The method of numerical simulation of the hydrodynamics of a developing steady-state pulsating small-amplitude laminar flow of an incompressible Newtonian liquid in a rectangular microchannel is presented based on the boundary-layer theory. The simulation was carried out for flow with Re = 100–2000. Distributions of the coefficients of hydraulic resistance and of skin friction of flow along the channel length are obtained. Conclusions are drawn on the length of the initial hydrodynamic segment and on the changes in the amplitude and phase of vibrations of the hydraulic resistance and skin friction coefficients and of longitudinal velocity. The distribution of the shear stress, as well as of its amplitude and phase over the channel perimeter, has been determined.
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M. A. Kadhim, N. Kapur, J. L. Summers, and H. Thompson, Rack level study of hybrid liquid/air cooled servers: The impact of fl ow distribution and pumping confi guration on central processing units temperature, Heat Transf. Eng., 41, Nos. 19–20, 1683–1698 (2020).
X. Zhao, Y. Xiao, Z. Wang, Y. Luo, and L. Cao, Unsteady fl ow and pressure pulsation characteristics analysis of rotating stall in centrifugal pumps under off-design conditions, J. Fluids Eng., 140, No. 2, 021105 (2017).
M. S. Purdin, Numerical modelling of heat transfer for the fi rst kind boundary condition in the pulsating laminar flow at the initial hydrodynamic section in the flat channel, IJAER, 13, No. 11, 9428–9432 (2018).
M. S. Purdin, Heat transfer in a developing low-amplitudes pulsating laminar flow in a square channel, IJERT, 12, No. 11, 2017–2022 (2019).
S. N. Bagayev, V. N. Zakharov, V. A. Orlov, S. V. Panov, A. V. Fedorov, V. M. Fomin, and T. A. Khmel′, Experimental and theoretical studies of the infl uence of pulse pressure oscillations on the processes of microhemocirculation, J. Eng. Phys. Thermophys., 85, No. 1, 92–100 (2012).
T. N. Gerasimenko, O. V. Kindeeva, V. A. Petrov, A. I. Khaustov, and E. V. Trushkin, Modelling and characterization of a pneumatically actuated peristaltic micropump, Appl. Math. Model., 52, 590–602 (2017).
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, No. 1, 7–14 (1929).
R. Siegel and M. Perlmutter, Heat transfer for pulsating laminar duct fl ow, J. Heat Transf., 84, No. 2, 111–122 (1962).
K. Haddad, Ö. Ertunç, M. Mishra, and A. Delgado, Pulsating laminar fully developed channel and pipe flows, Phys. Rev., 81, 016303-1–13 (2010).
E. P. Valueva and M. S. Purdin, Hydrodynamics and heat transfer for large amplitude pulsating laminar flow in channels, Thermophys. Aeromech., 25, No. 5, 705–716 (2018).
M. S. Purdin, Developing low-amplitude pulsating laminar flow in a flat channel, IJERT, 12, No. 4, 570–578 (2019).
C. Fan and B. T. Chao, Unsteady, laminar, incompressible flow through rectangular ducts, ZAMP, 16, 351–360 (1965).
A. Yakhot, M. Arad., and G. Ben-Dor, Numerical investigation of a laminar pulsating flow in a rectangular duct, Int. J. Numer. Methods Fluids, 29, No. 8, 935–950 (1999).
X. G. Qi, D. M. Scott, and D. I. Wilson, Modelling laminar pulsed flow in rectangular microchannels, Chem. Eng. Sci., 63, No. 10, 2682–2689 (2008).
N. Zhuang, S. Tan, H. Yuan, and C. Zhang, Flow resistance characteristics of pulsating laminar flow in rectangular channels, Ann. Nucl. Energy, 73, 398–407 (2014).
E. P. Valueva and M. S. Purdin, The pulsating laminar fl ow in a rectangular channel, Thermophys. Aeromech., 22, No. 6, 733–744 (2015).
R. Blythman, T. Persoons, N. Jeffers, K. P. Nolan, and D. B. Murray, Localised dynamics of laminar pulsatile flow in a rectangular channel, Int. J. Heat Fluid Flow, 66, 8–17 (2017).
R. Blythman, S. Alimohammadi, T. Persoons, N. Jeffers, and D. B. Murray, Parametric analysis of laminar pulsating flow in a rectangular channel, Heat Mass Transf., 54, 2177–2186 (2018).
J. S. Park, C. K. Choi, and K. D. Kihm, Optically sliced micro-PIV using confocal laser scanning microscopy (CLSM), Exp. Fluids, 37, 105–119 (2004).
J. S. Park and K. D. Kihm, Three-dimensional micro-PTV using deconvolution microscopy, Exp. Fluids, 40, 491–499 (2006).
H. Schlichting, Grenzschicht-Theorie, G. Braun Verlag, Karlsruhe (1965).
R. W. Hornbeck, Numerical Marching Techniques for Fluid Flows with Heat Transfer, NASA SP-297 (1973).
A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Izd. MGU, Moscow (1999).
M. S. Purdin, Program of Investigating the Hydrodynamics with a Developing Pulsating Laminar Flow in Rectangular Channels, State Registration Certifi cate No. 2019610316 of 10.01.2019.
M. S. Purdin, Program of Investigating the Hydrodynamics with a Developing Pulsating Laminar Flow with Small Amplitudes in a Square Channel, State Registration Certificate No. 2019663743 of 22.10.2019.
L. S. Han, Hydrodynamic entrance lenghts for incompressible laminar flow in rectangular ducts, J. Appl. Mech., 27, No. 3, 403–409 (1960).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 94, No. 5, pp. 1296–1308, September–October, 2021.
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Purdin, M.S. Developing Pulsating Small-Amplitude Laminar Flow in a Rectangular Channel. J Eng Phys Thermophy 94, 1266–1277 (2021). https://doi.org/10.1007/s10891-021-02407-5
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DOI: https://doi.org/10.1007/s10891-021-02407-5