Radiant Heat Transfer in Gas-filled Cylindrical Enclosure with Temperature Gradient

Abstract

Calculations of heat transfer rates in cylindrical furnaces, making rigorous allowance for axial radiant heat flux, were carried out, and the results were used to evaluate existing approximate methods of calculation. A Fortran program for the IBM 709 was written to calculate the radiantconvective heat fluxes for gas-filled cylindrical furnaces using the Hottel-Cohen method of zoned analysis and making use of the direct interchange areas for cylindrical furnaces calculated by H. Errku.The major assumptions made in the formulation of the program are that there are no radial temperature gradients or gas recirculation, i.e., plug flow of the combustion gases is assumed in the furnace.The heat transfer rates were calculated for eighteen sets of conditions. The design parameters investigated were length-to-diameter ratios of two and four and diameters of two and four feet. The operational variables studies were sink temperatures of 1460°K and 2460°K, and enthalpy feed rates of 100×104, 50×104 or 25×104, and 6.25×104 Btu/hr·cu.ft. The furnace walls were treated as heat sinks with an emissivity of 0.8 and the end walls as refractories with an emissivity of 0.5. The fuel was assumed to have a composition corresponding to (CH2) n and to be instantaneously burned with a stoichiometric amount of air. No flame luminosity was assumed.From the results it was found that 90% of the net heat flux to any wall zone originated in the gas zone contiguous with it and the adjacent gas or end zoned.The results of the computer runs were compared with two approximate methods of calculating furnace performance. One method, which formulates the heat flux neglecting the net radiation along the axis of the furnace but allowing for the axial gas temperature gradient, was found to give heat fluxes from 9.1% lower at high firing rates to as much as 12% higher at lowest firing rates. The error in heat flux distribution along the furnace was larger still, ranging from +24% to -12%.A completely stirred furnace approximation with the heat-transfer temperature equal to the exit temperature gave total fluxes which ranged from 1.2% to 18.7% lower than the computer calculations at high and low firing rate, respectively.The overall efficiencies of the eighteen runs were correlated as a function of dimensionless parameters defining the design and operational variables within 3%. Also, corrections to be added to the exit gas temperature to give the “effective” heat transfer temperature of a well-stirred chamber of equivalent performance were calculated and correlated as a function of a dimensionless parameter. The magnitude of the correction ranged from 570°F to 60°F. Either correlation gives a mean of predicting furnace performance for furnace where radial temperature gradients and gas recirculation are unimportant.The efficiencies of the plug-flow furnaces studied here and of the well-stirred furnaces bracket that of real furnaces. Consequently, the present calculations indicate the range of possible error in estimating the thermal efficiency of furnaces by various simple but inaccurate models.