Analysis of suddenly started laminar flow in the entrance region of a circular tube

1969 ◽  
Vol 21 (1) ◽  
pp. 248-259 ◽  
Author(s):  
X. J. R. Avula
Keyword(s):  
Laminar Flow ◽  
Circular Tube ◽  
Entrance Region

Laminar Flow in the Entrance Region of Elliptical Ducts

1983 ◽  
Vol 105 (3) ◽  
pp. 290-296 ◽  
Author(s):  
M. S. Bhatti
Keyword(s):  
Laminar Flow ◽  
Aspect Ratio ◽  
Unsolved Problem ◽  
Circular Tube ◽  
Entrance Region ◽  
Momentum Balance ◽  
Velocity Measurements ◽  
Fully Developed Flow ◽  
Closed Form Analytical Solution ◽  
Steady Laminar

A closed-form analytical solution is developed to hitherto unsolved problem of steady laminar flow of a Newtonian fluid in the entrance region of elliptical ducts. The analysis is based on the Karman-Pohlhausen integral method and entails solution of the integrated forms of the mass and the momentum balance equations. According to this analysis, the hydrodynamic entrance length based on 99 percent approach to the fully developed flow is equal to 0.5132λ/(1+λ2) where λ is the aspect ratio. Also, the fully developed incremental pressure defect is found to be 7/6 which is independent of the aspect ratio. In the limit when the flow becomes fully developed, the solution converges to the known exact asymptotic solution. Available, wide-ranging velocity measurements for a circular tube agree with the analytical predictions within 7 percent. Also, available pressure drop measurements near the inlet of a circular tube agree with the analytical predictions within 2 percent.

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

1964 ◽  
Vol 86 (4) ◽  
pp. 827-833 ◽  
Author(s):  
E. M. Sparrow ◽  
S. H. Lin
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Circular Tube ◽  
Outer Radius ◽  
Radius Ratio ◽  
Entrance Region ◽  
Flow Development ◽  
Inner Radius ◽  
Wide Range ◽  
Plate Channel

A new analytical method has been applied for determining the developing laminar flow in the hydrodynamic entrance region of annular ducts. Detailed results are presented for the development of the velocity distribution and the pressure drop over a wide range of annulus radius ratios r1/r2 (r1 = inner radius of annulus, r2 = outer radius of annulus). It is found that the pressure drop and flow development in annular ducts with radius ratios substantially less than unity is quite similar to that in a parallel-plate channel (r1/r2 → 1). On the other hand, the results far an annular duct with radius ratio as small as 0.001 depart significantly from those for a circular tube (r1/r2 = 0). The hydrodynamic entrance length, measured as a multiple of the hydraulic radius, increases as the duct radius ratio decreases at a fixed Reynolds number.

scholarly journals Second Law Analysis of Laminar Flow in a Circular Pipe Immersed in an Isothermal Fluid

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Vishal Anand ◽  
Krishna Nelanti
Keyword(s):  
Laminar Flow ◽  
Entropy Generation ◽  
Circular Tube ◽  
Dimensionless Temperature ◽  
Bejan Number ◽  
Uniform Wall Temperature ◽  
Thermal Boundary Conditions ◽  
Fluid Properties ◽  
Isothermal Fluid ◽  
Uniform Wall

Entropy generation and pumping power to heat transfer ratio (PPR) of a laminar flow, for a circular tube immersed in an isothermal fluid, are studied analytically in this paper. Two different fluids, namely, water and ethylene glycol, are chosen to study the influence of fluid properties on entropy generation and PPR. The expressions for dimensionless entropy generation, Bejan number and PPR are derived in a detailed way and their variations with Reynolds number, external Biot number, and the dimensionless temperature difference are illustrated. The results of the analysis are compared with those for a laminar flow in a circular tube with uniform wall temperature boundary condition. Finally, a criterion is established to determine which type of thermal boundary conditions is more suitable for a particular fluid, with respect to its influence on entropy generation.

Constrained Direct Optimisation of the Geometrical Parameters of a Twisted-Tape for Laminar Flow in a Circular Tube

2021 ◽  
pp. 1-17
Author(s):  
Luís G. Silva Junior ◽  
Felipe A. S. Silva ◽  
Tiago G. Faria ◽  
Martin P. Kessler ◽  
Leandro O. Salviano
Keyword(s):  
Laminar Flow ◽  
Circular Tube ◽  
Geometrical Parameters ◽  
Twisted Tape
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