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

Gupta, Ravikant R.; Kumar, Vineet; Chand, Shri

doi:10.1515/pjct-2017-0062

Abstract

Weakly permeable micro-tubes are employed in many applications involving heat and/or mass transfer. During these processes, either solute concentration builds up (mass transfer) or steep change in temperature (heat transfer) takes place near the permeable wall causing a change in the viscosity of the fluid. Results of the present work suggest that such change in viscosity leads to a considerable alteration in the flow behavior, and the commonly assumed parabolic velocity profile no longer exists. To solve the problem numerically, the equation of motion was simplified to represent permeation of incompressible, Newtonian fluid with changing viscosity through a micro-tube. Even after considerable simplification, the accuracy of the results was the same as that obtained by previously reported results for some specific cases using rigorous formulation. The algorithm developed in the present work is found to be numerically robust and simple so that it can be easily integrated with other simulations.

References

1. Olson, F.C.W. (1949). Flow through a pipe with a porous wall. J. Appl. Mech. 16(1), 53–54.10.1115/1.4009893
Search in Google Scholar Back to article
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 DOI Search in Google Scholar Back to article
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-120039343
Search in Google Scholar Back to article
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.2011.03.009
Open DOI Search in Google Scholar Back to article
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.2005.06.001
Search in Google Scholar Back to article
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.2014.07.039
Open DOI Search in Google Scholar Back to article
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.2015.6.6.513
Open DOI Search in Google Scholar Back to article
8. Berman, A.S. (1953). Laminar flow in channels with porous walls. J. Appl. Phys. 24(9), 1232–1235. DOI: 10.1063/1.1721476.10.1063/1.1721476
Open DOI Search in Google Scholar Back to article
9. Yuan, S.W. & Finkelstein, A.B. (1956). Laminar pipe flow with injection and suction through a porous wall. Trans. ASME. 78, 719–724.10.1115/1.4013794
Search in Google Scholar Back to article
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/i160035a033
Search in Google Scholar Back to article
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.13823
Open DOI Search in Google Scholar Back to article
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.12430
Search in Google Scholar Back to article
13. Bird, R.B., Stewart, W.E. & Lightfoot, E.N. (2002). Transport phenomena (2^nd ed.). John Wiley & Sons.
Search in Google Scholar Back to article
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.12713
Open DOI Search in Google Scholar Back to article
15. Granger, J., Dodds, J. & Midoux, N. (1989). Laminar flow in channels with porous walls. The Chem. Eng. J. 42(3), 193–204. DOI: 10.1063/1.1721476.10.1063/1.1721476
Open DOI Search in Google Scholar Back to article

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

Abstract

Paradigm

My account