Parabolic Heat Conduction Model Research Articles

Effect of Radiative Losses on the Parabolic Two-Step Heat Conduction Model

The effects of radiative thermal losses on the thermal behavior of thin metal films, as described by the parabolic two-step heat conduction model, are investigated. Different criteria, which determine the ranges within which thermal losses are significant, are derived. The effects of these criteria on the thermal losses from the thin film are investigated. It is found that radiative losses from metal films are significant when the ratio of the diffused energy within the electron gas to the exchanged energy between the electron gas and the solid lattice is larger than one. Also, it is found that radiative losses are significant when the ratio of the radiative lost energy to the exchanged energy between the electron gas and the solid lattice is larger than 10-5.

On the Strict Heat Conduction Model with Stochastic Inputs

This paper is concerned with the construction of the strict model of the heat conduction phenomena with random inputs. It is well known that the parabolic heat equation has an infinite thermal propagation speed. This fact is a drawback of the parabolic heat conduction model. Since this drawback comes from Fourier's law, by revising Fourier's law from the physical view point, the stochastic hyperbolic heat conduction model with stochastic inputs is proposed. In the stochastic hyperbolic heat conduction model, thermal propagation speed becomes finite. It should be noted that the influence of the input to the hyperbolic heat conduction model is not simply additive, but the term related to the time delay of the thermal propagation appeared. In this paper, the existence of the unique solution of the stochastic hyperbolic heat equation is proved. Finally, the comparison between the solution processes of the parabolic equation and the hyperbolic one is shown through simulation experiments.

Thermal modelling and stress analysis in the continuous casting of arbitrary sections

A three‐dimensional parabolic heat conduction model has been developed to analyze heat transfer and solidification in variously shaped continuous casters. A fixed grid source based enthalpy method was used to model solidification during a casting process. In order to correctly model arbitrary cross‐sectional shaped castings, a body‐fitted coordinate transformation (BFT) technique was employed to transform the physical space on to a rectangular computational domain. The transformed governing equations and boundary conditions were solved in the transformed plane. Two arbitrarily shaped casters, having dog‐bone, and hexagonal cross‐sections, were tested in this study. The governing equations were discretized using the control‐volume finite difference approach, wherein an implicit solution technique was employed to solve the set of discretized algebraic equations.From the temperature field predicted by heat flow model, a quasi‐non‐linear stress analysis was carried out within the solidifying shell of the beam blank (dog bone) section. The effect of roller arrangement on the distortion of solidified shell was investigated.