How can I solve stiff equations by method of line (MOL)?

I want to solve 7 coupled equations.I use method of line(MOL) and discrete the equation in Length and radius and convert them to a system of ODEs in time.and use ode15s to solve them in MATLAB. But an error occur:

Warning: Failure at t=5.422028e-006. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (1.355253e-020) at time t.

It means that equations are too stiff. How can i solve them? Is there another method? I really confused.please help me. I attached my code and equations. Thanks.

[Are Mjaavatten]

The most likely cause is that there is some error or inconsistency in your function for the derivatives, or you may possibly have hit a singularity. Inspect the the values of the derivatives at t=0 to see if they look reasonable. You may also try to run ode15s over a very short interval, e.g. to t = 1e-6 or t = 5e-6 and inpect how your variables change.