Numerical Computation of Unsteady Flows with an Implicit Spectral Method over a Disk in Still Air

REFERENCES

• H. Schlichting , Boundary-Layer Theory , McGraw-Hill , New York , 1979 .
   Google Scholar
• H. Fasel , Investigation of the Stability of Boundary Layers by a Finite-Difference Model of the Navier-Stokes Equations , J. Fluid Mech. , vol. 78 , pp. 355 – 383 , 1976 .
   Web of Science ®Google Scholar
• C. Basdevant , M. Deville , P. Haldenwa , J. M. Lacroix , J. Quazzani , R. Peyret , P. Orlandi , and A. T. Patera , Spectral and Finite-Difference Solutions of Burgers-Equation , Comput. Fluids , vol. 14 , pp. 23 – 41 , 1986 .
   Web of Science ®Google Scholar
• C. Canuto , M. Y. Hussaini , A. Quarteroni , and T. A. Zang , Spectral Methods in Fluid Dynamics , Springer-Verlag, Heidelberg , 1988 .
   Google Scholar
• R. D. Richtmyer and K. V. Morton , Difference Methods for Initial Value Problems , Interscience, New York , 1967 .
   Google Scholar
• D. L. Book , Finite Difference Techniques for Vectorized Fluid Dynamics Calculations , Springer-Verlag, Berlin , 1981 .
   Google Scholar
• J. D. Hoffman , Numerical Methods for Engineering and Scientists , McGraw-Hill , New York , 1993 .
   Google Scholar
• Y. Wang and K. Hutter , Comparison of Numerical Methods with Respect to Convectively Dominated Problems , I. J. Num. Meth. Fluids , vol. 37 , pp. 721 – 745 , 2001 .
   Web of Science ®Google Scholar
• J. Crank and P. Nicolson , A Practical Method for Numerical Evaluation of Solutions of Partial Differential Equations of the Heat-Conduction Type , Proc. Camb. Phil. Soc. , vol. 43 , pp. 50 – 67 , 1947 .
   Web of Science ®Google Scholar
• H. C. Yee , Construction of Explicit and Implicit Symmetric TVD Schemes and Their Applications , J. Comput. Phys. , vol. 68 , pp. 151 – 179 , 1987 .
   Web of Science ®Google Scholar
• W. Shyy , M. H. Chen , R. Mittal , and H. S. Udaykumar , On the Suppression of Numerical Oscillations using a Non-Linear Filter , J. Comput. Phys. , vol. 102 , pp. 49 – 62 , 1992 .
   Web of Science ®Google Scholar
• D. Britz , O. Qsterby , and J. Strutwolf , Damping of Crank-Nicolson Error Oscillations , Comput. Biol. Chem. , vol. 27 , p. 253 , 2003 .
   PubMed Web of Science ®Google Scholar
• H. A. Attia , Unsteady MHD Flow Near a Rotating Porous Disk with Uniform Suction or Injection , Fluid Dyn. Res. , vol. 23 , pp. 283 – 290 , 1998 .
   Web of Science ®Google Scholar
• M. A. Hossain , A. Hossain , and M. Wilson , Unsteady Flow of Viscous Incompressible Fluid with Temperature-Dependent Viscosity due to a Rotating Disc in the Presence of Transverse Magnetic Field and Heat Transfer , Int. J. Therm. Sci. , vol. 40 , pp. 11 – 20 , 2001 .
   Web of Science ®Google Scholar
• W. J. Minkowycz and E. M. Sparrow , Numerical Solution Scheme for Local Non-Similarity Boundary Layer Analysis , Numer. Heat Transfer, Part A , vol. 1 , pp. 69 – 85 , 1978 .
   Google Scholar
• J. Gary , D. R. Kassory , H. Tadjeran , and A. Zebib , The Effect of Significant Viscosity Variation on Convective Heat Transport in Water-Saturated Porous Media , J. Fluid Mech. , vol. 117 , pp. 233 – 249 , 1982 .
   Web of Science ®Google Scholar
• K. N. Mehta and S. Sood , Transient Free Convection Flow with Temperature Dependent Viscosity in Fluid Saturated Porous Medium , Int. J. Eng. Sci. , vol. 30 , pp. 1083 – 1087 , 1992 .
   Web of Science ®Google Scholar
• W. F. Ames , Numerical Methods in Partial Differential Equations , Academic Press , New York , 1977 .
   Google Scholar
• H. A. Attia , Time Varying Rotating Disk Flow and Heat Transfer of a Conducting Fluid with Suction or Injection , Int. Comm. Heat Mass Transfer , vol. 30 , pp. 1041 – 1049 , 2003 .
   Web of Science ®Google Scholar
• J. M. Owen and R. H. Rogers , Flow and Heat Transfer in Rotating-Disk Systems, vol. 1: Rotor-Stator Systems , Research Studies Press, England , 1989 .
   Google Scholar
• W. T. Cheng and H. T. Lin , Wärme und Stoffübertragung , vol. 30 , pp. 101 – 108 , 1994 .
   Google Scholar
• J. S. Yoo , Unsteady Heat Transfer from a Rotating Disk with Solidification , Numer. Heat Transfer , vol. 31 , pp. 765 – 781 , 1997 .
   Web of Science ®Google Scholar
• T. Indinger and I. V. Shevchuk , Transient Laminar Conjugate Heat Transfer of a Rotating Disk: Theory and Numerical Simulations , Int. J. Heat and Mass Transfer , vol. 47 , pp. 3577 – 3581 , 2004 .
   Web of Science ®Google Scholar
• I. V. Shevchuk , Unsteady Conjugate Laminar Heat Transfer of a Rotating Non-Uniformly Heated Disk: Application to the Transient Experimental Technique, Int. J. Heat and Mass Transfer , vol. 49, pp. 3530–3537, 2006.
   Web of Science ®Google Scholar
• N. Alilat , A. Bairi , and N. Laraqi , Three-Dimensional Calculation of Temperature in a Rotating Disk Subjected to an Eccentric Circular Heat Source and Surface Cooling , Numer. Heat Transfer A , vol. 46 , pp. 167 – 180 , 2004 .
   Web of Science ®Google Scholar
• D. T. V. Lin , H. Y. Li , and W. M. Yan , Estimating the Wall Heat Flux of Unsteady Conjugated Forced Convection Between Two Corotating Disks Using an Inverse Solution Scheme , J. of Heat Transfer , vol. 130 , p. 121702 , 2008 .
   Web of Science ®Google Scholar
• M. M. Awad , Heat Transfer from a Rotating Disk to Fluids for a Wide Range of Prandtl Numbers using the Asymptotic Model , J. of Heat Transfer , vol. 130 , p. 014505 , 2008 .
   Web of Science ®Google Scholar
• M. M. Rahman and J. C. Lallave , Transient Conjugate Heat Transfer during Free Liquid Jet Impingement on a Rotating Solid Disk , Numer. Heat Transfer A , vol. 55 , pp. 229 – 251 , 2009 .
   Web of Science ®Google Scholar
• R. W. Hill and K. S. Ball , Parallel Implementation of a Fourier-Chebyshev Collocation Method for Incompressible Fluid Flow and Heat Transfer , Numer. Heat Transfer B , vol. 36 , pp. 309 – 329 , 1999 .
   Web of Science ®Google Scholar
• M. Turkyilmazoglu , Linear Absolute and Convective Instabilities of Some Two- and Three-Dimensional Flows , Ph.D. thesis , University of Manchester , Manchester, England , 1998 .
   Google Scholar
• S. K. Kumar , W. I. Thacker , and L. T. Watson , Magnetohydrodynamic Flow and Heat Transfer about a Rotating Disk with Suction and Injection at the Disk Surface , Comp. Fluids , vol. 16 , pp. 183 – 193 , 1988 .
   Web of Science ®Google Scholar
• M. Molki and M. K. Nagalla , Flow Characteristics of Rotating Disks Simulating a Computer Hard Drive , Numer. Heat Transfer A , vol. 48 , pp. 745 – 761 , 2005 .
   Web of Science ®Google Scholar
• H. I. Andersson and M. Rousselet , Slip Flow Over a Lubricated Rotating Disk , Int. J. Heat and Fluid Flow , vol. 27 , pp. 329 – 335 , 2006 .
   Web of Science ®Google Scholar