VelocityGradient as a function of temperature
 

mu*du/dy = A* dT/dy + B*dC/dy ;

A and B are constants.
v = 0

Is it possible to define above equation as boundary condition using Groovy BC or using library for it ?
please help how to write this Boundary Condition.
I am attaching the library which I used but the result are not good. It is a 2D cavity with temperature and concentration given to the side walls and the surafce tension is linearly varying with the temperature. The solver is for the OpenFoam 5.0.
Is it necessary to initialize the test case using setFields for the concentration?

thanks.