A finite-difference analysis of turbulent, axisymmetric, buoyant jets and plumes

Heat transfer in in-tube flow of non-Newtonian fluids

“…The Dufort-Frankel finite difference approximations do not have severe stability constraints [52,55,58]. In the present solution, the apparent viscosity is a function of local velocity gradient (3U/3Y)j •• This has some ramifications on the stability of the finite-J difference scheme.…”

Prediction of laminar and turbulent flow heat transfer in annular passages

“…Shear stress at any point in the flow can be determined by has made use of an explicit three level finite-difference scheme of the type which has earlier been used for predicting flow in wall boundary layers [137], circular pipe [138] and jet flow [139]. This scheme does not have severe stability constraints and permits the use of fairly large streamwise steps.…”

“…Following the analysis given in [139], the stability constraint for Eq. (3.9) can be given as, with AY'^ = AY_ = AY, …”