有内热源多孔介质通道中对流换热的研究—精确解
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摘要
采用Darcy-Brinkman方程描述完全填充多孔介质平行平板通道内流动,分别利用局部非热平衡和局部热平衡模型,得出了温度分布和努塞尔数Nu的表达式。分别讨论了内热源、达西数Da、固相有效导热系数与流体有效导热系数之比κ和毕渥数Bi对无因次温度分布的影响,将两种模型计算得到的努塞尔数进行对比。结果表明,对于特定的参数,壁面处会出现热流分歧现象。达西数很小时,流体内部热源对无因次温度分布几乎无影响。存在内热源时,局部热平衡模型不再适用。
In this study,the Darcy-Brinkman equation is utilized as the momentum equation for the flow in a parallel channel fully filled with porous media.By using local thermal equilibrium and local thermal non-equilibrium model respectively,exact expressions of temperature distribution and Nusselt number are derived.Effects of internal heat generation,Darcy number,the ratio of effective thermal conductivity of solid phase and effective thermal conductivity of fluid phase k,Biot number Bi on temperature distribution are discussed respectively.Finally,the Nusselt number results calculated by the two models are compared.The results show that depending on the specific parameter,the phenomenon of heat flux bifurcation will occur on the wall.When the Darcy number is quite small,the influence of internal heat generation in fluid phase can be neglected.With the presence of internal heat generation,the local thermal equilibrium model is invalid.
In this study,the Darcy-Brinkman equation is utilized as the momentum equation for the flow in a parallel channel fully filled with porous media.By using local thermal equilibrium and local thermal non-equilibrium model respectively,exact expressions of temperature distribution and Nusselt number are derived.Effects of internal heat generation,Darcy number,the ratio of effective thermal conductivity of solid phase and effective thermal conductivity of fluid phase k,Biot number Bi on temperature distribution are discussed respectively.Finally,the Nusselt number results calculated by the two models are compared.The results show that depending on the specific parameter,the phenomenon of heat flux bifurcation will occur on the wall.When the Darcy number is quite small,the influence of internal heat generation in fluid phase can be neglected.With the presence of internal heat generation,the local thermal equilibrium model is invalid.
引文
[1]Yang K,Vafai K.Transient Aspects of Heat Flux Bifurcation in Porous Media:an Exact Solution[J].Journal of Heat Transfer,2011,133(5):052602-1-052602-12
[2]Yang K,Vafai K.Restrictions on the Validity of the Thermal Conditions at the Porous-Fluid Interface-an Exact Solution[J].Journal of Heat Transfer,2011,133(11):112601-1-112601-12
[3]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(25/26):5286-5297
[4]Xu H J,Qu Z G,Lu T J,et al.Thermal Modeling of Forced Convection in a Parallel-Plate Channel Partially Filled With Metallic Foams[J].Journal of Heat Transfer,2011,133(9):092603-1-092603-9
[5]Ouyang X L,Vafai K,Jiang P X.Analysis of Thermally Developing Flow in Porous Media Under Local Thermal Non-Equilibrium Conditions[J].International Journal of Heat and Mass Transfer,2013,67:768-775
[6]Lee D,Vafai K.Analytical Characterization and Conceptual Assessment of Solid and Fluid Temperature Differentials in Porous Media[J].International Journal of Heat and Mass Transfer,1999.42(3):423-435
[7]Mahjoob S.Vafai K.Analytical Characterization of Heat Transport Through Biological Media Incorporating Hyperthermia Treatment[J].International Journal of Heat and Mass Transfer,2009,52(5):1608-1618
[8]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):4316-4325
[2]Yang K,Vafai K.Restrictions on the Validity of the Thermal Conditions at the Porous-Fluid Interface-an Exact Solution[J].Journal of Heat Transfer,2011,133(11):112601-1-112601-12
[3]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(25/26):5286-5297
[4]Xu H J,Qu Z G,Lu T J,et al.Thermal Modeling of Forced Convection in a Parallel-Plate Channel Partially Filled With Metallic Foams[J].Journal of Heat Transfer,2011,133(9):092603-1-092603-9
[5]Ouyang X L,Vafai K,Jiang P X.Analysis of Thermally Developing Flow in Porous Media Under Local Thermal Non-Equilibrium Conditions[J].International Journal of Heat and Mass Transfer,2013,67:768-775
[6]Lee D,Vafai K.Analytical Characterization and Conceptual Assessment of Solid and Fluid Temperature Differentials in Porous Media[J].International Journal of Heat and Mass Transfer,1999.42(3):423-435
[7]Mahjoob S.Vafai K.Analytical Characterization of Heat Transport Through Biological Media Incorporating Hyperthermia Treatment[J].International Journal of Heat and Mass Transfer,2009,52(5):1608-1618
[8]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):4316-4325