how can i choose the wire gauge for transformer design????

I'll bet that you can buy one for much less than you can make one. Have you even priced them?

If you want to make one that is unconventional, then you need a lot more education than can be gotten from CR4, so answering the question, "is the current density is same for power or auto transformers?," is very simply, 'not all you need to know.'

i am agreed with u sir.actually i have knowledge regarding transformers but i want to know about the values of current density selected while designing power transformers,auto transformers,welding sets etc.what are the factors that effect the current density value in transformers design.

Current density is merely a function of wire size, e. g. amperes per square mil, etc., and to the extent that there is some "skin effect" at 50-60 Hz, you must increase wire size to compensate for that. Additionally, transformer windings are in close proximity to each other and typically in layers, virtually making a copper, iron and kraft paper solid for which a thermodynamic model must be made to predict temperature rise. Wire size must be increased beyond conductor sizes used in free air.

Most electrical code books will have tables for temperature compensation which are good for a first pass as they have a fair margin for error. Copper has a resistivity that accounts for loss as heat. Heat must be dissipated by the transformer to prevent unlimited temperature rise. Wire insulation has a limit of operating temperature and the inner windings must be kept at or below that temperature.

I clicked on the link given by "Guest" pointing you to a treatise on transformers at the University of Colorado, and I found it to be very informative. If you look at the Wikipedia page on current density, you'll find more than I intend to type.

You can do a look at the Transformer Design chapter from the Introduction to Power Electronics Course at University of Colorado http://ece-www.colorado.edu/~ecen5797/course_material/Ch15slides.pdf

Wire gauge is determined by the heat developed in primary and secondary winding due to the copper resistance in one hand and the coil/core size capable to cool this heat by normal air flow around and the normal air temperature. These factors are included in tables that for given power give the size of the core and the gauge of the wires. So the solution of your problem are contained in these tables. Good luck and regards, Faruk.