Influence of interfacial convective heat transfer coefficient on heat transfer in partially filled porous channel under LTNE condition

doi:10.11949/0438-1157.20201662

Abstract

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

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

CLC Number:

TK 124

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.

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.

Figures/Tables 9

Fig.1 Physical model of the porous-fluid channel

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

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%

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

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

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

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

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

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

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