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Utilization of heat from gases leaving the waelz process is a promising way to increase its energy efficiency and nvironmental safety. Taking into account the gas dustiness, the most rational is the use of a loop air heater, which is a multi-pass and multi-section heat exchanger with a complex mixed scheme of coolant movement. In modern conditions, when the methods and means of calculation of such devices are simplified, the task of obtaining improved methods and means of calculation, determining the efficiency and reliability of their work is relevant. Two mathematical models of the process of heat transfer and hydroaerodynamics in a multi-pass tubular air heater with a cross-circuit of coolants are used. The developed models for the loop air heater are based on the main methods of thermal calculation: a simpler method of correction factor to the average logarithmic temperature pressure and a discrete P-NTU method, which allows obtaining local thermal characteristics of the surface. Diagrams of distribution of heat transfer coefficients, heat transfer, local temperatures of flue gases, air and pipe walls are constructed. The influence of dust and dust particle size on heat transfer is determined. When the flue gas dust is 50 g/Nm3 and with a dust particle size of 1 μm, the heat transfer coefficient increases by 12 %. The application of the air heater design with different schemes of coolant movement is substantiated. The developed universal methods allow determining the thermal productivity of heat exchangers and obtaining the distribution of local temperature characteristics on the heating surface. It is also possible to identify places of possible overheating of the heat exchange surface and the course of corrosion processes, taking into account the design of recuperators, operating conditions, operating modes and different schemes of coolant movement

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