FIELD: continuous casting of melt metal by pouring it in conveyor type casting machines having one or more endless, flexible, moving, heat conductive belt conveyors for casting. SUBSTANCE: invention is concerned with hydrodynamic process realized at using permanent magnets and apparatuses for stabilizing moving, flexible, thin-sheet, heat conductive magnetically soft ferromagnetic casting belt conveyor relative to its thermal deformations during motion of conveyor along molding cavity and heating its frontal surface by means of heat emitted from melt cast metal at simultaneously cooling its back surface by means of flow of pumped liquid cooling agent. Hydromagnetic apparatuses are in the form of grid in which streams of liquid cooling agent pass through fixed throttling passages for supplying pressure pockets turned to back surface of belt conveyor. Said pockets are framed by magnetic pole shoes. Cooling agent discharges out of pressure pocket in the form of quickly moving films for cooling back surface of belt conveyor and for raising up said conveyor over pole shoes at simultaneously stabilizing flat state of belt conveyor due to use of intensive magnetic attraction efforts. Novelty is possibility for using reaching pulling effort created by means of unique magnetic materials forming magnetic circuits for overcoming gap between pole shoes of magnetic circuits and moving heat conductive casting belt conveyor of magnetically soft ferromagnetic material in order to attract deformed portions of belt conveyor towards faces of magnetic poles for holding belt conveyor inside narrow range in preset stabilized flat state in zones where conveyor is supported by means of hydrodynamic forces created by flows of pumped cooling agent. It provides motion of belt conveyor along predetermined path in such a way that conveyors hangs over in stabilized flat state without rubbing and sliding on stationary fixed objects because it moves on water film without friction. EFFECT: improved design, enhanced reliability of stabilizing belt conveyor. 62 cl, 19 dwg, 2 tbl
