Skip to main content
SpringerLink
Log in

Simulation of conjugate heat transfer in a microchannel system by a hybrid algorithm

  • Published:
Journal of Applied and Industrial Mathematics Aims and scope Submit manuscript

Abstract

A new hybrid method is proposed for solving the problems of fluid dynamics and heat transfer in complex hydraulic systems. The peculiarity of the method consists in the idea that some elements of the model are represented as network elements, where the solving of the flow distribution problem is carried out on the basis of the hydraulic circuit theory, whereas the flow in the remaining elements is calculated by the spatial methods of computational fluid dynamics (CFD). The results are presented of testing the proposed hybrid method for the problems of fluid dynamics and heat transfer in microchannels. The test calculations demonstrate high efficiency of the method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. P. Merenkov and V. Ya. Khasilev, Theory of Hydraulic Circuits (Nauka, Moscow, 1985) [in Russian].

    Google Scholar 

  2. N. N. Novitskii, E. V. Sennova, M. G. Sukharev, et al., Hydraulic Circuits. Theory Development and Applications (Nauka, Novosibirsk, 2000) [in Russian].

    Google Scholar 

  3. D. J. Twigt, E. D. De Goede, F. Zijl, D. Schwanenberg, and A. Y. W. Chiu, “Coupled 1D–3D Hydrodynamic Modelling with Application to the Pearl River Delta,” Ocean Dynamics 59, 1077–1093 (2009).

    Article  Google Scholar 

  4. W. Zhang, S. Lyu, Yu. Zhu, and X. Chen, “A Coupled Model of the 1D River Network and 3D Estuary Based on Hydrodynamics and Suspended Sediment Simulations,” J. Appl. Math. (2014) URL: http://dx.doi.org/10.1155/2014/798579.

    Google Scholar 

  5. C. D’Angelo and A. Quarteroni, On the Coupling of 1D and 3D Diffusion-Reaction Equations. Applications to Tissue Perfusion Problems, MOX-Report No. 28/2008.

    Google Scholar 

  6. E. D. Fernandez-Nietoa, J. Marinb, and J. Monnierc, “Coupling Superposed 1D and 2D Shallow-Water Models: Source Terms in Finite Volume Schemes,” Computers & Fluids 39, 1070–1082 (2010).

    Article  MathSciNet  Google Scholar 

  7. L. Formaggia, F. Nobile, A. Quarteroni, and A. Veneziani, “Multiscale Modelling of the Circulatory System: A Preliminary Analysis,” Computing and Visualization in Sci. No. 2, 75–83 (1999).

    Article  MATH  Google Scholar 

  8. H. Harvey et al., “A Hybrid 1D and 3D Approach to Hemo Dynamics Modelling for a Patient-Specific Cerebral Vasculature and Aneurysm,” in Lecture Notes in Computer Science, Vol. 5762 (Springer, Heidelberg, 2009), pp. 323–330.

    Google Scholar 

  9. E. V. Astrakhantseva, V. Yu. Gidaspov, and D. L. Reviznikov, “Mathematical Modeling of Hemodynamics of Large Blood Vessels,” Mat. Model. 17 (8), 61–80 (2005).

    MATH  Google Scholar 

  10. A. F. Voevodin and V. S. Nikiforovskaya, “Numerical Modeling of Unsteady-State Hydrothermal Processes in Water Objects,” in International Conference “Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment, and Practice” Dedicated to the 90th Anniversary of Academician N. N. Yanenko (Inst. Teoret. Prikl.Mekh., Novosibirsk, 2011), p. 16.

    Google Scholar 

  11. T. K. Dobroserdova, Numerical Modeling of Blood Flow under Presence of Vascular Implants or Pathology, Candidate’s Dissertation inMathematics and Physics (Inst. Vychisl.Mat.,Moscow, 2013).

    Google Scholar 

  12. J. Alastruey, K. H. Parker, J. Peirò, and S. J. Sherwin, “Lumped Parameter Outflow Models for 1D Blood Flow Simulations: Effect on Pulse Waves and Parameter Estimation,” Comm. Comput. Phys. 4 (2), 317–336 (2008).

    Google Scholar 

  13. S. I. Fadeev, E. G. Kostsov, and D. O. Pimanov, “Numerical Study of Mathematical Models of Microelectromechanical Resonators of Various Types,” Sibirsk. Zh. Industr. Mat. 17 (4), 120–135 (2014) [J. Appl. Indust. Math. 9 (1), 47–60 (2015)].

    MathSciNet  Google Scholar 

  14. V. Ya Rudyak, A. V. Minakov, A. A. Gavrilov, and A. A. Dekterev, “Application of New Numerical Algorithm for Solving the Navier–Stokes Equations for Modelling theWork of a Viscometer of the Physical Pendulum Type,” Thermophysics and Aeromechanics 15, 333–345 (2008).

    Article  Google Scholar 

  15. V. Ya Rudyak, A. V. Minakov, A. A. Gavrilov, and A. A. Dekterev, “Modelling of Flows in Micromixers,” Thermophysics and Aeromechanics 17, 565–576 (2010).

    Article  Google Scholar 

  16. V. Ya. Rudyak, A. V. Minakov, A. A. Gavrilov, and A. A. Dekterev, “Mixing in a T-Shaped Micromixer at Moderate Reynolds Numbers,” Thermophysics and Aeromechanics 19, 385–395 (2012).

    Article  Google Scholar 

  17. A. Minakov, V. Rudyak, A. Dekterev, and A. Gavrilov, “Investigation of Slip Boundary Conditions in the T-Shaped Microchannel,” Internat. J. Heat and Fluid Flow 43, 161–169 (2013).

    Article  Google Scholar 

  18. A. A. Gavrilov, A. V. Minakov, A. A. Dekterev, and V. Ya. Rudyak, “A Numerical Algorithm for Modeling Laminar Flows in an Annular Channel with Eccentricity,” Sibirsk. Zh. Industr. Mat. 13 (4), 3–14 (2010) [J. Appl. Indust. Math. 5 (4), 559–568 (2011)].

    MATH  MathSciNet  Google Scholar 

  19. A. V. Minakov, “Numerical Algorithm for Moving-Boundary Fluid Dynamics Problems and Its Testing,” Zh. Vychisl.Mat. Mat. Fiz. 54 (1), 61–72 (2014) [Comput.Math.Math. Phys. 54 (10), 1560–1570 (2014)].

    MathSciNet  Google Scholar 

  20. A. A. Dekterev, A. A. Gavrilov, and A. V. Minakov, “Up-to-Date Features of the CFD Code SigmaFlow for Solving the Thermal Physical Problems,” Sovremennaya Nauka: Issled., Idei, Result., Tekhnol. 4 (2), 117–122 (2010).

    Google Scholar 

  21. A. A. Gavrilov, A. V. Minakov, A. A. Dekterev, and V. Ya. Rudyak, “A Numerical Algorithm for Modeling Laminar Flows in an Annular Channel with Eccentricity,” Sibirsk. Zh. Industr. Mat. 13 (4), 3–14 (2010) [J. Appl. Indust. Math. 5 (4), 559–568 (2011)].

    MATH  MathSciNet  Google Scholar 

  22. N. N. Novitskii, M. G. Sukharev, S. A. Sardanashvili, et al., “A Hybrid Approach to Solution of the Problems of Theory of Hydraulic Circuits That Include Some Space Elements,” in Pipeline Systems of Energetics: Mathematical and Computer Modeling (Melentiev Energy Systems Inst., Irkutsk, 2014), pp. 46–55.

    Google Scholar 

  23. S. A. Filimonov, A. A. Dekterev, and D. V. Boikov, “Numerical Modeling of a Shell-and-Tube Heat- Exchanger by a Hybrid Algorithm,” Teplovye Protsessy v Tekhnike 6 (8), 343–348 (2014).

    Google Scholar 

  24. S. V. Patankar, Numerical Heat Transfer and Fluid Flow (Hemisphere, Washington, 1980; Energoatomizdat, Moscow, 1984).

    MATH  Google Scholar 

  25. X.-Q. Wang, A. S. Mujumdar, and C. Yap, “Thermal Characteristics of Tree-Shaped Microchannel Nets for Cooling of a Rectangular Heat Sink,” Intern. J. Thermal Sci. 45, 1103–1112 (2006).

    Article  Google Scholar 

  26. S. Khandekar, G. Agarwal, and M. K. Moharana, “Thermo-Hydrodynamics of Developing Flow in a Rectangular Mini-Channel Array,” in Proceedings of the 20th National and 9th International ISHMT-ASME Heat and Mass Transfer Conference (Bombay, 2010), pp. 1342–1349.

    Google Scholar 

  27. A. S. Lobasov, A. V, Minakov, and A. A. Dekterev, “Modeling of Hydrodynamics and Convective Heat Transfer in Microchannels,” Vychisl. Mekh. Sploshn. Sred 5 (4), 481–488 (2012).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. OOO “TORINS,”, Akademgorodok 50/44, Krasnoyarsk, 660036, Russia

    S. A. Filimonov

  2. Siberian Federal University, pr. Svobodnyi 79/10, Krasnoyarsk, 660041, Russia

    A. A. Dekterev, A. V. Sentyabov & A. V. Minakov

  3. Kutateladze Institute of Thermophysics, pr. Akad. Lavrent’eva 1, Novosibirsk, 630090, Russia

    A. A. Dekterev, A. V. Sentyabov & A. V. Minakov

Authors
  1. S. A. Filimonov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Dekterev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. V. Sentyabov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. V. Minakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to S. A. Filimonov or A. A. Dekterev.

Additional information

Original Russian Text © S.A. Filimonov, A.A. Dekterev, A.V. Sentyabov, A.V. Minakov, 2015, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2015, Vol. XVIII, No. 3, pp. 86–97.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Filimonov, S.A., Dekterev, A.A., Sentyabov, A.V. et al. Simulation of conjugate heat transfer in a microchannel system by a hybrid algorithm. J. Appl. Ind. Math. 9, 469–479 (2015). https://doi.org/10.1134/S1990478915040031

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1990478915040031

Keywords

Search

Navigation