Abstract

In the thermal processing of continuous casting and rolling, the metal is continuously moving. The sections of the moving metal can be rod, sheet or other structural ones. Usually, the thermal conductivity of metals will vary with temperature. In this paper, the spectral collocation method (SCM) is presented and formulated to simulate the heat transfer process in a continuously moving convective-radiative rod with variable thermal conductivity. In this approach, the dimensionless temperature is approximated by Chebyshev polynomials and discretized by Chebyshev–Gauss–Lobatto collocation points. A particular algorithm is used to reduce the nonlinearity of the energy conservation equation. Compared with those available data in literature, the SCM can provide good accuracy for a wide range of parameters, such as the dimensionless thermal conductivity coefficient, the convective–conductive parameter, the radiative-conductive parameter, the Peclet number, the dimensionless convective sink temperature, and the dimensionless radiative sink temperature. Meanwhile, the SCM can provide exponential convergence rate against node for the present problem. Moreover, the effects of various aforementioned parameters on the dimensionless temperature distribution and the dimensionless tip temperature are discussed and physically interpreted.

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