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《Journal of Northeastern University(Natural Science)》 1981-03
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Ning Baolin Shang Deyi  
The predictive calculations of the distribution of temperature and of heat flux in a reheating furnace may represent the roost important prediction of industrial furnaces.It is helpful not only to simplify the automatic control of furnaces but also to enhance the efficiency of thermotechnical automation.Main predictive calculation for this purpose performed nowadays is based on the zone method by H.C.Hotte[1],Since this method has only a restricted application in that the elementary gsseous zones (or surface zones) must be divided into the form of cubes (or into squares),it is necessary to introduce a new method for calculating the one-way direct exchange area by which the prediction for industrial furnaces can be used more widely and conveniently.With the replacement of cubic (or square) zones by rectangular zones,the induced formulae for calculating one-way direct exchange areas under eight different conditions are derived.Two types of induced formulae,which may be considered as the representatives of those under eight different conditions,are offered in this paper.In one case the direct exchange area lies between two parallel planes,and in other the exchange area lies between two gaseous zones.The induced formulae derived,determining the allowed values of exchange areas and providing for the equations of heat equilibrium,are applicable to the mathematical models of computers.The results computed are relatively precise.A group of equations of heat equilibrium in which all the divided zones in a furnace are involved may be solved simultaneously by a computer.Therefore,the space distribution of the temperature of gas and surface and that of the heat flux can be determined.Finally,the accuracy of results calculated by a computer is discussed and a ratio of length to width of divided zones of not more than 1.2 is proposed.NOMENCLATUREs——surface zone;g——gaseous zone;i,j——signs of segments divided from a zone;"__"——top line up the sign shows the direct exchange area;Q——radiation ability of one-way heat transfer (kcal/h);E——radiation intensity (kcal/m2·h);T——absolute temperature (K);V——volume (m3);K——gas absorbance (1/m);m,n——positive integers;r——central distance between two zones or two elements;x,y,z——cartisian coordinates (m);θ——plane angle (rad.);ψ——space angle (rad.);A,B,C——signs of divided zones (in addition,B is also the marginaldimension of zone); a,b,c,d,e and f——dimensions (m);":="——assigned symbol;xi——calculated value of direct exchange area between two zones;(xi)N——theoretical value of xi;ηΔ——relative error
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