Temperature fluctuations in a half-space under spatially inhomogeneous heat-transfer conditions

An unsteady two-dimensional heat-conduction problem without initial conditions is considered for a half-space under boundary conditions of the I, II, and III types. It is assumed that the boundary value functions (including heat-transfer coefficient) are periodic functions of time and a spatial variable. Cyclic solutions to the problem are found in the form of double trigonometric Fourier series. The application of the obtained dependences is demonstrated with several specific examples. The conditions under which the quasi-one-dimensional solutions can be used are studied.