UHMLE: Program description user guide

A program which computes maximum likelihood estimates for the general normal mixture is introduced. The program allows the user to fix any subsets of the mixture parameters; this fixed set may be redefined at various times in the iteration process. There is considerable time saved in computing the likelihoods if the diagonal form is specified. Hence, in the early iterations the diagonal assumption might be used, changing over to the full covariance mode later in the iteration process for a more refined solution. This flexibility allows the user to choose the sequence of parameter configurations in the iteration process which he feels will optimize the computation time required as well as possibly avoid convergence to suboptimal local maxima of the likelihood function

The Developing Laminar Flow and Pressure Drop in the Entrance Region of Annular Ducts

BRIEF NOTES the most frequently used assumption is that of uniform flow at inlet, which simulates the actual condition of well-rounded entrance. This assumption was adopted in the present analysis and thus, at x = 0, the axial velocity and pressure are uniform with values u 0 and p 0 , respectively. Following the procedure suggested in TT/32, 2.03 for ex = TT/16, 1.92 for a = ir/8, and 1.86 for a = 7r/4) seem to conform with the asymptotic value of 1.82 obtained in The most commonly used parameters for presenting the pressure results are the product of the friction factor and Reynolds number fRe, and the pressure defect K. In the present analysis, the friction factor was defined as: f=(D h /2)(-dp/dx)/(pu 2 b ), and hence The pressure defect is normally defined as: , which reduces to the following nondimensional form: Results based on equations Acknowledgments The authors gratefully acknowledge the support provided for this research by the Natural Sciences and Engineering Research Council of Canada. References 1 Shah, R. K., and London, A. L., Laminar Flow Forced Convection in Duels, Academic Press, 1978. 2 Wendt, R. L., and Wiginton, C. L., "Incompressible Laminar Entrance Flow in a Circular Sector Duct," JOURNAL OF APPLIED MECHANICS, Vol. 98, 1976, pp.357-359. 3 Munis, A A., "Analysis of Laminar Fluid Flow in the Entrance Region of Circular Sector Ducts," M.Sc. Thesis, University of-Manitoba, 1981. 4 Sparrow, E. M., Lin, S. H., and Lundgren, T. S., "Flow Development in the Hydrodynamic Entrance Region of Tubes and Ducts," Physics of Fluids, Vol. 7, 1964, pp. 338-347. 5 Sparrow, E. M., and Lin, S. H., "The Developing Laminar Flow and Pressure Drop in the Entrance Region of Annular Ducts," Journal of Bask Engineering, Vol. 86,1964, pp. 827-834. 6 Fleming, D. P., and Sparrow, E. M., "Flow in the Hydrodynamic Entrance Region of Ducts of Arbitrary Cross-Section," ASME Journal of Heat Transfer, Vol. 91,1969, pp. 345-354. Numerical Results The resulting values of Le are listed i