WANG Ke-yong, WANG Da-zhong, LI Pei-chao. Two Decoupling Methods for the Heat Transfer Model of a Plate Channel Filled With a Porous Medium[J]. Applied Mathematics and Mechanics, 2015, 36(5): 494-504. doi: 10.3879/j.issn.1000-0887.2015.05.005
Citation: WANG Ke-yong, WANG Da-zhong, LI Pei-chao. Two Decoupling Methods for the Heat Transfer Model of a Plate Channel Filled With a Porous Medium[J]. Applied Mathematics and Mechanics, 2015, 36(5): 494-504. doi: 10.3879/j.issn.1000-0887.2015.05.005

Two Decoupling Methods for the Heat Transfer Model of a Plate Channel Filled With a Porous Medium

doi: 10.3879/j.issn.1000-0887.2015.05.005
  • Received Date: 2014-09-16
  • Rev Recd Date: 2015-03-11
  • Publish Date: 2015-05-15
  • A general heat transfer model of a parallel plate channel filled with a porous medium was constructed based on the Brinkman-Darcy extended model and the local thermal non-equilibrium model in view of the internal heat sources in fluid and solid phases. The temperature field of the porous medium under the fully developed heat transfer condition was respectively formulated with the direct and indirect decoupling methods of solving the fluid-phase and solid-phase energy equations. Compared to the direct decoupling method, the indirect one is more convenient to be employed to solve the 2nd-order differential equations under the original boundary conditions. The equivalence of the 2 decoupling methods was verified through comparison of the coefficients in the dimensionless temperature expressions and the temperature distributions between them. A good agreement was found between the temperature distributions obtained with the indirect decoupling method and those reported in the previous literatures in 2 limit cases, meanwhile the better generality of the proposed model was also proved to some extent. The parametric study shows that the temperature difference between the fluid and solid phases decreases with the Biot number or the effective thermal conductivity ratio, and the Nusselt number decreases with the internal heat source ratio.
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  • [1]
    Whitaker S. Transient diffusion, adsorption and reaction in porous catalysis: the reaction controlled, quasi-steady catalytic surface[J].Chemical Engineering Science,1986,41(12): 3015-3022.
    [2]
    Cheng P. Heat transfer in geothermal systems[J].Advances in Heat Transfer,1979,14: 1-105.
    [3]
    Kim S J, Jang S P. Effects of the Darcy number, the Prandtl number, and the Reynolds number on local thermal non-equilibrium[J].International Journal of Heat and Mass Transfer,2002,45(19): 3885-3896.
    [4]
    Kim S J, Vafai K. Analysis of natural convection about avertical plate embedded in a porous medium[J].International Journal of Heat and Mass Transfer,1989,32(4): 665-677.
    [5]
    Celli M, Barletta A, Storesletten L. Local thermal non-equilibrium effects in the Darcy-Bénard instability of a porous layer heated from below by a uniform flux[J].International Journal of Heat and Mass Transfer,2013,67: 902-912.
    [6]
    Vafai K, Sozen M. Analysis of energy and momentum transport for fluid flow through a porous bed[J].Journal of Heat Transfer,1990,112(3): 690-699.
    [7]
    Quintard M, Whitaker S. Two-phase flow in heterogeneous porous media (I): the influence of large spatial and temporal gradients[J].Transport in Porous Media,1990,5(4): 341-379.
    [8]
    Marafie A, Vafai K. Analysis of non-Darcian effects on temperature differentials in porous media[J].International Journal of Heat and Mass Transfer,2001,44(23): 4401-4411.
    [9]
    李明春, 田彦文, 翟玉春. 非热平衡多孔介质内反应与传热传质耦合过程[J]. 化工学报, 2006,57(5): 1079-1083.(LI Ming-chun, TIAN Yan-wen, ZHAI Yu-chun. Coupled processes of chemical reaction, heat and mass transfer in non-thermal equilibrium porous medium[J].Journal of Chemical Industry and Engineering,2006,57(5): 1079-1083.(in Chinese))
    [10]
    杨骁, 刘雪梅. 多孔介质平板通道发展传热中非局部热平衡时的温度分布特征[J]. 应用数学和力学, 2006,27(8): 978-986.(YANG Xiao, LIU Xue-mei. Temperature profiles of local thermal nonequilibrium for thermal developing forced convection in a porous medium parallel platechannel[J].Applied Mathematics and Mechanics,2006,27(8): 978-986.(in Chinese))
    [11]
    Yang K, Vafai K. Analysis of temperature gradient bifurcation in porous media—an exact solution[J].International Journal of Heat and Mass Transfer,2010,53(19/20): 4316-4325.
    [12]
    Yang K, Vafai K. Analysis of heat flux bifurcation inside porous media incorporating inertial and dispersion effects—an exact solution[J].International Journal of Heat and Mass Transfer,2011,54(25): 5286-5297.
    [13]
    何颖, 邵宝东, 程赫明. 等边三角形微通道内层流的流动特性和换热特性的研究[J]. 应用数学和力学, 2014,〖STHZ〗 35(3): 313-321.(HE Ying, SHAO Bao-dong, CHENG He-ming. Laminar flow and heat transfer in equilateral triangle micro-channels[J].Applied Mathematics and Mechanics,2014,35(3): 313-321.(in Chinese))
    [14]
    Buonomo B, Manca O, Lauriat G. Forced convection in micro-channels filled with porous media in local thermal non-equilibrium conditions[J].International Journal of Thermal Sciences,2014,77: 206-222.
    [15]
    Dukhan N,Al-Rammahi M A, Suleiman A S. Fluid temperature measurements inside metal foam and comparison to Brinkman-Darcy flow convection analysis[J].International Journal of Heat and Mass Transfer,2013,67: 877-884.
    [16]
    刘伟, 明廷臻. 管内核心流分层填充多孔介质的传热强化分析[J]. 中国电机工程学报, 2008,28(32): 66-71.(LIU Wei, MING Ting-zhen. Analysis for heat transfer enhancement in the core flow of a tube filled with porous media at different layers[J].Proceedings of the CSEE,2008,28(32): 66-71.(in Chinese))
    [17]
    Qu Z G, Xu H J, Tao W Q. Fully developed forced convective heat transfer in an annulus partially filled with metallic foams: an analytical solution[J].International Journal of Heat and Mass Transfer,2012,55(25): 7508-7519.
    [18]
    公维平, 曹玉荣. 多孔介质强化传热的理论与实验研究[J]. 水动力学研究与进展, 2003,18(3): 276-282.(GONG Wei-ping, CAO Yu-rong. Thoretical and experimental investigation on heat transfer augmentation in porous medium[J].Journal of Hydrodynamics,2003,18(3): 276-282.(in Chinese))
    [19]
    Nouri-Borujerdi A, Noghrehabadi A R, Rees D A S. Onset of convection in a horizontal porous channel with uniform heat generation using a thermal nonequilibrium model[J].Transport in Porous Media,2007,69(3): 343-357.
    [20]
    Nield D A, Kuznetsov A V, Xiong M. Effect of local thermal non-equilibrium on thermally developing forced convection in a porous medium[J].International Journal of Heat and Mass Transfer,2002,45(25): 4949-4955.
    [21]
    许飞, 郭钢, 胡康, 韩松燕, 马晓楠, 李再顺. 稠油油藏中含内热源多孔介质的传热研究[J]. 石油化工应用, 2012,31(2): 28-32.(XU Fei, GUO Gang, HU Kang, HAN Song-yan, MA Xiao-nan, LI Zai-shun. The research on heat transfer of combustible porous meida with inner heat source[J].Petrochemical Industry Application,2012,31(2): 28-32.(in Chinese))
    [22]
    Keangin P, Vafai K, Rattanadecho P. Electromagnetic field effects on biological materials[J].International Journal of Heat and Mass Transfer,2013,65: 389-399.
    [23]
    Mahjoob S, Vafai K. Analytical characterization of heat transfer through biological media incorporating hyperthermia treatment[J].International Journal of Heat and Mass Transfer,2009,52: 1608-1618.
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