Journal of Applied Science and Engineering

Published by Tamkang University Press


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Chii-Dong Ho  1, Gwo-Geng Lin1, Jing-Min Tang2, Li-Chien Liu1, Li-Pang Lin1 and Jr-Wei Tu1

1Department of Chemical and Materials Engineering, Tamkang University, New Taipei City, Taiwan 25137, R.O.C.
2Department of Aerospace Engineering, Tamkang University, New Taipei City, Taiwan 25137, R.O.C.


Received: January 21, 2019
Accepted: May 16, 2019
Publication Date: September 1, 2019

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The influences of external recycle at the ends on double-pass laminar counterflow concentrictube massexchangers with sinusoidal wall flux distribution are investigated analytically. An analytical method is proposed to obtain a general solution by using the complex functions in combining the original boundary value problem into an ordinary differential equation with the aid of Frobenius method. Theoretical results show that a suitable adjustment of the permeable-barrier position can effectively enhance the masstransfer rate, leading to an improved device performance in masstransfer efficiency as compared with that in the single-pass operation (without a permeable barrier inserted in parallel into a circular tube). The mass-transfer efficiency enhancement due to the desirable effect of forced-convection increment in two flow patterns of double-pass devices has been illustrated with the recycle ratio, mass-transfer Graetz number, permeable-barrier location and dimensionless permeablebarrier parameter as parameters.

Keywords: Sinusoidal Wall Fluxes, Orthogonal Expansion Technique, Double-pass Operation, Mass Exchanger, Recycle


  1. [1] Shah, R. K., and A. L. London (1978) Laminar flow forced convection in ducts, Academic Press, New York, 169207.
  2. [2] Ramachandran, P. A. (1993) Boundary integral solution method for the Graetz problem, Numerical Heat Transfer Part B 23, 257268. doi: 10.1080/104077 99308914900
  3. [3] Laouadi, A., N. Galanis, and C. T. Nguyen (1994) Laminar fully developed mixed convection in inclined tubes uniform heated on their outer surface, Numerical Heat Transfer Part A 26, 719738. doi: 10.1080/ 10407789408956019
  4. [4] Bernier, M. A., and B. R. Baliga (1992) Conjugate conduction and laminar mixed convection in vertical pipes for upward flow and uniform wall heat flux, Numerical Heat Transfer Part A 21, 313332. doi: 10. 1080/10407789208944879
  5. [5] Amin,M.R., and J. A. Khan (1996) Effectsof multiple obstructions on conjugate forced convection heat transfer in tube, Numerical Heat Transfer Part A 26, 265 279. doi: 10.1080/10407789608913792
  6. [6] Ho, C. D., Y. C. Tsai, and J. W. Tu (2007) Improvement on device performance in multi-pass heat transfer through a parallel-plate channel with external recycle, International Journal of Heat and Mass Transfer 50, 48054811. doi: 10.1016/j.ijheatmasstransfer.2007. 03.010
  7. [7] Weigand, B., and D. Lauffer (2004) The extended Graetz problem with piecewise constant wall temperature for pipe and channel flows, International Journal of Heat and Mass Transfer 47, 53035312. doi: 10. 1016/j.ijheatmasstransfer.2004.06.027
  8. [8] Manca, O., and S. Nardini (2007) Experimental investigation on natural convection in horizontal channels with the upper wall at uniform heat flux, International Journal of Heat and Mass Transfer 50, 10751086. doi: 10.1016/j.ijheatmasstransfer.2006.07.038
  9. [9] Cess, R. D., and E. C. Shaffer (1959) Laminar heat transfer between parallel plates with an unsymmetrically prescribed heat flux at the walls, Applied Science Research 9, 6470. doi: 10.1007/BF00382190
  10. [10] Hatton, A. P., and A. Quarmby(1963) The effectof axially varying and unsymmetrical boundary conditions on heat transfer with turbulent flow between parallel plates, International Journal of Heat and Mass Transfer 6, 903914. doi: 10.1016/0017-9310(63)90081-4
  11. [11] Cooney, D. O., S. S. Kim, and E. J. Davis (1974) Analyses of mass transfer in hemodialyzers for laminar blood flow and homogeneous dialysate, Chemical Engineering and Science 29, 17311738. doi: 10.1016/ 0009-2509(74)87031-4
  12. [12] Ho, C. D., H. M. Yeh, and S. C. Chiang (2001) Mass transfer enhancement in double-pass laminar countercurrent massexchangers with external refluxes, Industrial and Engineering Chemistry Research 40, 5839 5846. doi: 10.1021/ie0009334
  13. [13] Mitrovoc, J., B. Maletic, and B. S. Baclic (2006) Some peculiarities of the asymmetric Graetz problem, International Journal of Engineering Science 44, 436455. doi: 10.1016/j.ijengsci.2006.02.003
  14. [14] Barletta, A. (1995) Laminar forced convection with sinusoidal wall heat flux distribution: axially periodic regime, Heat and Mass Transfer 31, 4148. doi: 10. 1007/BF02537420
  15. [15] Lee, D. Y., S. J. Park, and S. T. Ro (1995) Heat transfer by oscillating flow in a circular pipe with a sinusoidal wall temperature distribution, International Journal of Heat and Mass Transfer 38, 25292537. doi: 10.1016/ 0017-9310(95)00020-A
  16. [16] Nieken, U., G. Kolios, and G. Eigenberger (1994) Fixed bed reactors with periodic flow reversal: experimental results for catalytic combustion, Catalysis Today20,335350.doi:10.1016/0920-5861(94)80130-4
  17. [17] Choi, B. S., and C. A. J. Fletcher (1998) Turbulent particle dispersion in an electrostatic precipitator, Applied MathematicalModelling,22,10091021.doi:10.1016/ S0307-904X(98)10034-3
  18. [18] Choi,C.K., J.Y.Park, W.C.Park, and J.J.Kim(1999) Study on dynamic separation of silicaslurryusing arotating membrane filter: 2. modeling of cake formation, Journal of Membrane Science 57, 177187. doi: 10. 1016/S0376-7388(98)00377-9
  19. [19] Curcio, S., V. Calabro, and G. Iorio (2006) A theoretical and experimental analysis of a membrane bioreactor performance in recycle configuration, Journal of Membrane Science 273, 129142. doi: 10.1016/j. memsci.2005.10.006
  20. [20] Al-Bastaki, N., and A. Abbas (2003) Permeate recycle to improve the performance of a spiral-wound RO plant, Desalination 158, 119126. doi: 10.1016/S00119164(03)00442-9
  21. [21] Daigger, G. T., and T. E. Sadick (1998) Evaluation of methods to detect and control nitrification inhibition with specific application to incinerator flue-gas scrubber water, Water Environment Research 70, 1248 1257. doi: 10.2175/106143098X123606
  22. [22] Evren, V., T. Cagatay, and A. R. Ozdural (1999) Carbon dioxide-air mixtures: mass transfer in recycling packed-bed absorption columns operating under high liquid flow rates, Separation and Purification Technology 17, 8996. doi: 10.1016/S1383-5866(99) 00014-3
  23. [23] Ho, C. D., J. W. Tu, and L. C. Liu (2008) Sinusoidal wall fluxes in double-pass laminar counterflow concentric-tube mass exchangers, Journal of Chemical Engineering of Japan 41, 10831095. doi: 10.1252/ jcej.08we118



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