anyway what is your idea about using Al value from known core with similar dimension to unknown one
Dimensions really don't play a major role in this (they do...but)
That's cause a core with relevant permeability of 4300 will have let's say an inductance of 4mH with 48 turns
and a core with relevant permeability of 2300 will need 65 turns to have the same inductance.
Since you are switching the coil on a certain frequency, that's gonna affect the current through your coil.
And the current in your coil is gonna affect the strength of your magnetic field in the core.
Note that you can't impose a current on a coil, as you can't impose a voltage on a capacitor.
Further more the less current the less power stored in the core, and the less can be extracted from it on the other side.
So it's not all that of black magic in the end. It's what you need and what you get...
In the end, it's a golden ratio that you should keep. As from what you get the energy at the second coil is the magnetic field in the core
and depends on both the current that runs the first coil, but also the number of turns...
Best Regards, Lefteris