Convective heat transfer augmentation through vortex shedding in sinusoidal constricted tube

Purpose – The purpose of this paper is to analyse the convective heat transfer of an unsteady pulsed, laminar, incompressible flow in axisymmetric tubes with periodic sections. The flow is supposed to be developing dynamically and thermally from the duct inlet. The wall is heated at constant and uniform temperature.Design/methodology/approach – The problem is written with classical homogeneous boundary conditions. We use a shift operator to impose non‐homogeneous boundary conditions. Consequently, this method introduces source terms in the Galerkin formulation. The momentum equations and the energy equation which govern this problem are numerically solved in space by a spectral Galerkin method especially oriented to this situation. A Crank‐Nicolson scheme permits the resolution in time.Findings – From the temperature field, the heat transfer phenomenon is presented, discussed and compared to those obtained in straight cylindrical pipes. This study showed the existence of zones of dead fluid that locally h...

[1]  B. Ai,et al.  Numerical Study of Pulsating Flow Through a Tapered Artery with Stenosis , 2004 .

[2]  A. Gelfgat Stability and slightly supercritical oscillatory regimes of natural convection in a 8:1 cavity: solution of the benchmark problem by a global Galerkin method , 2004 .

[3]  Francesco Fedele,et al.  Revisiting the stability of pulsatile pipe flow , 2003 .

[4]  C. Bernardi,et al.  Approximations spectrales de problèmes aux limites elliptiques , 2003 .

[5]  H. Hemida,et al.  Theoretical analysis of heat transfer in laminar pulsating flow , 2002 .

[6]  J. Tsamopoulos,et al.  Concentric core-annular flow in a circular tube of slowly varying cross-section , 2000 .

[7]  I. Kang,et al.  Chaotic mixing and mass transfer enhancement bypulsatile laminar flow in an axisymmetric wavy channel , 1999 .

[8]  Santabrata Chakravarty,et al.  A nonlinear mathematical model of blood flow in a constricted artery experiencing body acceleration , 1999 .

[9]  Jae Min Hyun,et al.  Forced convection heat transfer from two heated blocks in pulsating channel flow , 1998 .

[10]  Jie Shen,et al.  Efficient Spectral-Galerkin Methods III: Polar and Cylindrical Geometries , 1997, SIAM J. Sci. Comput..

[11]  T. Moschandreou,et al.  Heat transfer in a tube with pulsating flow and constant heat flux , 1997 .

[12]  H. Sung,et al.  Analysis of the Nusselt number in pulsating pipe flow , 1997 .

[13]  Jie Shen,et al.  Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials , 1994, SIAM J. Sci. Comput..

[14]  Anthony T. Patera,et al.  Numerical investigation of incompressible flow in grooved channels. Part 2. Resonance and oscillatory heat-transfer enhancement , 1986, Journal of Fluid Mechanics.

[15]  R. Creff,et al.  Etude des conditions particulieres de frequence favorisant les transferts thermiques en ecoulements pulses en canalisation cylindrique , 1981 .

[16]  I. Sobey On flow through furrowed channels. Part 1. Calculated flow patterns , 1980, Journal of Fluid Mechanics.

[17]  Tuncer Cebeci,et al.  A Model for Eddy Conductivity and Turbulent Prandtl Number , 1973 .

[18]  Shigeo Uchida,et al.  The pulsating viscous flow superposed on the steady laminar motion of incompressible fluid in a circular pipe , 1956 .

[19]  Macaire Batchi Etude mathématique et numérique des phénomènes de transferts thermiques liés aux écoulements instationnaires en géométrie axisymétrique. , 2005 .

[20]  K. M. Guleren,et al.  STEADY LAMINAR FLOW COMPUTATION THROUGH VASCULAR TUBE CONSTRICTIONS , 2002 .

[21]  Jie Shen,et al.  Efficient Spectral-Galerkin Method II. Direct Solvers of Second- and Fourth-Order Equations Using Chebyshev Polynomials , 1995, SIAM J. Sci. Comput..

[22]  J. Batina Etude numérique des écoulements instationnaires pulsés en canalisation cylindrique , 1995 .

[23]  S. Blancher Transfert convectif stationnaire et stabilité hydrodynamique en géométrie périodique , 1991 .