Microscopic vs. macroscopic hyperbolic heat conduction: Validation criterion under the effect of a moving heating source

The validity of using the microscopic hyperbolic heat conduction model under the effect of a moving heating source is investigated. In macroscopic heat conduction, the solid lattice and the electron gas have the same temperature, while in the microscopic heat conduction model, the solid lattice and electron gas do not have the same temperature. Two configurations are considered: the finite and the semi-infinite domains. For each configuration, two types of thermal boundary conditions are considered: the isothermal and the insulated types. Four parameters are found to control the thermal behavior of the considered problem: the dimensionless heating source speed, heat capacity ratio, dimensionless relaxation time, and dimensionless plate thickness for the finite domain configuration. It is found that using the microscopic hyperbolic heat conduction model instead of the hyperbolic macroscopic model is essential when the dimensionless speed of the source is greater than 0.01. The heat capacity ratio is found to have an insignificant effect on the domain thermal behavior and this is true for small values of the relaxation time. However, the deviation between the microscopic and macroscopic models increases as the dimensionless plate thickness for the finite domain decreases. The deviation between the two models is significant within the very early stage of time.