LTNE条件下界面对流传热系数对部分填充多孔介质通道传热特性的影响

doi:10.11949/0438-1157.20201662

摘要/Abstract

摘要：

在多孔介质区考虑局部非热平衡，采用Brinkman-extended Darcy模型结合应力跳跃条件对部分填充多孔介质通道内流体传热特性进行分析。获得了各区域温度分布及Nusselt数解析解，并分析了各参数对温度及Nusselt数的影响。结果表明：界面对流传热系数H_s较小时，界面应力跳跃系数β和Darcy数Da的增加会减小流固两相间温差。而在高H_s下，Da减小也会减小两相温差。在Da、H_s和固流两相热导率之比K较大且空心率S（自由流体区高度与通道高度之比）和Biot数Bi较小时，流固两相间会在接近多孔介质区中部出现最大温差，而该最大温差会随着S增加和Da及H_s的减小向界面区移动。对于不同K与Bi，Nusselt数Nu与S的关系曲线存在不同的类型，与模型A（界面处多孔介质固相和流相根据各自温度梯度和热导率划分总热流）不同的是，采用模型C（界面处固相热流分配与自由流体区流相的热交换相关）所获得的Nu曲线类型与H_s有关。在K较小时，β对Nu的影响大于H_s对Nu的影响；而在K较大时，H_s对Nu的影响要远大于β对Nu的影响，且H_s增加会明显提高通道内的Nu。

关键词: 多孔介质, 局部热非平衡模型, Brinkman-extended Darcy 模型, 传热, 流体力学

Abstract:

Considering local non-thermal equilibrium in porous region and using the Brinkman-extended Darcy model with stress jump conditions, the heat transfer characteristics in a partially filled porous media channel are analyzed. The analytical solutions of temperature fields and Nusselt number in fluid and solid regions are obtained, and the influences of different parameters on temperature fields and Nusselt number are analyzed. The results show that when interfacial convection heat transfer coefficient, H_s, is small, the increasing of the interfacial stress jump coefficient, β, and Darcy number, Da, will reduce the two phases temperature difference between fluid and solid phases. While at a high H_s, decreasing of Da will also decrease two phases temperature difference. When Da, H_s and thermal conductivity ratio, K, are large, hollow ratio, S (ratio of the free region height to the channel height), and Biot number, Bi, are small, there is a maximum temperature difference between fluid and solid phases occurs near the core of porous region, and this maximum temperature difference will move to the interface region with the increase of S, and the decrease of Da and H_s. For different K and Bi, the curves of the relationship between Nusselt number Nu and S have different types for model C (the heat flux distribution of solid phase at the interface is related to the heat exchange of the fluid phase in the free fluid region) in this study and the curves' type is related with H_s, which is different from model A (the total heat flux division between the solid and fluid phases is based on their effective conductivities and the corresponding temperature gradients). When K is small, the influence of β on Nu is greater than that of H_s on Nu. When K is large, the influence of H_s on Nu is much greater than that of β on Nu, and the increase of H_s will significantly increase Nu in the channel.

Key words: porous media, local thermal non-equilibrium model, Brinkman-extended Darcy model, heat transfer, fluid mechanics

中图分类号:

TK 124

李琪, 张容铭, 胡鹏飞. LTNE条件下界面对流传热系数对部分填充多孔介质通道传热特性的影响[J]. 化工学报, 2021, 72(8): 4121-4133.

Qi LI, Rongming ZHANG, Pengfei HU. Influence of interfacial convective heat transfer coefficient on heat transfer in partially filled porous channel under LTNE condition[J]. CIESC Journal, 2021, 72(8): 4121-4133.

图/表 9

图1 多孔介质-自由流体通道物理模型

Fig.1 Physical model of the porous-fluid channel

图2 在β=0，S=0.5，K=2，Bi=10，Da=10-3，ε=0.5时，本文温度场计算结果与文献[22]的比较

Fig.2 The comparison between the calculated results of temperature field in this paper and Ref. [22] at β=0，S=0.5，K=2，Bi=10，Da=10-3，ε=0.5

表1 在Bi=10，Da=10-5，ε=0.9，Hs=1，S→0时，本文与文献［12］Nu计算结果的对比

Table 1 Comparison between the calculated results of Nu in this paper and those in Ref. ［12］ at Bi=10，Da=10-5，ε=0.9，Hs=1，S→0

K	Nu^[12]	本文Nu	Error
0.1	12.9530	12.8899	0.49%
1	21.4964	21.5458	0.23%
10	105.8775	106.3187	0.42%
100	941.2251	940.3360	0.09%

图3 在Da=10-3，K=10，Bi=0.1，β=0时，Hs对不同S下温度场的影响

Fig.3 Effect of Hs on the temperature field in different S at Da=10-3, K=10, Bi=0.1 and β=0

图4 在S=0.1，ε=0.9，β=0时，Hs对不同K，Bi和Da下温度场的影响

Fig.4 Effect of Hs on the temperature field in different K, Bi and Da at S=0.1, ε=0.9 and β=0

图5 在S=0.1，ε=0.9，Hs=0.1，Da=10-3时，不同K和Bi下β对温度场的影响

Fig.5 Effect of β on the temperature field in different K and Bi at S=0.1, ε=0.9, Hs=0.1 and Da=10-3

图6 Da=10-3，ε=0.9，β=0时，不同Bi，Hs及S下，Nusselt数与热导率比之间的关系

Fig.6 Nusselt number versus effctive thermal conductivity ratio in different Bi, Hs and S at Da=10-3, ε=0.9, β=0

图7 在ε=0.9，β =0时，不同Hs，K，Da和Bi下Nusselt数与空心率（S>0）的关系

Fig.7 Nusselt number versus hollow ratio （S>0）at ε=0.9, β =0 with different values of Hs, K, Da and Bi

图8 在ε=0.9，Hs=0.1时，不同β，K，Da和Bi下Nusselt数与空心率（S>0）的关系

Fig.8 Nusselt number versus hollow ratio （S>0）at ε=0.9, Hs=0.1 with different values of β, K, Da and Bi

参考文献 30

1	Vafai K, Hadim H. Handbook of Porous Media [M]. 2nd ed. CRC Press, 2000.
2	Amiri A, Vafai K, Kuzay T M. Effects of boundary conditions on non-darcian heat transfer through porous media and experimental comparisons[J]. Numerical Heat Transfer, Part A: Applications, 1995, 27(6): 651-664.
3	Lee D Y, 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.
4	Mhimid A, Ben Nasrallah S, Fohr J P. Heat and mass transfer during drying of granular products—simulation with convective and conductive boundary conditions[J]. International Journal of Heat and Mass Transfer, 2000, 43(15): 2779-2791.
5	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.
6	Alazmi B, Vafai K. Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer[J]. International Journal of Heat and Mass Transfer, 2001, 44(9): 1735-1749.
7	Alazmi B, Vafai K. Constant wall heat flux boundary conditions in porous media under local thermal non-equilibrium conditions[J]. International Journal of Heat and Mass Transfer, 2002, 45(15): 3071-3087.
8	Min J Y, Kim S J. A novel methodology for thermal analysis of a composite system consisting of a porous medium and an adjacent fluid layer[J]. Journal of Heat Transfer, 2005, 127(6): 648-656.
9	Dehghan M, Valipour M S, Keshmiri A, et al. On the thermally developing forced convection through a porous material under the local thermal non-equilibrium condition: an analytical study[J]. International Journal of Heat and Mass Transfer, 2016, 92: 815-823.
10	Dehghan M, Valipour M S, Saedodin S, et al. Thermally developing flow inside a porous-filled channel in the presence of internal heat generation under local thermal non-equilibrium condition: a perturbation analysis[J]. Applied Thermal Engineering, 2016, 98: 827-834.
11	Dehghan M, Valipour M S, Saedodin S, et al. Investigation of forced convection through entrance region of a porous-filled microchannel: an analytical study based on the scale analysis[J]. Applied Thermal Engineering, 2016, 99: 446-454.
12	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.
13	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.
14	Vafai K, Yang K. A note on local thermal non-equilibrium in porous media and heat flux bifurcation phenomenon in porous media[J]. Transport in Porous Media, 2013, 96(1): 169-172.
15	Mahmoudi Y, Maerefat M. Analytical investigation of heat transfer enhancement in a channel partially filled with a porous material under local thermal non-equilibrium condition[J]. International Journal of Thermal Sciences, 2011, 50(12): 2386-2401.
16	Mahmoudi Y, Karimi N, Mazaheri K. Analytical investigation of heat transfer enhancement in a channel partially filled with a porous material under local thermal non-equilibrium condition: effects of different thermal boundary conditions at the porous-fluid interface[J]. International Journal of Heat and Mass Transfer, 2014, 70: 875-891.
17	Ochoa-Tapia J A, Whitaker S. Heat transfer at the boundary between a porous medium and a homogeneous fluid[J]. International Journal of Heat and Mass Transfer, 1997, 40(11): 2691-2707.
18	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.
19	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.
20	Torabi M, Zhang K L, Yang G C, et al. Heat transfer and entropy generation analyses in a channel partially filled with porous media using local thermal non-equilibrium model[J]. Energy, 2015, 82: 922-938.
21	Torabi M, Karimi N, Zhang K L. Heat transfer and second law analyses of forced convection in a channel partially filled by porous media and featuring internal heat sources[J]. Energy, 2015, 93: 106-127.
22	Torabi M, Karimi N, Zhang K L, et al. Generation of entropy and forced convection of heat in a conduit partially filled with porous media—local thermal non-equilibrium and exothermicity effects[J]. Applied Thermal Engineering, 2016, 106: 518-536.
23	Li Q, Hu P F. Analytical solutions of fluid flow and heat transfer in a partial porous channel with stress jump and continuity interface conditions using LTNE model[J]. International Journal of Heat and Mass Transfer, 2019, 128: 1280-1295.
24	Hu P F, Li Q. Effect of heat source on forced convection in a partially-filled porous channel under LTNE condition[J]. International Communications in Heat and Mass Transfer, 2020, 114: 104578.
25	Ochoa-Tapia J A, Whitaker S. Momentum transfer at the boundary between a porous medium and a homogeneous fluid(Ⅰ): Theoretical development[J]. International Journal of Heat and Mass Transfer, 1995, 38(14): 2635-2646.
26	Ochoa-Tapia J A, Whitaker S. Momentum transfer at the boundary between a porous medium and a homogeneous fluid(Ⅱ): Comparison with experiment[J]. International Journal of Heat and Mass Transfer, 1995, 38(14): 2647-2655.
27	Beavers G S, Joseph D D. Boundary conditions at a naturally permeable wall[J]. Journal of Fluid Mechanics, 1967, 30(1): 197-207.
28	李琪, 赵一远, 胡鹏飞. 多孔介质-自由流界面应力跳跃条件下流动特性解析解[J]. 力学学报, 2018, 50(2): 415-426.
	Li Q, Zhao Y Y, Hu P F. Analytical solution for porous-fluid flow characteristics with stress jump interfacial condition[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2): 415-426.
29	Rohsenow W M, Hartnett J P. Handbook of Heat Transfer[M]. Osborne McGraw-Hill, 1973.
30	Jiang P X, Ren Z P. Numerical investigation of forced convection heat transfer in porous media using a thermal non-equilibrium model[J]. International Journal of Heat and Fluid Flow, 2001, 22(1): 102-110.

[1]	张双星, 刘舫辰, 张义飞, 杜文静. R-134a脉动热管相变蓄放热实验研究[J]. 化工学报, 2023, 74(S1): 165-171.
[2]	张义飞, 刘舫辰, 张双星, 杜文静. 超临界二氧化碳用印刷电路板式换热器性能分析[J]. 化工学报, 2023, 74(S1): 183-190.
[3]	陈爱强, 代艳奇, 刘悦, 刘斌, 吴翰铭. 基板温度对HFE7100液滴蒸发过程的影响研究[J]. 化工学报, 2023, 74(S1): 191-197.
[4]	刘明栖, 吴延鹏. 导光管直径和长度对传热影响的模拟分析[J]. 化工学报, 2023, 74(S1): 206-212.
[5]	王志国, 薛孟, 董芋双, 张田震, 秦晓凯, 韩强. 基于裂隙粗糙性表征方法的地热岩体热流耦合数值模拟与分析[J]. 化工学报, 2023, 74(S1): 223-234.
[6]	张思雨, 殷勇高, 贾鹏琦, 叶威. 双U型地埋管群跨季节蓄热特性研究[J]. 化工学报, 2023, 74(S1): 295-301.
[7]	晁京伟, 许嘉兴, 李廷贤. 基于无管束蒸发换热强化策略的吸附热池的供热性能研究[J]. 化工学报, 2023, 74(S1): 302-310.
[8]	程成, 段钟弟, 孙浩然, 胡海涛, 薛鸿祥. 表面微结构对析晶沉积特性影响的格子Boltzmann模拟[J]. 化工学报, 2023, 74(S1): 74-86.
[9]	肖明堃, 杨光, 黄永华, 吴静怡. 浸没孔液氧气泡动力学数值研究[J]. 化工学报, 2023, 74(S1): 87-95.
[10]	李艺彤, 郭航, 陈浩, 叶芳. 催化剂非均匀分布的质子交换膜燃料电池操作条件研究[J]. 化工学报, 2023, 74(9): 3831-3840.
[11]	温凯杰, 郭力, 夏诏杰, 陈建华. 一种耦合CFD与深度学习的气固快速模拟方法[J]. 化工学报, 2023, 74(9): 3775-3785.
[12]	王玉兵, 李杰, 詹宏波, 朱光亚, 张大林. R134a在菱形离散肋微小通道内的流动沸腾换热实验研究[J]. 化工学报, 2023, 74(9): 3797-3806.
[13]	李科, 文键, 忻碧平. 耦合蒸气冷却屏的真空多层绝热结构对液氢储罐自增压过程的影响机制研究[J]. 化工学报, 2023, 74(9): 3786-3796.
[14]	齐聪, 丁子, 余杰, 汤茂清, 梁林. 基于选择吸收纳米薄膜的太阳能温差发电特性研究[J]. 化工学报, 2023, 74(9): 3921-3930.
[15]	杨越, 张丹, 郑巨淦, 涂茂萍, 杨庆忠. NaCl水溶液喷射闪蒸-掺混蒸发的实验研究[J]. 化工学报, 2023, 74(8): 3279-3291.