Green’s functions for non-self-adjoint problems in heat conduction with steady motion

Abstract

Heat conduction in a rectangular parallelepiped that is in steady motion relative to a fluid is studied in this paper. The governing equation consists of the standard heat equation plus lower-order derivative terms with the space variables that represent the effects of the solid flow. The presence of the first-order-derivative terms with the space variables renders the spatial part of the governing differenial equation non-self-adjoint and care must be exercised in defining the new Green’s functions to be used in representing the solutions of initial- and boundary-value problems. It is illustrated how the Green’s functions may be constructed and how solutions of initial- and boundary-value problems may be obtained that lead to numerical results. Convergence properties of the solutions are also discussed.