Calculation of the number of Poiseuille for fully developed laminar flow in ducts of different cross sections.
DOI:
https://doi.org/10.15649/2346030X.843Keywords:
hydrodynamic boundary layer; thermal boundary layer; laminar flow; Poisuille number; differential equation of amount of movement and energy.Abstract
The use of pipelines is an important alternative in the transport of fluids, being a common engineering problem to obtain the
decrease (loss) of pressure or transfer of heat in the fluid. To evaluate these phenomena, the number of Poiseuille (f ReDh) is especially
important. In this article, this number has been calculated for fully developed laminar flow in ducts of different cross sections using TRANSCAL
software, which has been developed by the Laboratory of Numerical Simulation in Fluid Mechanics and Heat Transfer - SINMEC-, of the
Federal University of Santa Catarina. In the implementation of the calculations made in the software, the parameters were introduced using the
analogy between the differential equation of amount of movement in the direction of flow and the differential equation of energy of the fluid,
in order to obtain the average fluid velocity in the pipeline.
References
C. Mataix, "Mecánica de Fluidos y Máquinas Hidráulicas", 2nd ed. Mexico D.F., 2004.
Y.A. Cengel y J.M. Cimbala, "Mecánica de Fluidos, fundamentos y aplicaciones", 1st ed. México, 2006.
A. Olivares, R. Guerra, M. Alfaro, E. Notte-Cuello y L. Puentes, “Evaluación experimental de correlaciones para el cálculo del factor de fricción para flujo turbulento en tuberías cilíndricas,” Rev. Int. métodos numéricos para cálculo y diseño en Ing., vol. 35, no. 1, 2019.
I. Santos-Ruiz, J.R. Bermúdez, F.R. López-Estrada, V. Puig y L. Torres, “Estimación experimental de la rugosidad y del factor de fricción en una tubería,” in Memorias Del Congreso Nacional De Control Automático, San Luis Potosí, San Luis Potosí, México, 2018, pp. 10–12.
A.A. Lozano-Povis y J.L. Sánchez-Ochoa, “Evaluación experimental de una ecuación empírica para la caída de presión en flujo gaseoso,” 2017.
M.F. Marinet y S. Tardu, "Convective Heat Transfer", 1st ed. Londres, Inglaterra, 2008.
L.C. Burmeister, "Convective Heat Transfer", 2nd ed. Estados Unidos, 1993.
M. Maerefat y A. Davari, “Numerical Analysis of Fluid Flow and Heat Transfer in Entrance and Fully Developed Regions of a Channel With Porous Baffles,” J. Heat Transf., vol. 138, no. 6, 2016.
P.B. Dehkordi, A. Azdarpour y E. Mohammadian, “The hydrodynamic behavior of high viscous oil-water flow through horizontal pipe undergoing sudden expansion—CFD study and experimental validation,” Chem. Eng. Res. Des., vol. 139, pp. 144–161, 2018.
J. P. Meyer y M. Everts, “Single-phase mixed convection of developing and fully developed flow in smooth horizontal circular tubes in the laminar and transitional flow regimes,” Int. J. Heat Mass Transf., vol. 117, pp. 1251–1273, 2018.
E. Demirel y M.M. Aral, “Unified Analysis of Multi-Chamber Contact Tanks and Mixing Efficiency Based on Vorticity Field. Part I: Hydrodynamic Analysis,” Water, vol. 8, no. 11, p. 495, 2016.
G. Kewalramani, H. Gaurav, S. Sandip y A. Amit, “Empirical Correlation Of Laminar Forced Convective Flow In Trapezoidal Microchannel Based On Experimental,” J. Therm. Sci., vol. 142, pp. 422–433, 2019.
G. Kewalramani, H. Gaurav, S. Sandip y A. Amit, “Study of laminar single phase frictional factor and Nusselt number in In-line micro pin-fin heat sink for electronic cooling applications,” Int. J. Heat Mass Transf., vol. 138, pp. 796–808, 2019.
E. Florez, C. Peña y R. Laguado, “Aplicación del método de la ecuación de Boltzmann en redes para la simulación bidimensional de un problema típico de mecánica de fluidos.,” Rev. Colomb. Tecnol. Av., vol. 1, no. 25, pp. 118–125, 2017.
M. Moyers-Gonzalez y I. Frigaard, “The critical wall velocity for stabilization of plane Couette–Poiseuille flow of viscoelastic fluids,” J. Non-Newtonian Fluids Mech., vol. 165, pp. 441–447, 2010.
J. Xamán, G. Álvarez, J.O. Aguilar y C. Moo, “Determinación del Número de Nusselt Convectivo y Radiativo en una Habitación con una Pared Semitransparente,” Caos Concienc., vol. 9, no. 1, pp. 1–16, 2015.
A. Stikhun, “Análisis numérico de un regenerador de porosidad variable y su influencia en el rendimiento de un motor Stirling,” Universidad de Málaga, 2017.
C.A. Schvezov, A.R. Lespinard y M.R. Rosenberger, “Modelización de la transferencia de calor de un flujo laminar a través de un cuerpo cilíndrico,” Asoc. Argentina Mecánica Comput. Mecánica Comput., vol. 36, no. 47, pp. 2189–2200, 2018.
L.A. Patino-Carrillo y H.J. Espinoza-Bejarano, “Convección de calor intersticial en el flujo de fluidos a través de medios porosos,” Tecnol. y ciencias del agua, vol. 19, no. 2, pp. 37–51, 2004.
A. Bejan, Convection Heat Transfer, 4th ed. New Delhi, 2004.
S. Yiallourou y G. Georgiou, “Newtonian Poiseuille flow in ducts of annular-sector cross-sections with Navier slip,” Eur. J. Mech. - B/Fluids, vol. 72, pp. 87–102, 2018.
K. Dutkowski, “Experimental investigations of Poiseuille number laminar flow of water and air in minichannels,” Int. J. Heat Mass Transf., vol. 51, no. 25, pp. 5983–5990, 2008.
G. Breyiannis, S. Varoutis y D. Valougeorgis, “Rarefied gas flow in concentric annular tube: Estimation of the Poiseuille number and the exact hydraulic diameter,” Eur. J. Mech. - B/Fluids, vol. 27, no. 5, pp. 609–622, 2008.
S. Salah, E.G. Filali y S. Djellouli, “Numerical investigation of Reynolds number and scaling effects in microchannels flows,” J. Hydrodyn., vol. 29, no. 4, pp. 647–658, 2017.
M.F. Zambrano, “Estimación de pérdidas de carga en tuberías a presión mediante un modelo hidráulico de laboratorio,” Universidad Estatal del Sur de Manabí, Ecuador, 2019.
G.L. Morini, “Viscous heating in liquid flows in micro-channels,” Int. J. Heat Mass Transf., vol. 48, no. 17, pp. 3637–3647, 2005.
D. Rehman, G.L. Morini y C.A. Hong, “Rehman, D., Morini, G. L., y Hong, "C. A comparison of data reduction methods for average friction factor calculation of adiabatic gas flows in microchannels Micromachines, 10(3), 171.,” Micromachines, vol. 10, no. 3, p. 171, 2019.
B. Kim, “n experimental study on fully developed laminar flow and heat transfer in rectangular microchannels,” Int. J. Heat Fluid Flow, vol. 62, pp. 224–232, 2016.
T. Ishida y T. Tsukahara, “Friction factor of annular Poiseuille flow in a transitional regime.,” Adv. Mech. Eng., vol. 9, no. 1, p. 1687814016683358, 2016.
Z. Duan, P. Liang, H. Ma, N. Ma y B. He, “Numerical simulation of pressure drop for three-dimensional rectangular microchannels,” Eng. Comput., vol. 35, no. 6, pp. 2234–2254, 2018.
S.K. Das y F. Tahmouresi, “Analytical solution of fully developed gaseous slip flow in elliptic microchannel,” Int. J. Adv. Appl. Math. Mech., vol. 3, no. 3, pp. 1–15, 2016.
V. Alves Dos-Santos, et al., “Heavy Oil Laminar Flow in Corrugated Ducts: A Numerical Study Using the Galerkin-Based Integral Method,” Energies, vol. 13, no. 6, p. 1363, 2020.
N. Ma et al., “Lattice Boltzmann Simulation of the Hydrodynamic Entrance Region of Rectangular Microchannels in the Slip Regime,” Micromachines, vol. 9, no. 2, p. 87, 2018.
S. Etemad y F. Bakhtiari, “General equation for fully developed fluid flow and heat transfer characteristics in complex geometries,” Int. Commun. Heat Mass Transf., vol. 26, no. 2, pp. 229–238, 1999.
Downloads
Published
How to Cite
Downloads
Issue
Section
License
The journal offers open access under a Creative Commons Attibution License
This work is under license Creative Commons Attribution (CC BY 4.0).
