The Validity of Using the Microscopic Parabolic Heat Conduction Model in Place of the Macroscopic Parabolic Model Under the Effect of a Moving Heating Source

Abstract

The validity of the use of the microscopic parabolic heat conduction model under the effect of a moving heating source is investigated. Two configurations are considered which are the finite and the semi-infinite domains. For each configuration, two types of thermal boundary conditions are considered which are the isothermal and the insulated types. Four dimensionless parameters are found to control the thermal behavior of the considered problem which are the dimensionless heating source speed U, heat capacity ratio CR, dimensionless amplitude of the heating source S0, and dimensionless plate thickness ξ0 for the finite domain configuration. It is found that the use of the microscopic parabolic heat conduction model instead of the parabolic macroscopic model is essential when the dimensionless speed of the source U > 0.1 The heat capacity ratio CR is found to have insignificant effect on the domain thermal behavior. However, the deviation between the microscopic and macroscopic models increases as ξ0 decreases. The deviation between the two models is significant within the very early stages of time.