Analytical solution to the problem of convective heat transfer in a porous rectangular channel for thermal boundary conditions of the second genus

Analytical solution to the problem of convective heat transfer in a porous rectangular channel for thermal boundary conditions of the second genus

Автор: Ryazhskikh V.I., Konovalov D.A., Ryazhskikh A.V., Boger A.A., Dakhin S.V.

Журнал: Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование @vestnik-susu-mmp

Рубрика: Математическое моделирование

Статья в выпуске: 3 т.10, 2017 года.

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In the three-dimensional statement, we consider the Brinkman equation together with the equation of heterogeneous heat transfer for an unidirectional flow of the Newtonian fluid under laminar regime through horizontal porous channel having a constant rectangular cross-section with known thermal flows at the boundary and small values of the Darcy numbers. Due to the linearity of the formulated system of model equations, we obtain analytical solution of the system using the Laplace and Fourier integral transformation. The obtained solution allows to estimate the length of the input hydrodynamic section, the coefficient of hydraulic resistance, and the local Nusselt numbers. The results obtained for the hydrodynamic subproblem with a large porosity and thermal subproblem with a stationary temperature field agree with the classical data.

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Porous medium, convective heat transfer, rectangular channel, coefficient of hydraulic resistance, initial hydrodynamic section

Короткий адрес: https://sciup.org/147159441

IDR: 147159441   |   DOI: 10.14529/mmp170304

Список литературы Analytical solution to the problem of convective heat transfer in a porous rectangular channel for thermal boundary conditions of the second genus

  • Delavar M.A., Azimi M.I. Using Porous for Heat Transfer Enhancement in Heat Exchangers: Review. Journal of Engineering Science and Technology Review, 2013, vol. 6, no. 1, pp. 14-16.
  • Bayomy A.M., Saghir M.Z. Heat Transfer Characteristics of Aluminum Metal Foam Subjected to a Pulsating Steady Water Flow: Experimental and Numerical Approach. International Journal of Heat and Mass Transfer, 2016, vol. 97, pp. 318-336. DOI: 10.1016/j.ijheatmasstransfer.2016.02.009
  • Emerging Technologies and Techniques in Porous Media. Eds: D. Ingham, A. Bejan, E. Mamut, I. Pop. Springer Netherlands, 2004. 507 p DOI: 10.1007/978-94-007-0971-3
  • Hung T.C., Hung Y.S., Yan W.M. Design of Porous-Microchannel Heat Sinks with Different Porous Configurations. International Journal of Materials, Mechanics and Manufacturing, 2016, vol. 4, no. 2, pp. 89-94 DOI: 10.7763/IJMMM.2016.V4.231
  • Vafai K. Handbook of Porous Media. N.Y., CRC Press Taylor & Francis Group, 2005. 742 p.
  • Hooman K., Merrikh A.A. Analytical Solution of Forced Convection in a Duct of Rectangular Cross Section Saturated by a Porous Medium. Journal of Heat Transfer, 2006, vol. 128, no 6, pp. 596-600 DOI: 10.1115/1.2188510
  • Hooman K., Gurgenci H., Merrikh A.A. Heat Transfer and Entropy Generation Optimization of Forced Convection in Porous-Saturated Ducts of Rectangular Cross-Section. International Journal of Heat and Mass Transfer, 2007, vol. 50, no. 10, pp. 2051-2059. DOI: 10.1016/j.ijheatmasstransfer.2006.11.015
  • Kurtbas I., Celik N. Experimental Investigation of Forced and Mixed Convection Heat Transfer in a Foam-Filled Horizontal Rectangular Channel. International Journal of Heat and Mass Transfer, 2009, vol. 52, no. 9, pp. 1313-1325. DOI: 10.1016/j.ijheatmasstransfer.2008.07.050
  • Chen G.M., Tso C.P. A Two-Equation Model for Thermally Developing Forced Convection in Porous Medium with Viscous Dissipation. International Journal of Heat and Mass Transfer, 2011, vol. 54, no. 25-26, pp. 5406-5414. DOI: 10.1016/j.ijheatmasstransfer.2011.08.002
  • Teamah M.A., El-Maghlany W.M., Dawood M.M.K. Numerical Simulation of Laminar Forced Convection in Horizontal Pipe Partially or Completely Filled with Porous Material. International Journal of Thermal Science, 2011, vol. 50, no. 8, pp. 1512-1522 DOI: 10.1016/j.ijthermalsci.2011.03.003
  • Nield D.A., Bejan A. Convection in Porous Media. N.Y., Springer, 2006. 654 p.
  • Lu W., Zhao C.Y., Tassen S.A. Thermal Analysis on Metal-Foam Filled Heat Exchangers. International Journal Heat Mass Transfer, 2006, vol. 49, no. 11, pp. 2751-2770. DOI: 10.1016/j.ijheatmasstransfer.2005.12.012
  • Bear J., Bachmat Y. Introduction to Modeling of Transport Phenomena in Porous Media. Netherlands, Kluwer Academic Publishers, 1991. 553 p.
  • Hsu C.T., Cheng P. Thermal Dispersion in a Porous Medium. International Journal of Heat and Mass Transfer, 1990, vol. 33, no. 8, pp. 1587-1597 DOI: 10.1016/0017-9310(90)90015-M
  • Beji H., Gobin D. Influence of Thermal Dispersion on Natural-Convection Heat-Transfer in Porous-Media. Numerical of Heat Tranfer, Part A, 1992, vol. 22, pp. 487-500 DOI: 10.1080/10407789208944779
  • Gamal A.A., Furmanski P. Problems of Modeling Flow and Heat Transfer in Porous Media. Biuletyn Instytutu Techniki Cieplnej Politechniki Warszawskiej, 1997, no. 85, pp. 55-88.
  • Amiri A., Vafai K. Analysis of Dispersion Effects and Non Thermal Equilibrium, Non-Darsian Vairiable Porosity Incompressible Flow Through Porous Media. International Journal of Heat and Mass Transfer, 1994, vol. 37, no. 6, pp. 939-954 DOI: 10.1016/0017-9310(94)90219-4
  • Попов, И.А. Гидродинамика и теплообмен в пористых теплообменных элементах и аппаратах/И.А. Попов. -Казань: Центр информационных технологий, 2007. -240 с.
  • Transport Phenomena in Porous Media. III. Eds. D.B. Ingham, I. Pop. Oxford, Elsevier Ltd., 2005. 476 p.
  • Ezzati R., Rassoulinejad S.M. Application of Homotopy Perturbation Method for Solving Brinkman Momentum Equation for Fully Developed Forced Convection in a Porous Saturated Channel. Mathematical Science, 2011, vol. 5, no. 2, pp. 111-123.
  • Izadpanah M.R., Muller-Steinhagen H., Jamialahmadi M. Experimental and Theoretical Studies of Convective Heat Transfer in a Cylindrical Porous Medium. International Journal of Heat and Fluid Flow, 1998, vol. 19, pp. 629-635 DOI: 10.1016/S0142-727X(98)10035-8
  • Слезкин, Н.А. Динамика вязкой несжимаемой жидкости/Н.А. Слезкин. -М.: Гос. изд-во технико-теоретической лит-ры, 1955. -579 с.
  • Dotsch G. Anleitung zum praktischen gebrauch der Laplace-transformation und der z-transformation. Wien, 1967. (in Deutch)
  • Sneddon I.N. Fourier Transforms. N.Y., McGraw-Hill, 1951. 542 p.
  • Bird R.B., Stewart W.E., Lightfoot E.N. Transport Phenomena. N.Y., London, Journal Wiley & Sons, 2002. 914 p.
  • Ozlsik M.N. Heat Transfer: A Basic Approach. Singapore, McGraw -Hill Book Company, 1985. 576 p.
  • Lin J.N., Chron F.C., Tzeng P.Y. Theoretical Prediction of the Outset of Thermal Instability in the Thermal Entrance Region of Horizontal Rectangular Channels. International Journal of Heat and Fluid Flow, 1991, vol. 12, no. 3, pp. 218-224 DOI: 10.1016/0142-727X(91)90055-Z
  • Ряжских, В.И. Анализ математической модели теплосъема с плоской поверхности ламинарно движущимся хладагентом через сопряженную пористую среду/В.И. Ряжских, Д.А. Коновалов, М.И. Слюсарев, И.Г. Дроздов//Вестник ЮУрГУ. Серия: Математическое моделирование и программирование. -2016. -Т. 9, № 3. -С. 68-81.
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