The report is dedicated to the development of methods of steel ingots and billets heating in modern open gas furnaces aimed at reducing fuel rate and amount of scale. A number of mathematical models of conjugate heat transfer related to practically all patterns of reheating furnaces of rolling production - pusher-type, walking hearth, walking beam, circular furnace - were defined. The advantage of this approach lies in accounting of the main geometrical sizes of a smelting chamber of each furnace, refractory pattern, conditions of fuel combustion, gas burners arrangement, selectivity of irradiation, pitch of billet laying on the furnace hearth, etc.
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