Effect of Surface Radiation on Natural Convection in Parabolic Enclosures

The interaction of natural convection and surface radiation in two-dimensional parabolic cavities heated from below with insulated walls and flat top and bottom walls is studied numerically. The shape of the cavities arises from the design of non-imaging optics-based compound parabolic concentrators (CPC). A numerical model based on finite differences is developed to solve the mass, momentum, and energy equations. A coordinate transformation is used to map the parabolic shape into a rectangular domain where the governing equations are solved. The results show that surface radiation significantly changes the temperature distribution and local Nusselt number inside the parabolic enclosure. Solutions are obtained for two different parabolic geometries that correspond to two different levels of concentration.

[1]  I. Catton.  The effect of insulating vertical walls on the onset of motion in a fluid heated from below , 1972 .

[2]  Roland Winston,et al.  Principles of solar concentrators of a novel design , 1974 .

[3]  K.G.T. Hollands,et al.  Correlation equations for free convection heat transfer in horizontal layers of air and water , 1975 .

[4]  S. Abdel-Khalik,et al.  Natural Convection In Compound Parabolic Concentrators—A Finite-Element Solution , 1978 .

[5]  Y. Bayazitoglu,et al.  An Experimental Study of Natural Convection in Trapezoidal Enclosures , 1980 .

[6]  R. Tatara,et al.  Experimental natural convective studies within a compound parabolic concentrator enclosure , 1983 .

[7]  G. de Vahl Davis,et al.  Natural convection in a square cavity: A comparison exercise , 1983 .

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

[9]  T. S. Lee,et al.  Computational and experimental studies of convective fluid motion and heat transfer in inclined non-rectangular enclosures , 1984 .

[10]  Antonio C. M. Sousa,et al.  Transient laminar free convection in horizontal cylinders , 1986 .

[11]  A. W. Date,et al.  Numerical prediction of natural convection heat transfer in horizontal annulus , 1986 .

[12]  N. E. Wijeysundera,et al.  An Experimental Study of Free Convection in Compound Parabolic Concentrator (CPC) Cavities , 1988 .

[13]  Y. Karyakin.  Transient natural convection in prismatic enclosures of arbitrary cross-section , 1989 .

[14]  M. Modest.  Radiative heat transfer , 1993 .

[15]  H. M. Badr,et al.  Free convection from an elliptic cylinder with major axis vertical , 1993 .

[16]  S. P. Venkateshan,et al.  Interaction of surface radiation with free convection in a square cavity , 1993 .

[17]  柳下 立夫,et al.  Synechococcus sp.を用いた光合成微生物電池 : 第2報 Synechococcusと2-Hydroxy-1, 4-naphthoquinoneのカップリング部位 , 1994 .

[18]  M. Akiyama,et al.  NUMERICAL ANALYSIS OF NATURAL CONVECTION WITH SURFACE RADIATION IN A SQUARE ENCLOSURE , 1997 .

[19]  Decheng Wan,et al.  A NEW BENCHMARK QUALITY SOLUTION FOR THE BUOYANCY-DRIVEN CAVITY BY DISCRETE SINGULAR CONVOLUTION , 2001 .

[20]  R. Santander,et al.  COMPUTATION OF TRANSIENT NATURAL CONVECTION IN A SQUARE CAVITY BY AN IMPLICIT FINITE-DIFFERENCE SCHEME IN TERMS OF THE STREAM FUNCTION AND TEMPERATURE , 2002 .

[21]  Mosfequr Rahman,et al.  NUMERICAL STUDY OF LAMINAR NATURAL CONVECTION IN INCLINED RECTANGULAR ENCLOSURES OF VARIOUS ASPECT RATIOS , 2003 .

[22]  E. H. Ridouane,et al.  INTERACTION BETWEEN NATURAL CONVECTION AND RADIATION IN A SQUARE CAVITY HEATED FROM BELOW , 2004 .

[23]  Atipong Malatip,et al.  Streamline upwind finite element method for conjugate heat transfer problems , 2005 .

[24]  O. G. Martynenko,et al.  Free-Convective Heat Transfer: With Many Photographs of Flows and Heat Exchange , 2005 .

[25]  M. Hasnaoui,et al.  Effects of surface radiation on natural convection in a rayleigh-benard square enclosure: steady and unsteady conditions , 2005 .

[26]  A. Mhimid,et al.  Anisotropy Effects on Heat and Fluid Flow by Unsteady Natural Convection and Radiation in Saturated Porous Media , 2005 .

[27]  X. Cui,et al.  A Discontinuous Finite-Element Formulation for Radiative Transfer in Axisymmetric Finite Cylindrical Enclosures and Coupling with Other Mode Heat Transfer , 2005 .

[28]  O. Manca,et al.  Numerical Analysis of Radiative Effects on Natural Convection in Vertical Convergent and Symmetrically Heated Channels , 2006 .

[29]  Habib Sammouda,et al.  Effect of Surface Radiation on the Natural-Convection Stability in a Two-Dimensional Enclosure with Diffusely Emitting Boundary Walls , 2007 .