Spectral collocation method for convective-radiative transfer of a moving rod with variable thermal conductivity

A numerical study was conducted to convective-radiative heat transfer under continuous motion rod with temperature dependent thermal conductivity using the spectral collocation method (SCM). The energy conservation equation is expressed as non-dimensional form, and discretized by the Chebyshev collocation points. A particular algorithm is adopted to reduce the nonlinearity of the energy conservation equation. The accuracy of the SCM is systematically evaluated through comprising with analytical and available results in literature. Moreover, the effects of six dimensionless parameters on the dimensionless temperature distributions are discussed and physical interpreted. Fig. 1 shows the physical model of a moving rod with variable thermal conductivity.