Abstract Annealing furnaces are used to heat steel in order to change its chemical structure. In this paper we model an electric radiant furnace. One of the major defects in steel strips processed in such furnaces is a wave-like pattern near the edges of the strip, apparently due to extra heating near the edges. The aim of the paper is to model this effect and provide a way to calculate the elevated temperatures near the edges. We analyse two processes that are suspected to contribute to uneven heating. The modelling involves an asymptotic analysis of the effect of heat flux at the edges and a detailed analysis of the integral equations associated with radiant heat transfer in the furnace.
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