A method for supplying heat to a melting furnace for forming a molten product using ash-containing fuels. A fuel having an ash component is introduced into a slagging chamber of a slagging combustor and at least partially combusted with a first oxidant mixture and a second oxidant mixture within the slagging chamber. Ash component is collected as a layer of molten slag in the slagging chamber. Slagging combustor gas effluent is passed from the slagging chamber of the slagging combustor into the combustion space of the melting furnace at high temperature to supply heat to form the molten product. Molten slag is withdrawn from the slagging chamber of the slagging combustor and may be selectively introduced into the melting furnace or not introduced into the melting furnace.
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