Integral Equation for the Heat Transfer with the Moving Boundary

摘要

Using the same method that was initially proposed in Ref. 1, the relationship between the local temperature and local heat flux has been established for the homogeneous one-dimensional heat equation in a semi-infinite domain whose boundary moves with a constant velocity. This relationship has been written in the form of a convolution integral. The integral equation, relating the surface temperature and surface heat flux, has been solved numerically in the case of a constant heat flux value and in the case of a pulsing heat flux, mimicking fast laser heating of solid materials. The results obtained in the course of the numerical simulation show the following: 1) These results coincide with those results obtained by the same method in the case of a nonmoving boundary. 2) The value of the boundary speed influences the surface temperature value-if the former increases, the latter increases too-but not the shape of the time evolution curve. 3) The moving boundary effect is not very significant in the case of fast laser heating due to the shortness of the process.