Asymptotic solution of the heat conduction equation with weak nonlinearity and rapidly oscillating heat source

The paper examines the temporal and spatial dependence of the temperature field and thermal flows in a layered structure with rapidly oscillating heat source. For the problem solution we derive an analytical approach of the heat conduction equation by means of the generalized two-scale expansion method. A few practical examples are considered to illustrate the model. The computed results confirm the validity of the approximate solution technique.