Symmetrical velocity profiles for JefferyHamel flow
Abstract
JefferyHamel flow is one of the few known exact solutions of the NavierStokes equations. The symmetrical velocity profiles presented by Millsaps and Pohlhausen (1953) for flow in a 10deg channel are used to illustrate typical solutions. Recently, JefferyHamel flow has been employed as a test problem for assessing the performance of numerical schemes for obtaining approximate solutions to the NavierStokes equations by the finiteelement method. A summary of formulas for symmetrical profiles expressed in terms of Jacobian elliptic functions is presented. These formulas in conjunction with the relationships between Jacobian elliptic functions and theta functions, and a subroutine for generating theta functions, have been successfully employed to compute velocity profiles for the purpose of comparison with approximate numerical solutions by the finiteelement method.
 Publication:

ASME Journal of Applied Mechanics
 Pub Date:
 March 1979
 Bibcode:
 1979ATJAM..46..214M
 Keywords:

 Boundary Layer Flow;
 NavierStokes Equation;
 Velocity Distribution;
 Finite Element Method;
 Jacobi Integral;
 Nonlinearity;
 Radial Velocity;
 Reynolds Number;
 Fluid Mechanics and Heat Transfer