Yes, a diagram would help!

The two windings each have inductance Lp and Ls which is related to the absolute permeability of the core.

The maximum possible permeability of body centred cubic iron/steel is at absolute zero but varies with the magnetic field strength.

Considering Curie-Weiss (variation with temperature) at 30 C, the relative permeability of iron/steel can be estimated by an empirical approximation

Ur = 734000 / (H^0.92) Easy enough with a calculator, and H [A/m] is rms value

When the flux produced by the primary does not completely link the secondary, the coefficient of coupling reduces below 1.

For analysis of this , the Mutual Inductance is used.

M = k * sqrt( Lp*Ls)

Then the ideal transformer model ( neglecting magnetizing inductance) becomes a two loop Kirchoff

~~where the Lp, Ls are the diagonals,~~~~and M is the two off diagonals.~~By that method the all important leakage reactance can be calculated and compared with measurement. (coefficient of coupling k is abstract)

In the transient simulators (I use qucs, presume others too) The k value is entered by the user and the leakage reactance is internally calculated.

The difficulty with that k entry is that it can't be visualized and is crammed to nearly = 1 for ordinary transformers.

Also k is not an output in FEM models of inductors ( I used QuickField which outputs L & M and don't know if that is same in others)

I would recommend that those in transformer design /specification should have familiarity with the 2 loop transformer model.

Edit

Added a S Parameter simulation in qucs comparing qucs transformer model against 2 loop Kirchoff, showing inductances.

https://app.box.com/s/yx8s3wxb73xarhtzo198cmz06pvnhhaa