One embodiment of the invention consists of a vertical cylindrical process heater with an overhead convection section, a radiant section containing a contiguous, helical, down flow, tubular radiant coil, and one or more top, downward fired, pulverized coal burners. A second embodiment consists of a cabin type heater having a radiant section of rectangular cross section, a contiguous vertical tube serpentine coil, an overhead convection section, and one or more bottom, horizontally fired, pulverized coal, end wall burners. A third embodiment consists of a process heater with a radiant section and overhead convection section, the radiant section having a vertical cylindrical, contiguous, helical, down-flow tubular coil, contained in a refractory lined enclosure of square cross-section. A continuous chain grate coal stoker is provided at the base of the radiant section. A coarse coal feed with a minimum of fines is fed thru a hopper located at one end of the traveling chain grate and essentially coal free ash is removed at the opposite end of the chain grate, thru a nozzle provided with a water seal. One or more centrifugal solids-gas separators are provided at the radiant section flue gas outlets in the case of all three embodiments, for the purpose of removing ash particulates from the flue gas streams, before the latter enter the overhead convection sections. Since the flue gas enters the convection sections very nearly devoid of particulates, the convection sections may be of conventional design utilizing bare and/or finned tubes on closely spaced equilateral or quadrilateral centers.