Numerical Analysis, of Heat and Mass Transfer Problems in Laminar Flow(Part I:Application of Orthogonal Collocation Method to Velocity and Temperature Distributions of Laminar Flow in Circular Tube)

摘要

The developing profiles of the velocities and temperatures for laminar flow in a circular tube were numerically analyzed by means of two kinds of the orthogonal collocation methods, radial collocation method(RCM) and double collocation method(DCM). The numerical results of the velocities for the flow with the constant properties by the RCM and the DCM were compared with a finite-difference method(FDM) and the following results can be drawn: (1) Velocity profiles by the RCM show a satisfactory convergence on condition that the number of internal collocation points is greater than 11 and the dimensionless axial increment is less than 0.0005. (2) The profiles of the radial velocity by the DCM are inadequate at the first step because of the singularity, while the profiles of the axial velocity agree with the solutions by means of the RCM. (3) A good agreement betweent local Nusselt numbers by the DCM and those by the FDM is shown by use of 10 internal points in the radial direction and 1 point in the dimensionless axial increment of 0.0001. Consideration is also given to the fluid with the variable properties. Velocity and temperature distributions by the RCM are compared with those by the FDM and a good agreement between both solutions is generally obtained. When the number of the internal collocation point is selected 20 and the initial axial increment is 0.0001, the RCM can predict the saddle-backed profiles of the axial velocity under condition that dimensionless heat flux is 20.