Geodesic
Analytical solution to the problem of convective heat transfer in a porous rectangular channel for thermal boundary conditions of the second genus
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 3, pp. 40-53 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Keywords: porous medium; convective heat transfer; rectangular channel; coefficient of hydraulic resistance; initial hydrodynamic section. 
@article{VYURU_2017_10_3_a3,
     author = {V. I. Ryazhskikh and D. A. Konovalov and A. V. Ryazhskikh and A. A. Boger and S. V. Dakhin},
     title = {Analytical solution to the problem of convective heat transfer in a porous rectangular channel for thermal boundary conditions of the second genus},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {40--53},
     year = {2017},
     volume = {10},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2017_10_3_a3/}
}
TY  - JOUR
AU  - V. I. Ryazhskikh
AU  - D. A. Konovalov
AU  - A. V. Ryazhskikh
AU  - A. A. Boger
AU  - S. V. Dakhin
TI  - Analytical solution to the problem of convective heat transfer in a porous rectangular channel for thermal boundary conditions of the second genus
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2017
SP  - 40
EP  - 53
VL  - 10
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VYURU_2017_10_3_a3/
LA  - en
ID  - VYURU_2017_10_3_a3
ER  - 
%0 Journal Article
%A V. I. Ryazhskikh
%A D. A. Konovalov
%A A. V. Ryazhskikh
%A A. A. Boger
%A S. V. Dakhin
%T Analytical solution to the problem of convective heat transfer in a porous rectangular channel for thermal boundary conditions of the second genus
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2017
%P 40-53
%V 10
%N 3
%U http://geodesic.mathdoc.fr/item/VYURU_2017_10_3_a3/
%G en
%F VYURU_2017_10_3_a3
V. I. Ryazhskikh; D. A. Konovalov; A. V. Ryazhskikh; A. A. Boger; S. V. Dakhin. Analytical solution to the problem of convective heat transfer in a porous rectangular channel for thermal boundary conditions of the second genus. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 3, pp. 40-53. http://geodesic.mathdoc.fr/item/VYURU_2017_10_3_a3/

[1] Delavar M. A., Azimi M. I., “Using Porous for Heat Transfer Enhancement in Heat Exchangers: Review”, Journal of Engineering Science and Technology Review, 6:1 (2013), 14–16

[2] 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, 97 (2016), 318–336 | DOI

[3] D. Ingham, A. Bejan, E. Mamut, I. Pop (eds.), Emerging Technologies and Techniques in Porous Media, Springer Netherlands, 2004, 507 pp. | DOI | MR

[4] 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, 4:2 (2016), 89–94 | DOI

[5] Vafai K., Handbook of Porous Media, CRC Press Taylor Francis Group, N.Y., 2005, 742 pp.

[6] 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, 128:6 (2006), 596–600 | DOI

[7] 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, 50:10 (2007), 2051–2059 | DOI | Zbl

[8] 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, 52:9 (2009), 1313–1325 | DOI

[9] 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, 54:25–26 (2011), 5406–5414 | DOI | Zbl

[10] 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, 50:8 (2011), 1512–1522 | DOI

[11] Nield D. A., Bejan A., Convection in Porous Media, Springer, N.Y., 2006, 654 pp. | MR | Zbl

[12] Lu W., Zhao C. Y., Tassen S. A., “Thermal Analysis on Metal-Foam Filled Heat Exchangers”, International Journal Heat Mass Transfer, 49:11 (2006), 2751–2770 | DOI

[13] Bear J., Bachmat Y., Introduction to Modeling of Transport Phenomena in Porous Media, Kluwer Academic Publishers, Netherlands, 1991, 553 pp. | Zbl

[14] Hsu C. T., Cheng P., “Thermal Dispersion in a Porous Medium”, International Journal of Heat and Mass Transfer, 33:8 (1990), 1587–1597 | DOI | Zbl

[15] Beji H., Gobin D., “Influence of Thermal Dispersion on Natural-Convection Heat-Transfer in Porous-Media”, Numerical of Heat Tranfer, Part A, 22 (1992), 487–500 | DOI

[16] Gamal A. A., Furmanski P., “Problems of Modeling Flow and Heat Transfer in Porous Media”, Biuletyn Instytutu Techniki Cieplnej Politechniki Warszawskiej, 1997, no. 85, 55–88

[17] 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, 37:6 (1994), 939–954 | DOI

[18] И. А. Попов, Гидродинамика и теплообмен в пористых теплообменных элементах и аппаратах, Центр информационных технологий, Казань, 2007, 240 pp.

[19] D. B. Ingham, I. Pop (eds.), Transport Phenomena in Porous Media. III, Elsevier Ltd., Oxford, 2005, 476 pp. | MR

[20] 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, 5:2 (2011), 111–123 | MR | Zbl

[21] 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, 19 (1998), 629–635 | DOI

[22] Slyezkin N. A., The Viscous Incompressible Fluid Dynamics, Gosudarstvennoe izdatel'stvo tekhniko-teoreticheskoy literatury, M., 1955, 579 pp. | MR

[23] Dotsch G., Anleitung zum praktischen gebrauch der Laplace-transformation und der z-transformation, Wien, 1967 (in Deutch) | MR

[24] Sneddon I. N., Fourier Transforms, McGraw-Hill, N.Y., 1951, 542 pp. | MR

[25] Bird R. B., Stewart W. E., Lightfoot E. N., Transport Phenomena, John Wiley Sons, N.Y.–London, 2002, 914 pp.

[26] Ozlsik M. N., Heat Transfer: A Basic Approach, McGraw–Hill Book Company, Singapore, 1985, 576 pp.

[27] 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, 12:3 (1991), 218–224 | DOI

[28] В. И. Ряжских, Д. А. Коновалов, М. И. Слюсарев, И. Г. Дроздов, “Анализ математической модели теплосъема с плоской поверхности ламинарно движущимся хладагентом через сопряженную пористую среду”, Вестник ЮУрГУ. Серия: Математическое моделирование и программирование, 9:3 (2016), 68–81 | DOI | Zbl