Flow behavior in weakly permeable micro-tube with varying viscosity near the wall

1. Olson, F.C.W. (1949). Flow through a pipe with a porous wall. J. Appl. Mech. 16(1), 53–54.10.1115/1.4009893Search in Google Scholar

2. Cheng, Y.C. & Hwang, G.J. (1995). Experimental studies of laminar flow and heat transfer in a one-porous-wall square duct with wall injection. Int. J. Heat Mass Tran. 38(18), 3475–3484. DOI: 10.1016/0017-9310(95)00037-A.10.1016/0017-9310(95)00037-Open DOISearch in Google Scholar

3. Goosen, M.F.A., Sablani, S.S., Al-Hinai, H., Al-Obeidani, S., Al-Belushi, R. & Jackson, D. (2005). Fouling of reverse osmosis and ultrafiltration membranes: a critical review. Separ. Sci. Technol. 39(10), 2261–2297. DOI: 10.1081/SS-120039343.10.1081/SS-120039343Search in Google Scholar

4. Xinhui, S., Liancun, Z., Xinxin, Z. & Jianhong, Y. (2011). Homotopy analysis method for the heat transfer in a asymmetric porous channel with an expanding or contracting wall. Appl. Math. Model. 35(9), 4321–4329. DOI: 10.1016/j.apm.2011.03.009.10.1016/j.apm.2011.03.009Open DOISearch in Google Scholar

5. Ahmad, A.L., Lau, K.K., Bakar, M.A. & Shukor, S.A. (2005). Integrated CFD simulation of concentration polarization in narrow membrane channel. Comput. Chem. Eng. 29(10), 2087–2095. DOI: 10.1016/j.compchemeng.2005.06.001.10.1016/j.compchemeng.2005.06.001Search in Google Scholar

6. Liang, Y.Y., Chapman, M.B., Weihs, G.F. & Wiley, D.E. (2014). CFD modelling of electro-osmotic permeate flux enhancement on the feed side of a membrane module. J. Membr. Sci., 470, 378–388. DOI: 10.1016/j.memsci.2014.07.039.10.1016/j.memsci.2014.07.039Open DOISearch in Google Scholar

7. Jun, C.L., Xiang J.Y. & Dong, Hu Y. (2015). CFD simulations of the fluid flow behavior in a spacer-filled membrane module. Membr. Water Treat. 6(6), 513–524. DOI: 10.12989/mwt.2015.6.6.513.10.12989/mwt.2015.6.6.513Open DOISearch in Google Scholar

8. Berman, A.S. (1953). Laminar flow in channels with porous walls. J. Appl. Phys. 24(9), 1232–1235. DOI: 10.1063/1.1721476.10.1063/1.1721476Open DOISearch in Google Scholar

9. Yuan, S.W. & Finkelstein, A.B. (1956). Laminar pipe flow with injection and suction through a porous wall. Trans. ASME. 78, 719–724.10.1115/1.4013794Search in Google Scholar

10. Kozinski, A.A., Schmidt, F.P. & Lightfoot, E.N. (1970). Velocity Profiles in Porous-Walled Ducts. Ind. Eng. Chem. Fundam. 9(3), 502–505. DOI: 10.1021/i160035a033.10.1021/i160035a033Search in Google Scholar

11. Tilton, N., Martinand, D., Serre, E. & Lueptow, R.M. (2012). Incorporating Darcy’s law for pure solvent flow through porous tubes: Asymptotic solution and numerical simulations. AIChE J. 58(7), 2030–2044. DOI: 10.1002/aic.13823.10.1002/aic.13823Open DOISearch in Google Scholar

12. Kim, A.S. & Lee Y.T. (2011). Laminar flow with injection through a long dead-end cylindrical porous tube: Application to a hollow fiber membrane. AIChE J. 57(8), 1997–2006. DOI: 10.1002/aic.12430.10.1002/aic.12430Search in Google Scholar

13. Bird, R.B., Stewart, W.E. & Lightfoot, E.N. (2002). Transport phenomena (2^nd ed.). John Wiley & Sons.Search in Google Scholar

14. Vennela, N., Mondal, S., De, S. & Bhattacharjee, S. (2012). Sherwood number in flow through parallel porous plates (Microchannel) due to pressure and electroosmotic flow. AIChE J. 58(6), 1693–1703. DOI: 10.1002/aic.12713.10.1002/aic.12713Open DOISearch in Google Scholar

15. Granger, J., Dodds, J. & Midoux, N. (1989). Laminar flow in channels with porous walls. The Chem. Eng. J. 42(3), 193–204. DOI: 10.1063/1.1721476.10.1063/1.1721476Open DOISearch in Google Scholar