Abstract
The problem about laminar pulsating flow and heat transfer with high pulsation amplitudes of average cross-section velocity in a round tube and in a flat channel is solved using the finite element method. The difference scheme’s optimal parameters are determined. Data on the pulsation amplitude and phase are obtained for the hydraulic friction coefficient, tangential stress on the wall, liquid temperature, heat flux on the wall q w (at ϑw = const), and wall temperature ϑw (at q w = const) are obtained. Two characteristic modes, namely, quasi steady-state and high-frequency ones are separated based on the value of dimensionless pulsation frequency. During operation in the quasi steady-state mode, the values of all hydrodynamic and thermal quantities correspond to the values of time-average velocity at the given time instant. For operation in the high-frequency mode, it is shown that the dependences of the pulsating components of hydrodynamic and thermal quantities on the dimensionless pulsation frequency have the same pattern for rectilinear channels having different shapes of their cross section. It is found that certain nodal points exist on the distribution of thermal characteristics along the tube (liquid temperature, heat flux density on the wall at ϑw = const, and wall temperature at q w = const) in which the values of these quantities remain unchanged. The distances between the nodal points decrease with increasing the pulsation frequency. The pulsations of thermal quantities decay over the tube length.
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References
P. C. Huang, S. H. Nian, and C. F. Yang, “Enhancement heat source cooling by flow pulsation and porous block,” J. Thermophys. Heat Transfer 19, 460–470 (2005).
B. H. Yan and Y. H. Yang, “Forced convection with laminar pulsating flow in tube,” J. Heat and Mass Transfer 47, 197–202 (2011).
Y. Han, P. Ganatos, and S. Weinbaum, “Transmission of steady and oscillatory fluid shear stress across epithelial and endothelial surface structures,” Phys. Fluid. 17, Paper No. 031508 (2005).
T. A. Khmel’ and A. V. Fedorov, “Modeling of pulsating currents in blood capillaries,” Matem. Modeling 8 (1), 1–11 (2013).
D. Huh, B. D. Matthews, A. Mammoto, M. MontoyaZavala, H.- Y. Hsin, and D. E. Ingber, “Reconstituting organ-level lung functions on a chip,” Science 328, 1662–1668 (2010).
U. Marx, H. Walles, S. Hoffmann, G. Linder, R. Horland, F. Sonntag, U. Klotzbach, D. Sakharov, A. Tonevitsky, and R. Louster, “‘Human-on-a-chip’ developments: a translational cutting-edge alternative to systemic safety assessment and efficiency evaluation of substances in laboratory animals and man?” ATLA 40, 235–257 (2012).
E. G. Richardson and E. Tyler, “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 (1), 7–14 (1929).
T. Sexl and E. G. Uber, “Richardson entdeckten ‘annular Effekt’,” Z. Phys. 61 (6/7), 349–362 (1930).
S. Uchida, “The pulsating viscous flow superposed on the steady laminar motion of incompressible fluid in a circular pipe,” ZAMP 7 (5), 403–422 (1956).
R. Siegel and M. Perlmutter, “Heat transfer for pulsating laminar duct flow,” ASME J. Heat Transfer 84, 111–123 (1962).
D. A. Nield and A. V. Kuznetsov, “Forced convection with laminar pulsating flow in a channel or tube,” Int. J. Therm. Sci. 46 (7), 551–560 (2007).
Y. Kita, T. Hayashi, and K. Hirose, “Heat transfer in pulsating laminar flow in a pipe (a constant wall temperature),” Bull. JSME 25 (200), 217–224 (1982).
E. P. Valueva, V. N. Popov, and S. Yu. Romanova, “Heat transfer under laminar pulsating flow in a round tube,” Therm. Eng. 40 (8), 624 (1993).
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Original Russian Text © E.P. Valueva, M.S. Purdin, 2015, published in Teploenergetika.
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Valueva, E.P., Purdin, M.S. Hydrodynamics and heat transfer for pulsating laminar flow in channels. Therm. Eng. 62, 636–644 (2015). https://doi.org/10.1134/S0040601515090116
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DOI: https://doi.org/10.1134/S0040601515090116