Which process is noted for not depending on an external heat source?

The basic oxygen process stands out as the correct answer because it primarily utilizes the heat generated from the exothermic reaction between molten iron and oxygen to produce steel. In this method, pure oxygen is blown into molten iron, which reacts with the carbon present in the iron, releasing a significant amount of heat that can maintain the temperature of the process without the need for an external heat source.

In contrast, the other processes mentioned do rely on external heat sources. The electric arc process uses electrical energy to generate heat; the induction furnace process relies on electromagnetic induction to heat the metal; and the vacuum arc remelting process uses an electric arc in a vacuum environment, which also requires an external energy input. This makes the basic oxygen process unique in its ability to function effectively without external heating sources, relying solely on the chemical reactions taking place during the refining process.