TECHNICAL PAPERS: Forced Convection

Numerical Simulation of Reciprocating Flow Forced Convection in Two-Dimensional Channels

[+] Author and Article Information
Cuneyt Sert, Ali Beskok

Mechanical Engineering Department, Texas A&M University, College Station, TX 77840-3123

J. Heat Transfer 125(3), 403-412 (May 20, 2003) (10 pages) doi:10.1115/1.1565092 History: Received January 14, 2002; Revised December 04, 2002; Online May 20, 2003
Copyright © 2003 by ASME
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Shah, R. K., and London, A. L., 1978, “Laminar Flow Forced Convection in Ducts,” Advances in Heat Transfer, Irvine, T. F., Jr., and Hartnett J. P., eds., Academic Press, New York, NY.
Zamir, M., 2000, The Physics of Pulsatile Flow, Springer-Verlag, New York, NY.
Beskok,  A., and Warburton,  T. C., 2001, “Arbitrary Lagrangian Eulerian Analysis of a Bidirectional Micro-Pump Using Spectral Elements,” Int. J. Comput. Eng. Sci. 2 (1), pp. 43–57.
Yi, M., Bau, H. H., and Hu, H., 2000, “A Peristaltic Meso-Scale Mixer,” in Proceedings of ASME IMECE Meeting, MEMS, 2 , pp. 367–374.
Liao, Q. D., Yang, K. T., and Nee, V. W., 1995, “Microprocessor Chip Cooling by Channeled Zero-Mean Oscillatory Air Flow,” Advances in Electronics Packaging, EEP-Vol. 10-2, pp. 789–794.
Sert,  C., and Beskok,  A., 2002, “Oscillatory Flow Forced Convection in Micro Heat Spreaders,” Numer. Heat Transfer, Part A. 42(7), pp. 685–705.
Oddy,  M. H., Santiago,  J. G., and Mikkelsen,  J. C., 2001, “Electrokinetic Instability Micromixing,” Anal. Chem., 73–24, pp. 5822–5832.
Dutta,  P., and Beskok,  A., 2001, “Time Periodic Electroosmotic Flows: Analogies to Stokes’ Second Problem,” Anal. Chem., 73(21), pp. 5097–5102.
Siegel,  R., and Perlmutter,  M., 1962, “Heat Transfer for Pulsating Laminar Duct Flow,” ASME J. Heat Transfer, 84, pp. 111–123.
Siegel,  R., 1987, “Influence of Oscillation-Induced Diffusion on Heat Transfer in a Uniformly Heated Channel,” ASME J. Heat Transfer, 109, pp. 244–247.
Kim,  S. Y., Kang,  B. H., and Hyun,  J. M., 1993, “Heat Transfer in the Thermally Developing Region of a Pulsating Channel Flow,” Int. J. Heat Mass Transf., 36, pp. 4257–4266.
Moschandreou,  T., and Zamir,  M., 1997, “Heat Transfer in a Tube with Pulsating Flow and Constant Heat Flux,” Int. J. Heat Mass Transf., 40, pp. 2461–2466.
Zhao,  T., and Cheng,  P., 1995, “A Numerical Solution of Laminar Forced Convection in a Pipe Subjected to a Reciprocating Flow,” Int. J. Heat Mass Transf., 38, pp. 3011–3022.
Greiner, M., Fischer, P. F., and Tufo, H., 2001 “Numerical Simulations of Resonant Heat Transfer Augmentation at Low Reynolds Numbers,” in Proceedings of ASME International Mechanical Engineering Congress and Exposition, IMECE2001/HTD-24100, November 11–16, 2001, New York, NY.
Chatwin,  P. C., 1975, “The Longitudinal Dispersion of Passive Contaminant in Oscillating Flow in Tubes,” J. Fluid Mech., 71, pp. 513–527.
Kurzweg,  U. H., and Zhao,  L., 1984, “Heat Transfer by High-Frequency Oscillations: A New Hydrodynamic Technique For Achieving Large Effective Thermal Conductivities,” Phys. Fluids, 27, pp. 2624–2627.
Kurzweg,  U. H., 1985, “Enhanced Heat Conduction in Oscillating Viscous Flows Within Parallel-Plate Channels,” J. Fluid Mech., 156, pp. 291–300.
Li,  P., and Yang,  K. T., 2000, “Mechanisms for the Heat Transfer Enhancement in Zero-Mean Oscillatory Flows in Short Channels,” Int. J. Heat Mass Transf., 43, pp. 3551–3566.
Cooper,  W. L., Nee,  V. W., and Yang,  K. T., 1994, “An Experimental Investigation of Convective Heat Transfer From the Heated Floor of a Rectangular Duct to a Low Frequency Large Tidal Displacement Oscillatory Flow,” Int. J. Heat Mass Transf., 37, pp. 581–592.
Chou, F-C., Weng, J-G., and Tien, C-L., 1998, “Cooling of Micro Hot Spots by Oscillatory Flow,” Proceedings of the 11th International Symposium on Transport Phenomena, Hsinchu, Taiwan, pp. 324–329.
Richardson,  E. G., and Tyler,  E., 1929, “The Transverse Velocity Gradient Near The Mouths of Pipes in Which An Alternating or Continuous Flow of Air is Established,” Proc. Phys. Soc. London, 42, pp. 1–15.
Landau, L. D., and Lifshitz, E. M., 1987, Course of Theoretical Physics Volume 6-Fluid Mechanics, 2nd ed., Pergamon Press.
Karniadakis, G. M., and Sherwin, S. J., 1999, Spectral/hp Element Methods for CFD, Oxford University Press, New York.
Beskok,  A., and Warburton,  T. C., 2001, “An Unstructured H/P Finite Element Scheme for Fluid Flow and Heat Transport in Moving Domains,” J. Comput. Phys., 174, pp. 492–509.


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The geometry and thermal boundary conditions used in this study. On the top surface, uniform heat flux of q=1 is specified at 5≤x≤15. For 4≤x≤5 and 16≥x≥15, the heat flux varies from zero to unity sinusoidally. Zero wall temperature is specified for x≤4 and x≥16. Bottom wall is insulated, while side surfaces are periodic (cyclic/repeating).
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Schematic view of a hypothetical problem that consists of a channel with repeating heated and constant temperature boundaries
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Axial distribution of time-averaged Nusselt number for (a) reciprocating, (b) unidirectional steady flows. Simulation parameters are presented in Table 1.
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Analytical solution of the velocity profiles at various times during a cycle for (a) α=1, and (b) α=10 flow. Index i represents time within a period of the pressure pulse (t=i−1/8 τ).
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Top: Half of the actual mesh used in the simulations. Quadrature points for a 9th -order expansion are also shown for selected elements. A finer mesh is used at the Neumann/Dirichlet boundary interface on the top wall (4<x<4.5) to resolve large temperature variations. Bottom: A portion of the spectral element mesh showing only cross-channel discretization with different expansion orders (N). Thick lines show the elements, while thin lines show the collocation points. Progressively increasing the element order (N) by keeping the total number of elements fixed is known as p-type refinement.
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Space and time accuracy for α=10 flow. (a) Variation of L error as a function of the expansion order N (obtained using Δt=10−5). Exponential decay of the discretization error indicates spectral convergence. (b) Variation of L error as a function of the time step (obtained using 12th order elements). Shows second-order time accuracy.
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Instantaneous temperature contours for cases 2, 4, 6, and 8. Index i represents time within half a period of the pressure pulse (t=(i−1)τ/8). The flow and thermal conditions are presented in Table 1.
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Instantaneous temperature and velocity profiles at axial locations of x=5 (solid-lines) and x=10 (dashed-lines). Index i represents time within a period of the pressure pulse (t=(i−1)τ/8). Simulation parameters are presented in Table 1.
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Instantaneous top-wall temperatures. Index i represents time within half a period of the pressure pulse (t=(i−1)τ/8). Simulation parameters are presented in Table 1.
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Time-averaged wall-temperature (solid lines) and time-averaged bulk temperature (dashed-lines) variations for reciprocating flows. Wall temperature (dashed-dotted lines) and bulk temperature (dashed-dotted-dotted lines) variations for unidirectional steady flows are also shown. Simulation parameters are presented in Table 1.



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