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Finite difference analysis for developing laminar flow in circular tubes applied to forced and combined convection
Author(s) -
Collins M. W.
Publication year - 1980
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620150307
Subject(s) - laminar flow , mechanics , forced convection , heat transfer , boundary value problem , heat flux , thermodynamics , constant (computer programming) , viscosity , mathematics , partial differential equation , physics , mathematical analysis , computer science , programming language
The complete two‐dimensional partial differential equations for developing laminar flow in a circular tube have been treated by a finite difference analysis. Property variation with temperature, especially that of viscosity, is allowed for in a flexible manner. The continuity and momentum equations, and then the energy equations, are solved by direct elimination at each axial step, and marching procedure used in the axial direction. A new technique is that the stepwise energy balance is rigidly satisfied throughout by using it as a constituent equation in place of the ‘explicit’ wall thermal boundary condition normally used. The analysis predicts the complete developing hydrodynamic and thermal fields, together with friction factors and heat transfer coefficients. It has been tested for a range of fluid velocity and thermal boundary conditions and for various fluids, including high viscosity oils, water and air. Data for constant wall heat flux have already been published. 1,2 Predictions for constant wall temperature presented here are for forced and combined convection and are compared with experimental data of Test 3 and Zeldin and Schmidt 4 .