Numerical study of natural convection between a circular enclosure and a sinusoidal cylinder using control volume based finite element method

Abstract In this study natural convection heat transfer in a cold outer circular enclosure containing a hot inner sinusoidal cylinder is investigated numerically using the Control Volume based Finite Element Method (CVFEM). Both circular enclosure and inner cylinder are maintained at constant temperature and air filled the enclosure. The governing equations of fluid motion and heat transfer in their vorticity stream function form are used to simulate the fluid flow and heat transfer. The calculations were performed for different governing parameters such as the Rayleigh number (Ra = 103, 104, 105 and 106), values of amplitude (A = 0.1, 0.3 and 0.5) and the number of undulations of the inner cylinder (N = 2, 3, 5 and 6). The results show that streamlines, isotherms, and the number, size and formation of the cells inside the enclosure strongly depend on the Rayleigh number, values of amplitude and the number of undulations of the enclosure.

[1]  G. D. Davis.  Natural convection of air in a square cavity: A bench mark numerical solution , 1983 .

[2]  Davood Domiri Ganji,et al.  Magnetic field effects on natural convection around a horizontal circular cylinder inside a square enclosure filled with nanofluid , 2012 .

[3]  Davood Domiri Ganji,et al.  MHD natural convection in a nanofluid filled inclined enclosure with sinusoidal wall using CVFEM , 2012, Neural Computing and Applications.

[4]  H. Yoon,et al.  A numerical study of natural convection in a square enclosure with a circular cylinder at different vertical locations , 2008 .

[5]  Wanxie Zhong,et al.  Improved precise integration method for differential Riccati equation , 2013 .

[6]  Ioan Pop,et al.  Effect of magnetic field on natural convection in a triangular enclosure filled with nanofluid , 2012 .

[7]  Mohsen Sheikholeslami,et al.  Magnetic field effects on natural convection flow of a nanofluid in a horizontal cylindrical annulus using Lattice Boltzmann method , 2013 .

[8]  B. R. Baliga,et al.  A CONTROL VOLUME FINITE-ELEMENT METHOD FOR TWO-DIMENSIONAL FLUID FLOW AND HEAT TRANSFER , 1983 .

[9]  Chi-Wang Shu,et al.  Efficient computation of natural convection in a concentric annulus between an outer square cylinder and an inner circular cylinder , 2002 .

[10]  Ishak Hashim,et al.  Flow and Heat Transfer of Cu-Water Nanofluid between a Stretching Sheet and a Porous Surface in a Rotating System , 2012, J. Appl. Math..

[11]  M. Gorji-Bandpy,et al.  Free convection of nanofluid filled enclosure using lattice Boltzmann method (LBM) , 2013 .

[12]  Davood Domiri Ganji,et al.  Investigation of squeezing unsteady nanofluid flow using ADM , 2013 .

[13]  Man Yeong Ha,et al.  Natural convection in a square enclosure with a circular cylinder at different horizontal and diagonal locations , 2010 .

[14]  Davood Domiri Ganji,et al.  Natural convection of nanofluids in an enclosure between a circular and a sinusoidal cylinder in the presence of magnetic field , 2012 .

[15]  Amaresh Dalal,et al.  A numerical study of natural convection around a square, horizontal, heated cylinder placed in an enclosure , 2006 .

[16]  H. Bararnia,et al.  Natural convection between a circular enclosure and an elliptic cylinder using Control Volume based Finite Element Method , 2012 .

[17]  N. K. Ghaddar.  Natural convection heat transfer between a uniformly heated cylindrical element and its rectangular enclosure , 1992 .

[18]  Vaughan R. Voller,et al.  Basic Control Volume Finite Element Methods for Fluids and Solids , 2009, IISc Research Monographs Series.

[19]  R. Saidur,et al.  Experimental study of forced and free convective heat transfer in the thermal entry region of horizontal concentric annuli , 2010 .

[20]  M. Manzan,et al.  Natural convection from a horizontal cylinder in a rectangular cavity , 1999 .

[21]  Davood Domiri Ganji,et al.  Effect of a magnetic field on natural convection in an inclined half-annulus enclosure filled with Cu–water nanofluid using CVFEM , 2013 .

[22]  Ioan Pop,et al.  Free convection boundary layer flow past a horizontal flat plate embedded in porous medium filled by nanofluid containing gyrotactic microorganisms , 2012 .

[23]  Ephraim M Sparrow,et al.  Advances in Numerical Heat Transfer , 1996 .

[24]  Davood Domiri Ganji,et al.  Heat transfer of Cu-water nanofluid flow between parallel plates , 2013 .

[25]  K. Khanafer,et al.  BUOYANCY-DRIVEN HEAT TRANSFER ENHANCEMENT IN A TWO-DIMENSIONAL ENCLOSURE UTILIZING NANOFLUIDS , 2003 .

[26]  D. Ganji,et al.  Lattice Boltzmann simulation of natural convection around a horizontal elliptic cylinder inside a square enclosure , 2011 .

[27]  F. Moukalled,et al.  Natural convection in the annulus between concentric horizontal circular and square cylinders , 1996 .

[28]  D. Ganji,et al.  Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method , 2012 .

[29]  Davood Domiri Ganji,et al.  Natural convection heat transfer in a nanofluid filled semi-annulus enclosure ☆ , 2012 .

[30]  Davood Domiri Ganji,et al.  Nanofluid flow and heat transfer due to a stretching cylinder in the presence of magnetic field , 2013 .

[31]  S. Patankar,et al.  LAMINAR MIXED CONVECTION IN THE ENTRANCE REGION OF A HORIZONTAL ANNULUS , 1989 .

[32]  K. Cen,et al.  A numerical study of laminar natural convective heat transfer around a horizontal cylinder inside a concentric air-filled triangular enclosure , 2010 .

[33]  Davood Domiri Ganji,et al.  Natural convection heat transfer in a cavity with sinusoidal wall filled with CuO–water nanofluid in presence of magnetic field , 2014 .

[34]  John M. House,et al.  EFFECT OF A CENTERED CONDUCTING BODY ON NATURAL CONVECTION HEAT TRANSFER IN AN ENCLOSURE , 1990 .