Solution of the first and second boundary-value problems of nonstationary heat conduction for a triangular region

Abstract

Exact solutions of nonstationary problems of heat conduction are constructed in explicit form for a regular triangle of height h with Dirichlet and Neumann’s boundary conditions and an arbitrary initial condition having the property of triple symmetry in the region of the triangle. These very solutions remain valid also for the region of a rectangular triangle with an acute angle π/6, when there are no heat fluxes on the hypotenuse and smaller side, whereas Dirichlet or Neumann boundary conditions are prescribed on the larger side. Here, symmetry limitations are not imposed on the initial conditions.