A burner/injector panel apparatus to be mounted on the wall of a furnace, said panel apparatus comprising: A) a burner/injector panel that has a first end, a first transition region adjacent to the first end, a discharge end that opposes the first end and a mid-region that is disposed between the first transition region and the discharge end, the burner/injector panel comprising (a) a mounting end as the first end; (b) the first transition region; (c) the mid-region; and (d) a terminating region that includes the discharge end; the mid-region including: (i) a first cylindrical region; and optionally also: (ii) a second transition region and (iii) a second cylindrical region; and B) one or more bores that traverse the mounting end, the first transition region, the first cylindrical region, the optional second transition region, the optional second cylindrical region, and the terminating region of the burner/injector panel; and C) at least one injection apparatus selected from one or more of a thermal energy source, a particulate injector, or an oxygen injector; wherein the terminating region is in the shape of a half spheroid so as to make tangential contact at all points where the terminating region connects the adjacent cylindrical region (4, 6); the mounting end, the first transition region, the first cylindrical region, the optional second transition region, the optional second cylindrical region, and the terminating region of the burner/injector panel are in fluid communication with one another through the one or more bores that traverse the burner/injector panel; the first cylindrical region, the second transition region when present, and the second cylindrical region when present each include an upper outer surface that runs parallel to the one or more bores; the outer profile of the second transition region increases eccentrically from the first cylindrical region to the second cylindrical region; the at least one injection apparatus is positioned within the one or more bores; and the burner/injector panel when mounted on the furnace wall extends outward and downward from the furnace wall such that the discharge end of the burner/injector panel extends towards the metal melt line in the furnace. A) a burner/injector panel that has a first end, a first transition region adjacent to the first end, a discharge end that opposes the first end and a mid-region that is disposed between the first transition region and the discharge end, the burner/injector panel comprising (a) a mounting end as the first end; (b) the first transition region; (c) the mid-region; and (d) a terminating region that includes the discharge end; the mid-region including: (i) a first cylindrical region; and optionally also: (ii) a second transition region and (iii) a second cylindrical region; and (a) a mounting end as the first end; (b) the first transition region; (c) the mid-region; and (d) a terminating region that includes the discharge end; the mid-region including: (i) a first cylindrical region; and optionally also: (ii) a second transition region and (iii) a second cylindrical region; and (i) a first cylindrical region; and optionally also: (ii) a second transition region and (iii) a second cylindrical region; and B) one or more bores that traverse the mounting end, the first transition region, the first cylindrical region, the optional second transition region, the optional second cylindrical region, and the terminating region of the burner/injector panel; and C) at least one injection apparatus selected from one or more of a thermal energy source, a particulate injector, or an oxygen injector;