On the approximation error in the problems of conjugate convective heat transfer

Authors

  • S.I. Martynenko Central Institute of Aviation Motors

DOI:

https://doi.org/10.26089/NumMet.v20r438

Keywords:

conjugate heat transfer, computational fluid dynamics, mathematical modeling, roughness

Abstract

The effects of small boundary perturbation on the approximation error for a model boundary value problem are considered. It is shown that the ignorance of small perturbations of the boundary leads to an additional approximation error in the original differential problem. This error is independent of mesh size. The obtained results are of interest for the mathematical modeling of conjugate heat transfer, the modeling of flows with surface chemical reactions and other applications related to fluid flows near rough surfaces.

Author Biography

S.I. Martynenko

References

  1. A. M. Arkharov, I. A. Arkharov, V. I. Afanas’ev, et al., Heat Engineering (Bauman Gos. Tekh. Univ., Moscow, 2002) [in Russian].
  2. V. P. Isachenko, V. A. Osipova, and A. S. Sukomel, Heat Transfer (Enerhoizdat, Moscow, 1981) [in Russian].
  3. S. S. Kutateladze, Fundamentals of Heat Transfer (Atomizdat, Moscow, 1979; Academic, New York, 1963).
  4. S. S. Kutateladze and A. I. Leont’ev, Heat and Mass Transfer and Friction in a Turbulent Boundary Layer (Energiya, Moscow, 1972) [in Russian].
  5. A. V. Lykov, Theory of Thermal Conductivity (Vysshaya Shkola, Moscow, 1967) [in Russian].
  6. N. P. Mikhailova, E. U. Repik, and Yu. P. Sosedko, “Permissible Roughness Height in the Turbulent Boundary Layer on a Plate in an Incompressible Fluid,” Uchen. Zap. TsAGI 32 (1-2), 90-101 (2001).
  7. N. P. Mikhailova, E. U. Repik, and Yu. P. Sosedko, “Permissible Height of the Surface Roughness in a Turbulent Boundary Layer with a Streamwise Pressure Gradient,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 37-49 (2003) [Fluid Dyn. 38 (1), 32-42 (2003)].
  8. M. A. Mikheev and I. M. Mikheeva, Fundamentals of Heat Transfer (Energiya, Moscow, 1973) [in Russian].
  9. T. Cebeci and P. Bradshaw, Physical and Computational Aspects of Convective Heat Transfer (Springer, New York, 1984; Mir, Moscow, 1987).
  10. A. A. Sergienko and Ch. Waisin, “Friction and Heat Transfer in Jet Nozzles and Pipeline with Rough Surfaces,” in Problems and Prospect of Propulsion Engineering Development (Korolev Samara Gos. Aerokosm. Univ., Samara, 2003), Part 2, pp. 372-377.
  11. R. R. Chugaev, Hydraulics (Energoizdat, Leningrad, 1982) [in Russian].
  12. H. Schlichting, Boundary Layer Theory (McGraw-Hill, New York, 1968; Nauka, Moscow, 1969).

Published

29-10-2019

How to Cite

Мартыненко С.И. On the Approximation Error in the Problems of Conjugate Convective Heat Transfer // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2019. 20. 438-443. doi 10.26089/NumMet.v20r438

Issue

Section

Section 1. Numerical methods and applications

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