How can I patch a large hole in a metal bathtub?
What may have happened is the porcelain top coat has been compromised to the point that it exposed the cast iron metal to the water. It has oxidized so much it has disintegrated and left a hole. If you are adamant about repairing the tub for the short time until it is replaced the best repair would be with fiberglass cloth and resin. This is what is used in the boating world to repair holes in fiberglass hulls. Wire brush any loose material from the tub wall wipe surrounding area with a solvent like lacquer thinner to remove contaminants. Cut an over sized piece of fiberglass cloth so it covers an extra 2 inches beyond the repair area. Mix the resin as per label. Brush the tub surface to the cloth outline. Place cloth over repair and brush liberally with more resin making sure to saturate the cloth completely. Build up with more layers of cloth letting each layer cure first. May want to do this on the other side of the hole. Sand with progressively higher grits until it is smooth. Paint if desired to match existing color. 2 part epoxy would also make a strong repair material.