The Discrete Green's Function for Convective Heat Transfer—Part 2: Semi-Analytical Estimates of Boundary Layer Discrete Green's Function

Abstract

Abstract This is the second paper in a set that defines the discrete Green's function (DGF). This paper focuses first on the turbulent boundary layer and presents two different methods to estimate the DGF. The long-element formulation defines the DGF with just two simple algebraic equations, but it is not quantitatively accurate for short element lengths. A short element correction is derived, but must be recalculated for each selection of flow parameters and element lengths. A similarity solution is derived that allows accurate estimates of the DGF diagonal elements for laminar boundary layers and for turbulent boundary layers discretized with short element lengths. To illustrate other methods to derive DGFs in more complex flows, a low-resolution DGF for laminar stagnation line boundary layers is determined using the skin-friction formulation combined with similarity solutions for two different thermal boundary conditions. Stagnation line flow is shown to be highly sensitive to the thermal boundary condition, and this can be analyzed effectively using the DGF.