An electric induction reactive metal or alloy melting and holding furnace comprising: an upper furnace vessel; and an inductor furnace disposed below the upper furnace vessel; wherein the inductor furnace comprises a separable modular inductor furnace comprising: an upper inductor furnace module configured for removable connection to the upper furnace vessel, the upper inductor furnace module comprising: an upper cooling duct; and a melt-containing vessel for containment of a reactive metal or alloy melt, the melt-containing vessel communicably connected to the upper furnace vessel when connected to the upper furnace vessel; an induction coil module configured for removable connection to the upper inductor furnace module, the induction coil module comprising: an induction coil; and an enclosure surrounding the induction coil, the melt-containing vessel configured for positioning inside the induction coil, to form a gap between an outside surface of the melt-containing vessel and an inside surface of the induction coil with at least one feed port and at least one discharge port disposed at opposing upper and lower ends of the gap, the upper cooling duct in fluid communication with the at least one discharge port or the at least one feed port disposed at the upper end of the gap when connected to the upper inductor furnace module; and a lower inductor furnace module configured for removable connection around the induction coil module, the lower inductor furnace module comprising: a lower cooling duct in fluid communication with the at least one feed port or the at least one discharge port disposed at the lower end of the gap. an upper furnace vessel; and an inductor furnace disposed below the upper furnace vessel; wherein the inductor furnace comprises a separable modular inductor furnace comprising: an upper inductor furnace module configured for removable connection to the upper furnace vessel, the upper inductor furnace module comprising: an upper cooling duct; and a melt-containing vessel for containment of a reactive metal or alloy melt, the melt-containing vessel communicably connected to the upper furnace vessel when connected to the upper furnace vessel; an induction coil module configured for removable connection to the upper inductor furnace module, the induction coil module comprising: an induction coil; and an enclosure surrounding the induction coil, the melt-containing vessel configured for positioning inside the induction coil, to form a gap between an outside surface of the melt-containing vessel and an inside surface of the induction coil with at least one feed port and at least one discharge port disposed at opposing upper and lower ends of the gap, the upper cooling duct in fluid communication with the at least one discharge port or the at least one feed port disposed at the upper end of the gap when connected to the upper inductor furnace module; and a lower inductor furnace module configured for removable connection around the induction coil module, the lower inductor furnace module comprising: a lower cooling duct in fluid communication with the at least one feed port or the at least one discharge port disposed at the lower end of the gap. an upper inductor furnace module configured for removable connection to the upper furnace vessel, the upper inductor furnace module comprising: an upper cooling duct; and a melt-containing vessel for containment of a reactive metal or alloy melt, the melt-containing vessel communicably connected to the upper furnace vessel when connected to the upper furnace vessel; an upper cooling duct; and a melt-containing vessel for containment of a reactive metal or alloy melt, the melt-containing vessel communicably connected to the upper furnace vessel when connected to the upper furnace vessel; an induction coil module configured for removable connection to the upper inductor furnace module, the induction coil module comprising: an induction coil; and an enclosure surrounding the induction coil, the melt-containing vessel configured for positioning inside the induction coil, to form a gap between an outside surface of the melt-containing vessel and an inside surface of the induction coil with at least one feed port and at least one discharge port disposed at opposing upper and lower ends of the gap, the upper cooling duct in fluid communication with the at least one discharge port or the at least one feed port disposed at the upper end of the gap when connected to the upper inductor furnace module; and an induction coil; and an enclosure surrounding the induction coil, the melt-containing vessel configured for positioning inside the induction coil, to form a gap between an outside surface of the melt-containing vessel and an inside surface of the induction coil with at least one feed port and at least one discharge port disposed at opposing upper and lower ends of the gap, the upper cooling duct in fluid communication with the at least one discharge port or the at least one feed port disposed at the upper end of the gap when connected to the upper inductor furnace module; and a lower inductor furnace module configured for removable connection around the induction coil module, the lower inductor furnace module comprising: a lower cooling duct in fluid communication with the at least one feed port or the at least one discharge port disposed at the lower end of the gap. a lower cooling duct in fluid communication with the at least one feed port or the at least one discharge port disposed at the lower end of the gap.