Gwo-Geng Lin1, Chii-Dong Ho This email address is being protected from spambots. You need JavaScript enabled to view it.1 and Yu-Hsing Liao1

1Energy and Opto-Electronic Materials Research Center, Department of Chemical and Materials Engineering, Tamkang University, Tamsui, Taiwan 25137, R.O.C.


 

Received: March 23, 2018
Accepted: October 30, 2018
Publication Date: March 1, 2019

Download Citation: ||https://doi.org/10.6180/jase.201903_22(1).0007  

ABSTRACT


The Graetz heat-transfer problem in a double-pass parallel-plate heat exchanger for a power law flow subject to hybrid boundary conditions was investigated theoretically and verified experimentally. An impermeable plate with negligible thermal resistance was placed between two parallel plates to conduct double-pass operations, and the performance of the device was significantly improved. The mathematical model was solved analytically using the separation of variables along with the superposition principle and an orthogonal expansion of the power series. The present study was aimed at developing a high-performance heat exchanger with hybrid boundary conditions, such as a constant temperature at the lower wall and a uniform flux at the upper wall. A dimensionless number () was defined to characterize the relative magnitude of the two different boundary conditions. From the average Nusselt number, the boundary condition with a constant heat flux at the upper wall could play a more important role in the heat transfer than the constant temperature at the lower wall. The heat-transfer efficiency enhancement was higher for the power-law fluid with a larger power index. However, the double-pass device in this study was more suitable for power-law fluids with a small power index when considering both heat-transfer efficiency and power consumption.


Keywords: Power-law Fluid, Double-pass, Heat Exchanger, Hybrid Boundary Conditions


REFERENCES


  1. [1] Yin, X., and H. H. Bau (1996) The conjugated greatz problem with axial conduction, Transaction ASME 118(2), 482485. doi: 10.1115/1.2825871
  2. [2] Nunge, R.J.,andW.N.Gill(1966) Ananalytical study of laminar counter flow double-pipe heat exchangers, AIChE Journal 12, 279289. doi: 10.1002/aic. 690120214
  3. [3] Lee, D. L., and T. F. Irvine (1997) Shear rate dependent thermal conductivity measurements of non-newtonian fluids, Experimental Thermal and Fluid Science 15(1), 1624.doi:10.1016/S0894-1777(96)00099-4
  4. [4] Shah, R. K., and A. L. London (1978) Laminar Flow Forced Convection in Ducts, Academic Press, New York, 169207.
  5. [5] Dang, V. D., and M. Steinberg (1980) convective diffusion with homogeneous and heterogeneous reaction in a tube, J. Physical Chemistry 84(2), 214219. doi: 10.1021/j100439a018
  6. [6] Papoutsakis, E., and D. Ramkrishna (1981) Conjugated Graetz Problems. I: general formalism and a class of solid-fluid problems, Chemical Engineering Science 36, 13811390. doi: 10.1016/0009-2509(81) 80172-8
  7. [7] Davis, E. J., and S. Venkatesh (1979) The solution of conjugated multiphase heat and mass transfer problems, Chemical Engineering Science 34, 775787. doi: 10.1016/0009-2509(79)85133-7
  8. [8] Papoutsakis, E., and D. Ramkrishna (1981) Conjugated Graetz Problems.II: fluid-fluid problems,Chemical Engineering Science 36, 13931399. doi: 10.1016/ 0009-2509(81)80173-X
  9. [9] Bharti, R. P., P. Sivakumar, and R. P. Chhabra (2008) Forced convection heat transfer from an elliptical cylinder to power-law fluids, Int. Journal Heat and Mass Transfer 51, 18381853. doi: 10.1016/j. ijheatmasstransfer.2007.06.032
  10. [10] Bharti, R. P., R. P. Chhabra, and V. Eswaran (2007) Steady forced convection heat transfer from a heated circular cylinder to power-law fluids, Int. Journal Heat and Mass Transfer 50, 977990. doi: 10.1016/j. ijheatmasstransfer.2006.08.00
  11. [11] Lin, G. G., C. D. Ho, J. J. Huang, and Y. C. Chen (2012) An analytical study of power-law fluids in double-pass heat exchangers with external recycle, Int. Journal Heat and Mass Transfer 55, 22612267. doi: 10.1016/j.ijheatmasstransfer.2012.01.039
  12. [12] Ho, C. D., G. G. Lin, and W. H. Lan (2013) Analytical and experimental studies of power-law fluids in double-pass flat-plate heat exchangers under uniform heat fluxes, Int. Journal Heat and Mass Transfer 61, 464 474. doi: 10.1016/j.ijheatmasstransfer.2013.02.007
  13. [13] Brown, G. M. (1960) Heat or mass transfer in a fluid flow in a circular or flat conduit, AIChE Journal 6, 179183. doi: 10.1002/aic.690060204
  14. [14] Yeh, H. M., and C. D. Ho (2000) The improvement of performance in parallel-plate heat exchangers by inserting in parallel an impermeable sheet for doublepass operations, Chemical Engineering Communications 183, 3948. doi: 10.1080/00986440008960500
  15. [15] Korpijarvi, J., and P. Oinas (1999) Hydrodynamics and mass transfer in an airlift reactor, ChemicalEngineering Science 54, 22552262. doi: 10.1016/S00092509(98)00439-4
  16. [16] Santacesaria, E., and M. Di. Serio (1999) Mass transfer and kinetics in ethoxylation spray tower loop reactors, Chemical Engineering Science 54, 14991504. doi: 10.1016/S0009-2509(99)00042-1
  17. [17] GarcmHa-Calvo, E., A. RodrmHguez, A. Prados, and J. Klein (1999) Afuid dynamic model for three-phase airlift reactors, Chemical Engineering Science 54, 2359 2370. doi: 10.1016/S0009-2509(98)00302-9
  18. [18] Atenas, M., M. Clark, and V. Lazarova (1999) Holdup and liquid circulation velocity in a rectangular air-lift bioreactor, Industrial & Engineering Chemistry Research 38, 944949. doi: 10.1021/ie980052l
  19. [19] Goto, S., and P. D. Gaspillo (1992) The effect of static mixeron mass transfer in draft tube bubble column and in external loop column, Chemical Engineering Science 47, 35333539. doi: 10.1016/0009-2509(92) 85067-L
  20. [20] Kikuchi, K. I., H. Takahashi, Y. Takeda, and F. Sugawara (1999) Hydrodynamic behavior of single particles in a draft-tube bubble column, The Canadian Journal of Chemical Engineering 77, 573578. doi: 10.1002/cjce.5450770319
  21. [21] Cess, R. D., and E. C. Shaffer (1960) Laminar heat transfer between parallel plates with an unsymmetrically prescribed heat flux at the walls, Applied Scientific Research, Section A. 9, 64 70. doi: 10.1007/ BF00382190
  22. [22] Nield, D. A. (2004) Forced convection in a parallel plate channel with asymmetric heating, Int. Journal Heat and Mass Transfer 47, 56095612. doi: 10.1016/ j.ijheatmasstransfer.2004.07.006
  23. [23] Mitrovic, J., B. Maletic, and B. S. Baclic (2006) Some peculiarities of the asymmetric Graetz problem, Int. Journal of Engineering Science 44, 436455. doi: 10. 1016/j.ijengsci.2006.02.003
  24. [24] Barletta, A., and E. Rossi di Schio (1999) Effects of viscous dissipation on laminar forced convection with axially periodic wall heat flux, Heat and Mass Transfer 35, 916. doi: 10.1007/s002310050292
  25. [25] Ho, C. D., G. G. Lin, C. Y. Lin, and L. Y. Jen (2017) Analytical and experimental studies for power-law fluids in a double-pass parallel-plate heat exchanger under asymmetricisotherm conditions, Int. Journal Heat and Mass Transfer 106, 12421250. doi: 10.1016/ j.ijheatmasstransfer.2016.10.104
  26. [26] Tam, K. C. (1990) Rheology and Turbulent Flow of Polymer Solutions, Ph. D. Dissertation, University of Monash, Australia.
  27. [27] Lin, G. G., C. D. Ho, and Y. R. Chen (2014) Experimental and analytical study of the internal recycle-effect on the heat transfer for the power-law fluid in a double-pass flat-plate heat exchanger with constant wall temperature, Int. Communications in Heat and Mass Transfer 50, 4451. doi: 10.1016/j.icheatmasstransfer.2013.11.011
  28. [28] Chhabra, R. P., and J. F. Richardson (2008) Non-Newtonian Flow and Applied Rheology: Engineering Applications,2nd ed., Butterworth-Heinemann, Oxford, 126136.