like to solve the following 2D convection diffusion equation. Would it be possible using vanilla MATLAB pdetoolbox?

where

or the flow is laminar in simpler words.

[Torsten]

Why v_x ? Shouldn't it be v_y ?

For r=R, velocity should be 0. This is not the case for your formula.

Are you sure diffusion in x-direction is relevant compared to convection in y-direction ?

In other words: Don't you think it suffices to solve

dc/dt = -v_y * dc/dy - f(c)

?

[Hashim]

Hopefully I can explain my system using the domain/geometry image above. So, for my system I have a flow incoming E4 and through E2. This flow is laminar and I want it to be explained via the equation given in my original post. Now at E3 I have a heterogenous reaction at the surface of an electrode. This involves the species in the flow getting oxidized at E3 via some kinetics which I denoted by .

In this case the velocity component in the x or axial direction in the direction of y/radial is important which is why the inclusion. This is perhaps because only the flux perpendicular to the E3 is crucial to our response. Now my understanding so far is that the only the gradient across the y or radial direction is important or so suggests the literature.

Okay I have now made a little correction to the original PDE as the diffusion into y is what is important as well the convective effect on the concentrartion profile of the species of interest in the x direction. Would this possible to do in the pde toolbox? or do I need external toolboxes which I do know that I will need if my flow is turbulent.