Finite difference analysis for laminar flow heat transfer in concentric annuli with simultaneously developing hydrodynamic and thermal boundary layers

The results of a finite difference analysis are presented for the problem of incompressible laminar flow heat transfer in concentric annuli with simultaneously developing hydrodynamic and thermal boundary layers, the boundary conditions of one wall being isothermal and the other wall adiabatic. This corresponds to the fundamental solution of the third kind according to the four fundamental solutions classified by Reynolds, Lundberg and McCuen1. Firstly, the hydrodynamic entry length problem, based on the boundary layer simplifications of the Navier–Stokes equations, was solved by means of an extension of the linearized finite difference scheme used previously by Bodia and Osterle2 to solve a similar problem between parallel plates. The energy equation is then solved, using the velocity profiles previously obtained, by means of an implicit finite difference technique. The accuracy of the numerical solution was checked by comparing results for the annulus of radius ratio 0.25 with the avaiable solution of Shumway and McEligot3.