Lattice Boltzmann Simulation of Natural Convection in an Inclined Square Cavity with Spatial Temperature Variation

REFERENCES

• A. Bejan , Convection Heat Transfer , Wiley , New York , NY , 2004 .
   Google Scholar
• O. G. E. Martynenko and P. P. Khramtsov , Free-Convective Heat Transfer , Springer , Berlin , 2005 .
   Google Scholar
• T. Icoz and Y. Jaluria , Design of Cooling Systems for Electronic Equipment using both Experimental and Numerical Inputs , ASME J. Electron. Packag. , vol. 126 , pp. 465 – 471 , 2005 .
   Web of Science ®Google Scholar
• S.-W. Kang , W.-C. Wei , S.-H. Tsai , and C.-C. Huang , Experimental Investigation of Nanofluids on Sintered Heat Pipe Thermal Performance , Appl. Therm. Eng. , vol. 29 , pp. 973 – 979 , 2009 .
   Web of Science ®Google Scholar
• P. O. Iwanik and W. K. Chiu , Temperature Distribution of an Optical Fiber Traversing through a Chemical Vapor Deposition Reactor , Numer. Heat Transfer A , vol. 44 , pp. 221 – 237 , 2003 .
   Web of Science ®Google Scholar
• K.-O. Lim , K.-S. Lee , and T.-H. Song , Primary and Secondary Instabilities in a Glass-Melting Surface , Numer. Heat Transfer A , vol. 36 , pp. 309 – 325 , 1999 .
   Web of Science ®Google Scholar
• S. Singh and M. Sharif , Mixed Convective Cooling of a Rectangular Cavity with Inlet and Exit Openings on Differentially Heated Side Walls , Numer. Heat Transfer A , vol. 44 , pp. 233 – 253 , 2003 .
   Web of Science ®Google Scholar
• H. Singh and P. C. Eames , A Review of Natural Convective Heat Transfer Correlations in Rectangular Cross-Section Cavities and Their Potential Applications to Compound Parabolic Concentrating (CPC) Solar Collector Cavities , Appl. Therm. Eng. , vol. 31 , pp. 2186 – 2196 , 2011 .
   Web of Science ®Google Scholar
• M. M. Ganzarolli and L. F. Milanez , Natural Convection in Rectangular Enclosures Heated from Below and Symmetrically Cooled from the Sides , Int. J. Heat Mass Transfer , vol. 38 , pp. 1063 – 1073 , 1995 .
   Web of Science ®Google Scholar
• P. Kumar and V. Eswaran , The Effect of Radiation on Natural Convection in Slanted Cavities of Angle γ = 45° and 60° , Int. J. Therm. Sci. , vol. 67 , pp. 96 – 106 , 2013 .
   Web of Science ®Google Scholar
• A. W. Islam , M. A. Sharif , and E. S. Carlson , Mixed Convection in a Lid Driven Square Cavity with an Isothermally Heated Square Blockage Inside , Int. J. Heat Mass Transfer , vol. 55 , pp. 5244 – 5255 , 2012 .
   Web of Science ®Google Scholar
• Z. Bocu and Z. Altac , Laminar Natural Convection Heat Transfer and Air Flow in Three-Dimensional Rectangular Enclosures with Pin Arrays Attached to Hot Wall , Appl. Therm. Eng. , vol. 31 , pp. 3189 – 3195 , 2011 .
   Web of Science ®Google Scholar
• É. Fontana , C. A. Capeletto , A. da Silva , and V. C. Mariani , Three-Dimensional Analysis of Natural Convection in a Partially-Open Cavity with Internal Heat Source , Int. J. Heat Mass Transfer , vol. 61 , pp. 525 – 542 , 2013 .
   Web of Science ®Google Scholar
• V. I. Polezhaev , M. N. Myakshina , and S. A. Nikitin , Heat Transfer due to Buoyancy-Driven Convective Interaction in Enclosures: Fundamentals and Applications, Int. J. Heat Mass Transfer , vol. 55, pp. 156–165, 2012.
   Web of Science ®Google Scholar
• J. Moh , T. Bergman , and D. Kuo , Simulation of Two-Dimensional , Low-Pr Natural Convection in Harmonically Oscillated , Differentially Heated Enclosures , Numer. Heat Transfer A , vol. 31 , pp. 1 – 19 , 1997 .
   Web of Science ®Google Scholar
• J. Niu and Z. Zhu , Numerical Evaluation of Weakly Turbulent Flow Patterns of Natural Convection in a Square Enclosure with Differentially Heated Side Walls , Numer. Heat Transfer A , vol. 45 , pp. 551 – 568 , 2004 .
   Web of Science ®Google Scholar
• E. Lakhal , M. Hasnaoui , P. Vasseur , and E. Bilgen , Natural Convection in a Square Enclosure Heated Periodically from Part of the Bottom Wall , Numer. Heat Transfer A , vol. 27 , pp. 319 – 333 , 1995 .
   Web of Science ®Google Scholar
• T. Basak , S. Roy , and A. Balakrishnan , Effects of Thermal Boundary Conditions on Natural Convection Flows within a Square Cavity , Int. J. Heat Mass Transfer , vol. 49 , pp. 4525 – 4535 , 2006 .
   Web of Science ®Google Scholar
• N. H. Saeid and Y. Yaacob , Natural Convection in a Square Cavity with Spatial Side-Wall Temperature Variation , Numer. Heat Transfer A , vol. 49 , pp. 683 – 697 , 2006 .
   Web of Science ®Google Scholar
• Q.-H. Deng and J.-J. Chang , Natural Convection in a Rectangular Enclosure with Sinusoidal Temperature Distributions on both Side Walls , Numer. Heat Transfer A , vol. 54 , pp. 507 – 524 , 2008 .
   Web of Science ®Google Scholar
• I. Sarris , I. Lekakis , and N. Vlachos , Natural Convection in a 2-D Enclosure with Sinusoidal Upper Wall Temperature , Numer. Heat Transfer A , vol. 42 , pp. 513 – 530 , 2002 .
   Web of Science ®Google Scholar
• J. E. Hart , Stability of the Flow in a Differentially Heated Inclined Box , J. Fluid Mech. , vol. 47 , pp. 547 – 576 , 1971 .
   Web of Science ®Google Scholar
• K. Hollands and L. Konicek , Experimental Study of the Stability of Differentially Heated Inclined Air Layers , Int. J. Heat Mass Transfer , vol. 16 , pp. 1467 – 1476 , 1973 .
   Web of Science ®Google Scholar
• F. Hamady , J. Lloyd , H. Yang , and K. Yang , Study of Local Natural Convection Heat Transfer in an Inclined Enclosure , Int. J. Heat Mass Transfer , vol. 32 , pp. 1697 – 1708 , 1989 .
   Web of Science ®Google Scholar
• R. Kuyper , T. H. Van Der Meer , C. Hoogendoorn , and R. Henkes , Numerical Study of Laminar and Turbulent Natural Convection in an Inclined Square Cavity , Int. J. Heat Mass Transfer , vol. 36 , pp. 2899 – 2911 , 1993 .
   Web of Science ®Google Scholar
• O. Aydin , A. Unal , and T. Ayhan , A Numerical Study on Buoyancy-Driven Flow in an Inclined Square Enclosure Heated and Cooled on Adjacent Walls , Numer. Heat Transfer A , vol. 36 , pp. 585 – 599 , 1999 .
   Web of Science ®Google Scholar
• E. Abu-Nada and H. F. Oztop , Numerical Analysis of Al2O3/Water Nanofluids Natural Convection in a Wavy Walled Cavity , Numer. Heat Transfer A , vol. 59 , pp. 403 – 419 , 2011 .
   Web of Science ®Google Scholar
• M. Akhtari , M. Haghshenasfard , and M. Talaie , Numerical and Experimental Investigation of Heat Transfer of α-Al2O3/Water Nanofluid in Double Pipe and Shell and Tube Heat Exchangers , Numer. Heat Transfer A , vol. 63 , pp. 941 – 958 , 2013 .
   Web of Science ®Google Scholar
• H. Sajjadi , M. Gorji , G. Kefayati , and D. Ganji , Lattice Boltzmann Simulation of Turbulent Natural Convection in Tall Enclosures using Cu/Water Nanofluid , Numer. Heat Transfer A , vol. 62 , pp. 512 – 530 , 2012 .
   Web of Science ®Google Scholar
• G. Kefayati , Lattice Boltzmann Simulation of MHD Natural Convection in a Nanofluid-Filled Cavity with Sinusoidal Temperature Distribution , Powder Technol. , vol. 243 , pp. 171 – 183 , 2013 .
   Web of Science ®Google Scholar
• Y. Peng , C. Shu , and Y. Chew , Simplified Thermal Lattice Boltzmann Model for Incompressible Thermal Flows , Phys. Rev. E , vol. 68 , pp. 026701 , 2003 .
   Web of Science ®Google Scholar
• A. D'Orazio , M. Corcione , and G. P. Celata , Application to Natural Convection Enclosed Flows of a Lattice Boltzmann BGK Model Coupled with a General Purpose Thermal Boundary Condition , Int. J. Therm. Sci. , vol. 43 , pp. 575 – 586 , 2004 .
   Web of Science ®Google Scholar
• H. Dixit and V. Babu , Simulation of High Rayleigh Number Natural Convection in a Square Cavity using the Lattice Boltzmann Method, Int. J. Heat Mass Transfer , vol. 49, pp. 727–739, 2006.
   Web of Science ®Google Scholar
• G. Huelsz and R. Rechtman , Heat Transfer due to Natural Convection in an Inclined Square Cavity using the Lattice Boltzmann Equation Method , Int. J. Therm. Sci. , vol. 65 , pp. 111 – 119 , 2012 .
   Web of Science ®Google Scholar
• S.-K. Choi , S.-O. Kim , T.-H. Lee , Y.-I. Kim , and D. Hahn , Computation of Turbulent Natural Convection in a Rectangular Cavity with the Lattice Boltzmann Method , Numer. Heat Transfer B , vol. 61 , pp. 492 – 504 , 2012 .
   Web of Science ®Google Scholar
• S. C. Mishra , C. H. Krishna , and M. Y. Kim , Analysis of Conduction and Radiation Heat Transfer in a 2-D Cylindrical Medium using the Modified Discrete Ordinate Method and the Lattice Boltzmann Method , Numer. Heat Transfer A , vol. 60 , pp. 254 – 287 , 2011 .
   Web of Science ®Google Scholar
• P. Asinari , S. C. Mishra , and R. Borchiellini , A Lattice Boltzmann Formulation for the Analysis of Radiative Heat Transfer Problems in a Participating Medium , Numer. Heat Transfer B , vol. 57 , pp. 126 – 146 , 2010 .
   Web of Science ®Google Scholar
• V. Novozhilov and C. Byrne , Lattice Boltzmann Modeling of Thermal Explosion in Natural Convection Conditions , Numer. Heat Transfer A , vol. 63 , pp. 824 – 839 , 2013 .
   Web of Science ®Google Scholar
• D. D. Gray and A. Giorgini , The Validity of the Boussinesq Approximation for Liquids and Gases , Int. J. Heat Mass Transfer vol. 19 , pp. 545 – 551 , 1976 .
   Web of Science ®Google Scholar
• Z. Guo , B. Shi , and C. Zheng , A Coupled Lattice BGK Model for the Boussinesq Equations , Int. J. Num. Meth. Fluids , vol. 39 , pp. 325 – 342 , 2002 .
   Web of Science ®Google Scholar
• Q. Zou , S. Hou , S. Chen , and G. D. Doolen , An Improved Incompressible Lattice Boltzmann Model for Time-Independent Flows , J. Stat. Phys. , vol. 81 , pp. 35 – 48 , 1995 .
   Web of Science ®Google Scholar
• Z. Lin , H. Fang , and R. Tao , Improved Lattice Boltzmann Model for Incompressible Two-Dimensional Steady Flows , Phys. Rev. E , vol. 54 , pp. 6323 – 6330 , 1996 .
   PubMed Web of Science ®Google Scholar
• X. He and L.-S. Luo , Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation , J. Statistical Phys. , vol. 88 , pp. 927 – 944 , 1997 .
   Web of Science ®Google Scholar
• Z. Guo , B. Shi , and N. Wang , Lattice BGK Model for Incompressible Navier–Stokes Equation , J. Com. Phys. , vol. 165 , pp. 288 – 306 , 2000 .
   Web of Science ®Google Scholar
• Q. Li , Y. He , Y. Wang , and G. Tang , An Improved Thermal Lattice Boltzmann Model for Flows without Viscous Heat Dissipation and Compression Work , Int. J. Modern Phys. C , vol. 19 , pp. 125 – 150 , 2008 .
   Web of Science ®Google Scholar
• J. Buick and C. Greated , Gravity in a Lattice Boltzmann Model , Phys. Rev. E , vol. 61 , pp. 5307 – 5320 , 2000 .
   PubMed Web of Science ®Google Scholar
• P. Skordos , Initial and Boundary Conditions for the Lattice Boltzmann Method , Phys. Rev. E , vol. 48 , pp. 4823 – 4842 , 1993 .
   PubMed Web of Science ®Google Scholar
• B. Gebhart , Heat Transfer , chap. 8 , McGraw-Hill , New York , NY , 1971 .
   Google Scholar
• G. de Vahl Davis , Natural Convection of Air in a Square Cavity: A Bench Mark Numerical Solution , Int. J. Num. Meth. Fluids , vol. 3 , pp. 249 – 264 , 1983 .
   Web of Science ®Google Scholar