WANG Ke-yong, LI Pei-chao. Analysis of High Speed Flow in Circular and Annular Ducts Occupied by Bidisperse Porous Media[J]. Applied Mathematics and Mechanics, 2017, 38(2): 206-215. doi: 10.21656/1000-0887.370105
 Citation: WANG Ke-yong, LI Pei-chao. Analysis of High Speed Flow in Circular and Annular Ducts Occupied by Bidisperse Porous Media[J]. Applied Mathematics and Mechanics, 2017, 38(2): 206-215.

# Analysis of High Speed Flow in Circular and Annular Ducts Occupied by Bidisperse Porous Media

##### doi: 10.21656/1000-0887.370105
• Received Date: 2016-04-08
• Rev Recd Date: 2016-07-25
• Publish Date: 2017-02-15
• Based on the two-velocity Brinkman-extended Darcy flow model, the characteristics of high speed flow in circular and annular ducts occupied by bidisperse porous media were analyzed. The flow fields of the fracture (f) and porous (p) phases were inherently governed by the 4th-order system of coupled differential equations. The original governing equations were simplified to a 2nd-order system of decoupled differential equations with the normal mode reduction method. Furthermore, the analytical solutions of velocity distributions were readily derived for the f- and p-phases. Results from both the circular and the annular ducts show that an increase in the Darcy number leads to a reduction in not only the flow velocities of the two phases but their difference. However, the flow velocities of the two phases exhibit an opposite trend with the increase of the momentum transfer between the two phases, resulting in a decrease in the velocity difference.
•  [1] 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 plate channel[J]. Applied Mathematics and Mechanics,2006,27(8): 978-986.(in Chinese)) [2] 郭茶秀, 罗志军. 泡沫型多孔介质等效导热系数研究进展[J]. 储能科学与技术, 2013,2(6): 577-585.(GUO Cha-xiu, LUO Zhi-jun. Review on effective thermal conductivity of bubble type porous media[J]. Energy Storage Science and Technology,2013,2(6): 577-585.(in Chinese)) [3] 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): 494-504.(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.(in Chinese)) [4] Chen Z Q, Cheng P, Hsu C T. A theoretical and experimental study on stagnant thermal conductivity of bi-dispersed porous media[J]. International Communications in Heat and Mass Transfer,2000,27(5): 601-610. [5] Nield D A, Kuznetsov A V. A two-velocity two-temperature model for a bi-dispersed porous medium: forced convection in a channel[J]. Transport in Porous Media,2005, 59(3): 325-339. [6] Kuznetsov A V, Nield D A. Thermally developing forced convection in a bidisperse porous medium[J]. Journal of Porous Media,2006,9(5): 393-402. [7] Kuznetsov A V, Nield D A. Forced convection in a channel partly occupied by a bidisperse porous medium: asymmetric case[J]. International Journal of Heat and Mass Transfer,2010,53(23): 5167-5175. [8] Kuznetsov A V, Nield D A. Forced convection in a channel partly occupied by a bidisperse porous medium: symmetric case[J]. International Journal of Heat and Mass Transfer,2011,33(7): 072601-1-072601-9. [9] Cheng C Y. Natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium[J]. International Communications in Heat and Mass Transfer,2013,43: 69-74. [10] Narasimhan A, Reddy B V K, Dutta P. Thermal management using the bi-disperse porous medium approach[J]. International Journal of Heat and Mass Transfer,2012,55(4): 538-546. [11] Narasimhan A, Reddy B V K. Laminar forced convection in a heat generating bi-disperse porous medium channel[J]. International Journal of Heat and Mass Transfer,2011,54(1): 636-644. [12] Nield D A, Kuznetsov A V. A note on modeling high speed flow in a bidisperse porous medium[J]. Transport in Porous Media,2012,96(3): 495-499. [13] Nield D A, Kuznetsov A V. Heat transfer in bidisperse porous media[C]//Transport Phenomena in Porous Media III . Oxford: Elsevier, 2005: 34-59. [14] Magyari E. Normal mode analysis of the high speed channel flow in a bidisperse porous medium[J]. Transport in Porous Media,2013,97(3): 345-352. [15] Hooman K, Sauret E, Dahari M. Theoretical modelling of momentum transfer function of bi-disperse porous media[J]. Applied Thermal Engineering,2014,75: 867-870. [16] Hung Y M, Tso C P. Effects of viscous dissipation on fully developed forced convection in porous media[J]. International Communications in Heat and Mass Transfer,2009,36(6): 597-603. [17] 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. [18] Wang K Y, Tavakkoli F, Wang S J, et al. Forced convection gaseous slip flow in a porous circular microtube: an exact solution[J]. International Journal of Thermal Sciences,2015,97: 152-162. [19] Wang K Y, Tavakkoli F, Vafai K. Analysis of gaseous slip flow in a porous micro-annulus under local thermal non-equilibrium condition—an exact solution[J]. International Journal of Heat and Mass Transfer,2015,89(5): 1331-1341.

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

## Article Metrics

Article views (732) PDF downloads(482) Cited by()

/