NUMERICAL SIMULATION OF FLOW PATTERN FORMATION IN A BOTTOM HEATED CYLINDRICAL FLUID LAYER

References

• E. F. C. Somerscales and T. S. Dougherty , Observed Flow Patterns at the Initiation of Convection in a Horizontal Liquid Layer Heated from Below, J. Fluid Mech., vol. 42 , part. 4 , pp. 755 - 768 , 1970 .
   Google Scholar
• C. Q. Hoard , C. R. Robertson , and A. Acrivos , Experiments on the Cellular Structure in Bénard Convection , Int. J. Heat Mass Transfer , vol. 13 , pp. 849 - 856 , 1970 .
   Web of Science ®Google Scholar
• E. L. Koschmieder and S. G. Pallas , Heat Transfer Through a Shallow, Horizontal Convecting Fluid Layer , Int. J. Heat Mass Transfer , vol. 17 , pp. 991 - 1002 , 1974 .
   Google Scholar
• E. L. Koschmieder , On the Wavelength of Convective Motions , J. Fluid Mech ., vol. 35 , part. 3 , pp. 527 - 530 , 1969 .
   Google Scholar
• K. R. Kirchartz , U. Mulier , H. Oertel Jr., and J. Z. Karlsruhe , Axisymmetric and Non-Axisymmetric Convection in a Cylindrical Container , ACTA Mech ., vol. 40 , pp. 181 - 194 , 1980 .
   Google Scholar
• M. M. Chen and J. A. Whitehead , Evolution of Two-Dimensional Periodic Rayleigh Convection Cells of Arbitrary Wave-Numbers , J. Fluid Mech ., vol. 31 , part. 1 , pp. 1 - 15 , 1968 .
   Google Scholar
• V. Steinberg , G. Ahlers , and D. S. Cannell , Pattern Formation and Wave-Number Selection by Rayleigh-Bénard Convection in a Cylindrical Container , Phys. Scr ., vol. 32 , pp. 534 - 547 , 1985 .
   Google Scholar
• G. Ahlers and D. S. Cannell , Time Dependence of Flow Patterns near the Convective Threshold in Cylindrical Container , Phys. Reu. Lett ., vol. 54 , no. 13 , pp. 1373 - 1376 , 1985 .
   PubMed Web of Science ®Google Scholar
• C. W. Meyer , G. Ahlers , and D. S. Cannell , Initial Stages of Pattern Formation in Rayleigh-B6nard Convection , Phys. Rev. Lett ., vol. 59 , no. 14 , pp. 1577 - 1580 , 1987 .
   PubMed Web of Science ®Google Scholar
• C. W. Meyer , G. Ahlers , and D. S. Cannell , Stochastic Influences on Pattern Formation in Rayleigh-Bdnard Convection Ramping Experiments , Phys. Rev. A , vol. 44 , no. 4 , pp. 2514 - 2537 , 1991 .
   PubMed Web of Science ®Google Scholar
• M. S. Heutmaker and J. P. Gollub , Wave-Vector Field of Convective Flow Patterns , Phys. Rev. A vol. 35 , no. 1 , pp. 242 - 260 , 1987 .
   Web of Science ®Google Scholar
• V. Croquette , Convective Pattern Dynamics at Low Prandtl Number Part I , Contemporary Phys ., vol. 30 , no. 2 , pp. 113 - 133 , 1989 .
   Web of Science ®Google Scholar
• V. Croquette , Convective Pattern Dynamics at Low Prandtl Number Part II , Contemporary Phys ., vol. 30 , no. 3 , pp. 153 - 171 , 1989 .
   Web of Science ®Google Scholar
• Y. Hu , R. Ecke ,G, Ahlers, Convection near Threshold for Prandtl Numbers near 1 , Phys. Rev. E , vol. 48 , no. 6 , pp. 4399 - 4413 , 1993 .
   PubMed Web of Science ®Google Scholar
• S. W. Morris , E. Bodenschatz , D. S. Cannell , and G. Ahlers , Spiral Defect Chaos in Large Aspect Ratio Rayleigh-B6nard Convection , Phys. Rev. Lett ., vol. 71 , no. 13 , pp. 2026 - 2029 , 1993 .
   PubMed Web of Science ®Google Scholar
• G. S. Charlson and R. L. Sani , Thermoconvective Instability in a Bounded Cylindrical Fluid Layer , Int. J. Heat Transfer , vol. 13 , pp. 1479 - 1496 , 1970 .
   Google Scholar
• G. S. Charlson and R. L. Sani , On Thermoconvective Instability in a Bounded Cylindrical Fluid Layer , Int. J. Heat Transfer , vol. 14 , pp. 2157 - 2160 , 1971 .
   Google Scholar
• G. S. Charlson and R. L. Sani , Finite Amplitude Axisymmetric Thermoconvective Flows in a Bounded Cylindrical Layer of Fluid , J. Fluid Mech ., vol. 71 , part. 2 , pp. 209 - 229 , 1975 .
   Web of Science ®Google Scholar
• F. H. Harlow and J. E. Welch , Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface , Phys. Fluids , vol. 8 , pp. 2182 - 2189 , 1965 .
   Web of Science ®Google Scholar
• S. V. Patankar , Numerical Heat Transfer and Fluid Flow , Hemisphere , Washington , D.C ., 1980 .
   Google Scholar
• Address correspondence to Professor Tsing-Fa Lin, Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan, Republic of China. E-mail: [email protected]. tw
   Google Scholar