HEAT TRANSFER IN GRADIENT LAMINAR FLOWS
Abstract
The development of new areas of research in the field of theoretical thermophysics requires reliable analytical solutions that could take into account the main aspects of physical parameters in the studied objects. One such analytical technique is symmetry groups.
On the basis of symmetry groups the problem of heat transfer in gradient laminar flows is solved in the paper. For the first time, the symmetries of the energy equation for the boundary layer at an arbitrary changing velocity at marching direction are obtained. Examples of the use of group analysis methods for the study of heat transfer in the boundary layer of an incompressible fluid are demonstrated. The problems of heat transfer in the boundary layer on a heat-conducting wall with a constant temperature and on a heat-insulated wall are considered. Analytical relations for temperature and heat transfer coefficients distribution are obtained.
References
2.Ovsyannikov L.V. [Group analysis of differential equations], Moskva, Nauka, 1978. (Rus)
3.Oberlack M. Asymptotic expansion, symmetry groups, and invariant solutions of laminar and turbulent wall-bounded flows. ZAMM. 2000. 80, №11-12. P.791-800.
4. Avramenko A.A., Kobzar' S.G. [Application of Lie groups to the study of unsteady heat transfer processes around a sphere in the region of small Reynolds numbers], [Industrial heating technology], 1998. V.20, №2. P.47-50. (Rus.)
5. Avramenko A.A., Tyrinov A.I., Shevchuk I.V., Dmitrenko N.P., Kravchuk A.V. Mixed convection in a vertical flat microchannel. International Journal of Heat and Mass Transfer. 2017. 25, 106. P.1164-1173
6. Avramenko A.A., Tyrinov A.I., Shevchuk I.V. An analytical and numerical study on the start-up flow of slightly rarefied gases in a parallel-plate channel and a pipe. Physics of Fluids. 2015. 27 (4), 042001 21
7. Avramenko A.A., Tyrinov A.I., Shevchuk I.V. Start-up slip flow in a microchannel with a rectangular cross section. Theoretical and Computational Fluid Dynamics. 2015. 20, 29 (5), P.351-371
8. Avramenko A.A., Tyrinov A.I., Shevchuk I.V., Dmitrenko N.P. Dean instability of nanofluids with radial temperature and concentration non-uniformity. Physics of Fluids. 2016. 23. 28 (3), 034104
9. Avramenko A.A., Shevchuk I.V., Abdallah S., Blinov D.G., Harmand S. Symmetry analysis for film boiling of nanofluids on a vertical plate using a nonlinear approach. Journal of Molecular Liquids. 2016. 20, 223. P.156-164
10.Avramenko A.A., Kuznetsov A.V. The onset of convection in a suspension of gyrotactic microorganisms in superimposed fluid and porous layers: effect of vertical throughflow. Transport in porous media. 2006. 25, 65 (2). P.159-176
11. Shlihting G.[ Boundary layer theory]], Moskva, Nauka, 1974. (Rus)
12. Escuder M. P. Heat transfer to near-separating laminar boundary layer. Int. J. Heat and Mass Transf. 1974. V.17, № 1, P. 109 - 112.
13. Avramenko A.A. [Heat transfer in the separation zone of the boundary layer], [Industrial Heat Engineering], 1998. V.20, №4. P.20-22. (Rus.)
14. Evans H. L. Mass transfer through laminar boundary layers. 7. Future similar solutions to the b-equation when B = 0. Int. J. Heat and Mass Transf. 1962. №5, P. 35 - 37.
15. Imai I. On the heat transfer to constant property laminar boundary layer with power function free stream velocity and wall temperature distributions .Quart. Appl. Math. 1958. №16, P. 33 - 45.
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