Cilindros ocos 1-D com geração de calor: uma aproximação suficientemente geral de solução para problemas com condição de Dirichlet variável no tempo

In this work, a sufficiently approximated general solution to transient heat conduction problems in 1-D cylindrical geometry, with heat generation and time variable Dirichlet conditions, was presented using the Green’s function method. An important integral involving Bessel functions, that is part of the solution, has been solved in detail here. The results obtained from the use of this solution, when applied in some particular cases of practical interest, were aligned with the solutions reported by the literature. We have adopted, in this sense, a methodology that consists of addressing a non-homogeneous problem solution with non-homogeneous boundary conditions in a non-homogeneous problem solution with homogeneous border conditions and two more stationary solutions related to the given Dirichlet conditions. As a result, the solution obtained has no problems of convergence at the boundaries of the cylindrical region with the temperature prescribed conditions.