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Abstract

At the present stage of fundamental and applied scientific research, most problems of physical and mathematical modeling of heat and mass transfer processes and fluid flow usually involve the analysis and solution of various differential equations. In this case, it can be very useful to use symmetry groups (Lie groups) of differential equations.

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References

  1. Olver P (1986) Applications of Lie groups to differential equations. Springer, New York

    Book  Google Scholar 

  2. Ovsiannikov LV (1982) Group analysis of differential equations, 1st edn. Academic Press

    Google Scholar 

  3. Fletcher CAJ (1984) Computational Galerkin methods. Springer-Verlag, New York, Berlin, Heidelberg Tokyo

    Book  Google Scholar 

  4. Kamke E (1977) Differentialgleichungen: Losungsmethoden und Losungen, I, Gewöhnliche Differentialgleichungen, B. G. Teubner, Leipzig

    Google Scholar 

  5. Avramenko AA, Kobzar SG (1998) Lie group application to unsteady heat transfer over a sphere in the region of flow Reynolds numbers. Thermophys Therm Power Eng 20(2):47–50 (in Russian)

    Google Scholar 

  6. Avramenko AA, Kobzar SG, Shevchuk IV, Kuznetsov AV, Iwanisov LT (2001) Symmetry of turbulent boundary-layer flows: investigation of different eddy viscosity models. Acta Mech 151(1–2):1–14

    Article  Google Scholar 

  7. Çengel YA (2002) Heat transfer: a practical approach. 2nd edn. McGraw-Hill Education, Higher Education

    Google Scholar 

  8. Schlichting H, Gersten K (2004) Boundary layer theory. 8th ed. Springer

    Google Scholar 

  9. Chandrasekhar S (2013) Hydrodynamic and hydromagnetic stability. Courier Corporation

    Google Scholar 

  10. Avramenko AA, Kuznetsov AV (2010) The onset of bio-thermal convection in a suspension of gyrotactic microorganisms in a fluid layer with an inclined temperature gradient. Int J Numer Meth Heat Fluid Flow 20(1):111–129

    Article  Google Scholar 

  11. Avramenko AA, Kuznetsov AV (2010) Bio-thermal convection caused by combined effects of swimming of oxytactic bacteria and inclined temperature gradient in a shallow fluid layer. Int J Numer Meth Heat Fluid Flow 20(2):157–173

    Article  Google Scholar 

  12. Joseph DD (1976) Stability of Fluid Motions. In: Springer tracts in natural philosophy 27, 28, Vol. I, II. Springer, Berlin, Heidelberg, New York

    Google Scholar 

  13. Collatz L (1945) Eigenwertprobleme und ihre numerische Behandlung. Leipzig, Becker & Erler

    Google Scholar 

  14. Walowit J, Tsao S, Diprima R (1964) Stability of flow between arbitrarily spaced concentric cylindrical surfaces including the effect of a radial temperature gradient. J Appl Mech 585–593

    Google Scholar 

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Correspondence to Andriy A. Avramenko .

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Avramenko, A.A., Shevchuk, I.V. (2022). Analytical Methods. In: Modelling of Convective Heat and Mass Transfer in Nanofluids with and without Boiling and Condensation. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-95081-1_2

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  • DOI: https://doi.org/10.1007/978-3-030-95081-1_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-95080-4

  • Online ISBN: 978-3-030-95081-1

  • eBook Packages: EngineeringEngineering (R0)

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