A mathematical model using zone method to calculate radiating heat transfer is described. In the zone method

the system is divided into surface zones and gas zones and the number of which depends on the accuracy of results desired and calculation time required. The temperature profiles in a furnace are obtained by solving simultaneously energy balances on each zone. As originally developed by Hottel and Cohen

the direct exchange areas are limited to cubes and squares. In this paper

the derivation of the direct exchange area equations is extended between any two zones in the box or cylindrical furnace.These equations are adaptable to any dimension of rectangles

coaxial cylinder walls

end rings and other shapes. A design method for the primary reformer of hydrogen production unit and cylindrical furnace is proposed. By considering the reaction kinetics

convective heat transfer and pressure drop inside the tubes

the zone method has been adopted to predict temperature profiles of process gas

furnace gas

tube surface and refractory surface in such furnaces. Results of calculation agree well with data obtained from commercial units.