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Computer Research and Modeling, 2020, Volume 12, Issue 1, Pages 59–72
DOI: https://doi.org/10.20537/2076-7633-2020-12-1-59-72
(Mi crm772)
 

This article is cited in 3 scientific papers (total in 3 papers)

MODELS IN PHYSICS AND TECHNOLOGY

Numerical modeling of the natural convection of a non-newtonian fluid in a closed cavity

D. S. Loenko, M. A. Sheremet

National Research Tomsk State University, 36 Lenin av., Tomsk, 634050, Russia
References:
Abstract: In this paper, a time-dependent natural convective heat transfer in a closed square cavity filled with non-Newtonian fluid was considered in the presence of an isothermal energy source located on the lower wall of the region under consideration. The vertical boundaries were kept at constant low temperature, while the horizontal walls were completely insulated. The behavior of a non-Newtonian fluid was described by the Ostwald de Ville power law. The process under study was described by transient partial differential equations using dimensionless non-primitive variables “stream function – vorticity – temperature”. This method allows excluding the pressure field from the number of unknown parameters, while the non-dimensionalization allows generalizing the obtained results to a variety of physical formulations. The considered mathematical model with the corresponding boundary conditions was solved on the basis of the finite difference method. The algebraic equation for the stream function was solved by the method of successive lower relaxation. Discrete analogs of the vorticity equation and energy equation were solved by the Thomas algorithm. The developed numerical algorithm was tested in detail on a class of model problems and good agreement with other authors was achieved. Also during the study, the mesh sensitivity analysis was performed that allows choosing the optimal mesh.
As a result of numerical simulation of unsteady natural convection of a non-Newtonian power-law fluid in a closed square cavity with a local isothermal energy source, the influence of governing parameters was analyzed including the impact of the Rayleigh number in the range $10^{4}-10^{6}$, power-law index $n=0.6-1.4$, and also the position of the heating element on the flow structure and heat transfer performance inside the cavity. The analysis was carried out on the basis of the obtained distributions of streamlines and isotherms in the cavity, as well as on the basis of the dependences of the average Nusselt number. As a result, it was established that pseudoplastic fluids ($n<1$) intensify heat removal from the heater surface. The increase in the Rayleigh number and the central location of the heating element also correspond to the effective cooling of the heat source.
Keywords: natural convection, non-Newtonian fluid, local heat source.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation МД-821.2019.8
This work was supported by the Grants Council (under the President of the Russian Federation), Grant No. MD-821.2019.8.
Received: 02.08.2019
Revised: 19.10.2019
Accepted: 19.11.2019
Document Type: Article
UDC: 519.6:536.24
Language: Russian
Citation: D. S. Loenko, M. A. Sheremet, “Numerical modeling of the natural convection of a non-newtonian fluid in a closed cavity”, Computer Research and Modeling, 12:1 (2020), 59–72
Citation in format AMSBIB
\Bibitem{LoeShe20}
\by D.~S.~Loenko, M.~A.~Sheremet
\paper Numerical modeling of the natural convection of a non-newtonian fluid in a closed cavity
\jour Computer Research and Modeling
\yr 2020
\vol 12
\issue 1
\pages 59--72
\mathnet{http://mi.mathnet.ru/crm772}
\crossref{https://doi.org/10.20537/2076-7633-2020-12-1-59-72}
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  • This publication is cited in the following 3 articles:
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