Open AccessAmong the problems of unsteady heat conduction, tasks that can be solved in analytical closedform hold a special place. This species can be used both for parametric optimization of thermal protection of structures and for testing of computational algorithms.
The previous paper presented an analytical solution of the problem to find the half-space temperature field with the uniformly moving boundary, which was under the external heat flux of constant power. In this paper we consider a similar problem, but the law of the moving boundary is assumed to be arbitrary nondecreasing, and the power of the heat flux can vary over time.
An analytical dependence of the problem solution on the temperature of a moving boundary was obtained by using the Fourier transformation in the spatial variable. To determine the temperature of moving boundary, Volterra integral equation of the second kind was drawn. The solution of this equation was numerically conducted using a specially developed computational algorithm.
The obtained representation was used to research the most characteristic features of the process to form the temperature field in studied area when implementing the various laws of boundaries motion and different operating conditions for the external heat flux influence. Using computational experiments allowed us to find that the asymptotic nature of this dependence confirms the results obtained in previous work. It has been established that the nonlinear character of both the boundary motion law and the external heat flux power variation law mainly affect the specifics of the transition process.