For oxygen-acetylene cutting, 2 chemical reactions are occurring:

1) C2H2 + O2 --> 2CO + H2

1 mole of acetylene (C2H2) is combined with 1 mole oxygen gas (O2) in a combustion process initiated by a spark to produce 2 moles of carbon monoxide (CO) and 1 mole of hydrogen gas (H2). This takes place in the small bluish white cones closest to the cutting torch tip. This produces 448 kilojoules of heat per mole of acetylene gas, and is used to heat the metal to the melting point.

2) 2CO + H2 + 1.5O2 --> 2CO2 + H20(g)

The products of the first reaction are combined with excess oxygen to produce the products of the second reaction. 2 moles of carbon monoxide plus 1 mole of hydrogen gas is combined with 1.5 moles of oxygen gas to produce 2 moles of carbon dioxide and 1 mole of water vapor (H2O gas). This produces the outer flame.

Once the metal is heated to the melting point, a high velocity oxygen stream in the center of the cutting tip oxidizes the molten metal and blows it through the metal to produce a cutting action.

For Gas Metal Arc Welding (you called it wire-feed argon welding) the power source supplies a constant voltage (E) and the wire feeder speed controls the amperage (I) of the welding arc. The amount of power (W) in watts produced to heat the wire at the contact tip is: W = E x I. The amount of heat in joules (H) generated in the wire between the contact tip on the end of the wire feed gun and the metal being welded is: H = I x I x R. R is the resistance of the wire for the length of wire sticking out past the contact tip, also called stickout. The longer the stickout, the higher the resistance of the wire, so the heat produced will be higher. The argon provides an inert shielding gas to prevent the molten wire from oxidizing, and also controls arc characteristics.

It actually gets more detailed than the above, but that is probably a fair short description in scientific terms. Reference: AWS Welding Handbook Volume 1, 8th Edition, 1987, American Welding Society, Miami, FL.

Hope this helps.

Marty