Analytical solution of pulsating flow and forced convection heat transfer in a pipe filled with porous medium

Document Type : Research Paper

Authors

Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan, Iran

Abstract

In this paper, the pulsating flow and forced convection heat transfer in a pipe filled with porous medium is investigated. The pipe is under a constant heat flux. The governing equations of the problem includes continuity, Brinkman momentum equation and energy equation. Using complex analysis technique, an analytical solution for velocity profile and temperature distribution are obtained. Also, the effect of various design parameters on velocity profile and temperature distribution is studied. Results show that the pulsating effect on velocity and temperature profile increases with the increase of Darcy number and dimensionless amplitude of pressure gradient but decreases with the increase of viscosity ratio parameter, Prandtl number and dimensionless frequency. For high dimensionless frequency (Ω>30), the maximum velocity and temperature tend to be constant due to the decrease in wave amplitude.

Keywords

  • Womersley J.R., 1955, Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known, The Journal of physiology 127(3): 553-563.
  • Womersley J.R., 1955, Oscillatory motion of a viscous liquid in a thin-walled elastic tube-I: The linear approximation for long waves, Philosophical Magazine 46(373): 199-221.
  • Atabek H.B., Chang C.C., 1961, Oscillatory flow near the entry of a circular tube, Zeitschrift für angewandte Mathematik und Physik ZAMP 12(3): 185-201.
  • Zhao T., Cheng P., 1995, A numerical solution of laminar forced convection in a heated pipe subjected to a reciprocating flow, International Journal of Heat and Mass Transfer 38(16): 3011-3022.
  • Zhao T.S., Cheng P., 1996, Oscillatory heat transfer in a pipe subjected to a laminar reciprocating flow, Journal of Heat Transfer, 118(3): 592-597.
  • Guo Z., Sung H.J., 1997, Analysis of the Nusselt number in pulsating pipe flow, International Journal of Heat and Mass Transfer 40(10): 2486-2489.
  • Moschandreou T., Zamir M., 1997, Heat transfer in a tube with pulsating flow and constant heat flux, International Journal of Heat and Mass Transfer 40(10): 2461-2466.
  • Guo Z., Kim S.Y., Sung H.J., 1997, Pulsating flow and heat transfer in a pipe partially filled with a porous medium, International Journal of Heat and Mass Transfer 40(17): 4209-4218.
  • Habib M.A., Attya A.M., Eid A.I., Aly A.Z., 2002, Convective heat transfer characteristics of laminar pulsating pipe air flow, Heat and Mass Transfer 38(3): 221-232.
  • Hemida H.N., Sabry M.N., Abdel-Rahim A., Mansour H., 2002, Theoretical analysis of heat transfer in laminar pulsating flow, International Journal of Heat and Mass Transfer 45(8): 1767-1780.
  • Sert C., Beskok A., 2003, Numerical simulation of reciprocating flow forced convection in two-dimensional channels, Journal of Heat Transfer 125(3): 403-412.
  • Yu J.C., Li Z.X., Zhao. T.S, 2004, An analytical study of pulsating laminar heat convection in a circular tube with constant heat flux, International Journal of Heat and Mass Transfer 47(24): 5297-5301.
  • Tsangaris S., Kondaxakis D., Vlachakis N.W., 2006, Exact solution of the Navier–Stokes equations for the pulsating Dean flow in a channel with porous walls, International Journal of Engineering Science 44(20): 1498-1509.
  • Yin D., Ma H.B., 2013, Analytical solution of oscillating flow in a capillary tube, International Journal of Heat and Mass Transfer 66: 699-705.
  • Yin D., Ma H.B., 2014, Analytical solution of heat transfer of oscillating flow at a triangular pressure waveform, International Journal of Heat and Mass Transfer 70: 46-53.
  • Zallama B., Zili Ghedira L., Nasrallah S.B., 2016, Forced convection in a cylinder filled with porous medium, including viscous dissipation effects, Journal of Applied Fluid Mechanics 9(1): 139-145.
  • Feldmann D., Wagner C., 2016, On phase asymmetries in oscillatory pipe flow, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 132:113-122.
  • Jha B.K., Yusuf T.S, 2018, Transient-free convective flow with heat generation/absorption in an annular porous medium: a semi-analytical approach, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 232(5): 599-612.
  • Yadav S.L., Singh A.K., 2018, Transient flow in a circular cylinder filled with porous material, International Journal of Applied and Computational Mathematics 4(6): 1-13.
  • Brereton G.J., Jalil S.M., 2019, Axial conduction and dissipation in oscillatory laminar pipe flow at low and high frequencies, Physics of Fluids 31(8): 083607.
  • Karmakar T., Reza M., Raja Sekhar G.P., 2019, Forced convection in a fluid saturated anisotropic porous channel with isoflux boundaries, Physics of Fluids 31(11): 117109.
  • Jalil S.M., 2020, Numerical characterization of viscous heat dissipation rate in oscillatory air flow, Journal of Heat Transfer 142(1): 011801.
  • Song Y., Rau M.J., 2020, Viscous fluid flow inside an oscillating cylinder and its extension to Stokes’ second problem, Physics of Fluids 32(4): 043601.
  • Pier B., Schmid P.J., 2021, Optimal energy growth in pulsatile channel and pipe flows, HAL Archives-Ouvertes, HAL Id: hal-03084366v2, https://hal.archives-ouvertes.fr/hal-03084366v2, Accessed 12 July 2021.
  • Feldmann D., Morón D., Avila M., 2021, Spatiotemporal intermittency in pulsatile pipe flow, Entropy 23(1): 46.
  • Deghmoum M., Ghezal A., Abboudi S., 2015, Analytical and numerical study of a pulsatile flow in presence of a magnetic field, International Journal of Physical Sciences 10(24): 590-603.
  • Mahian O., Mahmud S., Pop I., 2012, Analysis of first and second laws of thermodynamics between two isothermal cylinders with relative rotation in the presence of MHD flow, International Journal of Heat and Mass Transfer 55: 4808-4816.
  • Hooman K., Gurgenci H., 2007, A theoretical analysis of forced convection in a porous-saturated circular tube: Brinkman–Forchheimer model, Transport in Porous Media 69(3): 289-300.
  • Rauf A., 2019, An analytical and semi-analytical study of the oscillating flow of generalized Burgers’ fluid through a circular porous medium, Journal of Applied and Computational Mechanics 5(5): 827-839.
Volume 52, Issue 4
December 2021
Pages 570-587
  • Receive Date: 13 July 2021
  • Revise Date: 25 October 2021
  • Accept Date: 01 December 2021
  • First Publish Date: 01 December 2021