多孔介质平板通道与空通道的速度分布和温度分布的解析解
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摘要
建立了平板通道内填充多孔介质和空通道两种情况传热模型,求解动量方程和能量方程的解析解,获得速度分布和温度分布,分析Da数、Bi数、有效导热系数比和孔隙率等参数对温度分布、局部非热平衡程度以及Nu数的影响。计算求解表明,通道内填充多孔介质后流体的速度分布和温度分布更均匀,速度边界层更薄;随着Bi数和有效导热系数比k的增大,θ_s-θ_f的值减小,局部非热平衡程度减弱,Bi越大,θ_s与θ_f越接近,即越接近局部热平衡状态。孔隙率对局部非热平衡程度和Nu数的影响不明显;Nu数随着有效导热系数比k和Da数的减小而增大,随着Bi数和孔隙率的增大而增大,当k<1时,变化明显,k>1时,变化不明显.
Heat transfer model of plate channels filled with porous medium and empty is set up respectively, and the momentum equation and energy equation is solved, then velocity distribution and temperature distribution is got. The influence of Darcy, Bi, ratio of effective thermal conductivity and porosity on temperature distribution, degree of local thermal equilibrium and Nu is analyzed.The conclusion indicated that velocity distribution and temperature distribution is more even and velocity boundary layer is thinner for the channel filled with porous medium; θ_s-θ_f is reduced and the local thermal equilibrium is less as Bi and k increases. When Bi is bigger, θ_f is get close to θ_s, which meet the local thermal equilibrium. The effect of degree local thermal equilibrium and Nu is not obvious for the porosity. Nu increases with reduction of k and Darcy and increase of Bi and porosity.When k < 1, Nu change obviously, but when k > 1, the change is not obvious.
Heat transfer model of plate channels filled with porous medium and empty is set up respectively, and the momentum equation and energy equation is solved, then velocity distribution and temperature distribution is got. The influence of Darcy, Bi, ratio of effective thermal conductivity and porosity on temperature distribution, degree of local thermal equilibrium and Nu is analyzed.The conclusion indicated that velocity distribution and temperature distribution is more even and velocity boundary layer is thinner for the channel filled with porous medium; θ_s-θ_f is reduced and the local thermal equilibrium is less as Bi and k increases. When Bi is bigger, θ_f is get close to θ_s, which meet the local thermal equilibrium. The effect of degree local thermal equilibrium and Nu is not obvious for the porosity. Nu increases with reduction of k and Darcy and increase of Bi and porosity.When k < 1, Nu change obviously, but when k > 1, the change is not obvious.
引文
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[2]张丹,李菊香.多孔泡沫金属内层流强制对流传热的相界面温差分析[J].材料导报,2010,24(16):256-264ZHANG Dan,LI Juxiang.Phase Interface Temperature Difference of Laminar Forced Convection in Porous Metal Foam[J].Materials Review,2010,24(16):256-264
[3]欧阳小龙.多孔介质传热局部非热平衡效应的基础问题研究[D].北京:清华大学,2014OUYANG Xiaolong.Research on the Local Thermal NonEquilibrium Effect for Heat Transfer in Porous Media[D].Beijing:Tsinghua University,2014
[4]Dehghan M,Valipour M S,Keshmiri A,et al.On the Thermally Developing Forced Convection Through a Porous Material Under the Local Thermal NonEquilibrium Condition:An Analytical Study[J].International Journal of Heat and Mass Transfer,2016,92:815-823
[5]Yasser Mahmoudi.Constant Wall Heat Flux Boundary Condition in Micro-Channels Filled With a Porous Medium With Internal Heat Generation Under Local Thermal Non-Equilibrium Condition[J].International Journal of Heat and Mass Transfer,2015,85:524-542
[6]Dehghan M,Valipour M S,Saedodin S.Temperature Dependent Conductivity in Forced Convection of Heat Exchangers Filled with Porous Media:A Perturbation Solution[J].Energy Conversion and Management,2015,91:259-266
[7]Dehghan M,Valipour M S,Saedodin S.Conjugate Heat Tansfer Inside Microchannels Filled With Porous Media:A Exact Solution[J].Journal of Thermophysics&Heat Transfer.2015,30(4):1-11
[8]Donald A.Nield,Adrian Bejan.Convection in Porous Media[M].4th Edition.New York:Springer,2013:69-87
[9]李勇铜,徐会金,巩亮,等.金属泡沫微流道热沉内流体流动与传热特性的数值研究[J].应用数学和力学,2014,35(3):287-294LI Yongtong,XU Huijin,GONG Liang,et al.Numerical Study of Fluid Flow and Heat Transfer Characteristics in Metal-Foam Filled Microchannel Heat Sink[J].Applied Mathematics and Mechanics,2014,35(3):287-294
[10]王克用,王大中,李培超.多孔介质平板通道传热模型的两种求解方法[J].应用数学和力学,2015,36(5):494-504WANG Keyong,WANG Dazhong,LI Peicha.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
[11]Maziar Dehghan,Mohammad Sadegh Valipour,Seyfolah Saedodin.Microchannels Enhanced by Porous Materials:Heat Transfer Enhancement or Pressure Drop Increment[J].Energy Conversion and Management,2016,110:22-32
[12]Nield DA,Kuznetsov AV.Forced Convection With SlipFlow in a Channel or Duct Occupied by a Hyper-Porous Medium Saturated by a Rarefied Gas[J].Trans Porous Media 2006,64:161-70