First order ODE for different layers

Hello,

I would like to solve the following ODE for a research and I was wondering how to approach this problem. Variables a(i) and up(i) representing the Area of the pore and its flow velocity, respectively, take different values depending on the i'th layer 1<= i <= m. Initials value conditions:

Then the area of the pore gets updated again using the new value of c(i), concentration of particles at the i'th layer

I have no direct experience working on Matlab and would appreciate any help and leads in coding the loop and choosing the ode solver to tackle the problem. Thank you,

[darova]

What is this?

Is it a constant?

[Hamad El Kahza]

Up(i) is the cross-sectionally averaged pore velocity within each pore. It is obtained from the following formula for superficial Darcy Velocity U :

Please note that the pores are connected on a complex braching model. i is the number of layers (rows).