Convection-radiation from a continuously moving, variable thermal conductivity sheet or rod undergoing thermal processing

A numerical study of the heat transfer process in a continuously moving sheet or rod of variable thermal conductivity that loses heat by simultaneous convection and radiation is reported. The process is governed by five dimensionless parameters, namely Peclet number Pe, thermal conductivity parameter a, convection-conduction parameter Nc, radiation-conduction parameter Nr, and sink-to-base temperature-ratio, θa. The effects of these parameters on the temperature distribution, base heat conduction rate, advection and surface heat loss are illustrated and explained. The dimensionless length parameter, L∗, that the material must traverse to cool to within one percent of the sink temperature is determined for various combinations of the five parameters. This information gives the designer the fabrication time if the material is moved at a certain speed or it gives the speed if the processing of the material is to be completed in a fixed period of time.