Solving a system of second order differential equations, with length and radial derivates, but the conditions are quite complex to me.

Hi!

I want to use for loop to solve these equations (for drying particles in a fluid bed), but there are two things which prevent me.

1.) I don't know how to write the second order derivate in a for loop

2.) The inital and boundry conditions are somewhat difficult for me to solve. Can you write a script with which it runs. please?