Comprehensive analytical study for convective–radiative continuously moving plates with multiple non-linearities

Thermal processing of metals may be moving, as in hot rolling, forging or extrusion, to shape materials in standard forms such as plates, sheets, rods, tubes and structural sections. The purpose of the present paper is to analyze the problem of convective–radiative heat transfer from a continuously moving plate with multiple nonlinearities. The thermal conductivity and surface emissivity of the plate’s material are considered as temperature-dependent. The heat transfer coefficient within the energy equation is assumed to be power-law function of temperature. The calculations are carried out by using the differential transformation method (DTM) which is an analytical solution technique that can be applied to various types of differential equations. The accuracy of the DTM solution is confirmed by comparing the obtained results with those from an analytical solution for a special case and previous publications. Results illustrate the effects of Peclet number, thermal conductivity, surface emissivity, convection–conduction parameter, radiation–conduction parameter, and dimensionless convection and radiation sink temperatures on the temperature of the plate.