skin effect and mutual coupling in stranded wire

If AC is appied to stranded copper wire, does skin effect come into play? It would seem that while the strands go from inside to out and back, they are NOT perfectly isolated, as in the case of litz wire, therefore that skin effect would come in to play as the frequency is increased. Does anyone have any research or cited material that can answer this? Is there any way to calculate how much the skin effect is effected by the wire jumping from out to center and back again?

"If a conductor is carrying high alternating currents, the distribution of current is not evenly distributed throughout the cross section of the conductor.

This is due to two independent effects known as the "Skin Effect" and the "Proximity Effect".

If a conductor is comprised of a large number of concentric circular elements or strands, those strands at the center of the overall conductor will be enveloped by a greater magnetic flux than those at the outside. Thus the self-induced back e.m.f. will be greater towards the center of the conductor thereby causing the current density at the center to be less than at the conductor surface. The extra concentration at the surface is known as the skin effect and results in an increase in the effective resistance of the conductor. The magnitude of the skin effect is influenced by the frequency, the size of the conductor, the amount of current flowing and the diameter of the conductor.

The proximity effect also increases the effective resistance and is associated with the fields of two conductors which are close together."

Reference "Electrical Cables Handbook" D. MCAllister

This 880 page book is out of print but hopefully it is in your company library or in an university engineering library near your location.

As you might imagine, the mathematical analysis is quite complex because of all the possible variations so your question regarding the skin effect of a strand or strands randomly moving in and out of the center of a few carefully defined conductors might be a great topic for a Masters or Ph.D. Thesis in Electrical Engineering, Engineering Physics or Theoretical Physics.

As far as Litz wire is concerned, take a look at this web page www.litz-wire.com/technical.html

Kindest regards,
Peter J. Stewart-Hay
Principal
Stewart-Hay Associates
www.Stewart-Hay.com