Conjugated heat transfer of power-law fluids in double-pass concentric circular heat exchangers with sinusoidal wall fluxes

Chii-Dong Ho; Gwo-Geng Lin; Thiam Leng Chew; Li-Pang Lin; Chii-Dong Ho; Gwo-Geng Lin; Thiam Leng Chew; Li-Pang Lin

doi:10.3934/mbe.2021282

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 5: 5592-5613. doi: 10.3934/mbe.2021282

Previous Article Next Article

Theory article Special Issues

Conjugated heat transfer of power-law fluids in double-pass concentric circular heat exchangers with sinusoidal wall fluxes

1.
Department of Chemical and Materials Engineering, Tamkang University, 151 Yingzhuan Road, Tamsui, New Taipei, Taiwan 251
2.
Department of Chemical Engineering, Faculty of Engineering, Universiti Teknologi Petronas, 32610 Seri Iskandar, Perak Darul Ridzuan, Malaysia
3.
CO2 Research Center (CO2RES), Institute of Contaminant Management, Universiti Teknologi Petronas, 32610 Seri Iskandar, Perak Darul Ridzuan, Malaysia

Received: 11 May 2021 Accepted: 11 June 2021 Published: 22 June 2021

An analytical formulation, referred to as conjugated Graetz problems, is developed to predict the temperature distribution and Nusselt numbers for the power-law fluid flowing in a double-pass concentric circular heat exchanger under sinusoidal wall fluxes. A new design of inserting an impermeable sheet into a concentric tube, in parallel, to conduct recycling double-pass operations has been studied theoretically in the fully developed region, resulting in substantial improvements in the performance of heat exchanger device. The analytical solution was derived using the complex functions by transforming the boundary value problem into ordinary differential equations with the aid of the Frobenius method. The influences of power-law index and impermeable-sheet position on average Nusselt numbers with various designs and operating parameters are also delineated. The theoretical predictions show that the heat transfer efficiency is considerably improved through operating the double-pass device compared to via a single-pass circular heat exchanger (where an impermeable sheet is not inserted). The economic feasibility of operating double-pass concentric circular heat exchanger for power-law fluids is exemplified by the ratio of the heat-transfer efficiency enhancement and the increment in power consumption. The double-pass effect from increasing the convective heat-transfer coefficient can compensate for the rise in power consumption, which serves as important economic advantage of this design.
- power-law fluids,
- sinusoidal wall fluxes,
- concentric circular heat exchangers,
- conjugated Graetz problem
Citation: Chii-Dong Ho, Gwo-Geng Lin, Thiam Leng Chew, Li-Pang Lin. Conjugated heat transfer of power-law fluids in double-pass concentric circular heat exchangers with sinusoidal wall fluxes[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 5592-5613. doi: 10.3934/mbe.2021282

Related Papers:

Abstract

An analytical formulation, referred to as conjugated Graetz problems, is developed to predict the temperature distribution and Nusselt numbers for the power-law fluid flowing in a double-pass concentric circular heat exchanger under sinusoidal wall fluxes. A new design of inserting an impermeable sheet into a concentric tube, in parallel, to conduct recycling double-pass operations has been studied theoretically in the fully developed region, resulting in substantial improvements in the performance of heat exchanger device. The analytical solution was derived using the complex functions by transforming the boundary value problem into ordinary differential equations with the aid of the Frobenius method. The influences of power-law index and impermeable-sheet position on average Nusselt numbers with various designs and operating parameters are also delineated. The theoretical predictions show that the heat transfer efficiency is considerably improved through operating the double-pass device compared to via a single-pass circular heat exchanger (where an impermeable sheet is not inserted). The economic feasibility of operating double-pass concentric circular heat exchanger for power-law fluids is exemplified by the ratio of the heat-transfer efficiency enhancement and the increment in power consumption. The double-pass effect from increasing the convective heat-transfer coefficient can compensate for the rise in power consumption, which serves as important economic advantage of this design.

References

[1]	R. K. Shah, A. L. London, Laminar flow forced convection in ducts, Academic Press, New York, USA, (1978), 196-207.
[2]	V. D. Dang, M. Steinberg, Convective diffusion with homogeneous and heterogeneous reaction in a tube, J. Phys. Chem., 84 (1980), 214-219. doi: 10.1021/j100439a018
[3]	E. Papoutsakis, D. Ramkrishna, Conjugated Graetz problems. I: General formalism and a class of solid-fluid problems, Chem. Eng. Sci., 36 (1981), 1381-1390. doi: 10.1016/0009-2509(81)80172-8
[4]	X. Yin, H. H. Bau, The Conjugated Greatz problem with axial conduction, Trans. ASME, 118 (1996), 482-485.
[5]	R. J. Nunge, W. N. Gill, An analytical study of laminar counterflow double-pipe heat exchangers, AIChE J., 12 (1966), 279-289. doi: 10.1002/aic.690120214
[6]	G. M. A. Ebadian, H. Y. Zhang, An exact solution of extended Graetz problem with axial heat conduction, Int. J. Heat Mass Transfer, 32 (1989), 1709-1717. doi: 10.1016/0017-9310(89)90053-7
[7]	F. Reyes, W. L. Luyben, Extensions of the simultaneous design of gas-phase adiabatic tubular reactor systems with gas recycle, Ind. Eng. Chem. Res., 40 (2001), 635-647. doi: 10.1021/ie000603j
[8]	C. M. C. Bonelli, A. F. Martins, E. B. Mano, C. L. Beatty, Effect of recycled polypropylene on polypropylene/high-density polyethylene blends, J. Appl. Polym. Sci., 80 (2001), 1305-1311. doi: 10.1002/app.1217
[9]	A. Fadavi, Y. Chisti, Gas-liquid mass transfer in a novel forced circulation loop reactor, Chem. Eng. J., 112 (2005), 73-80. doi: 10.1016/j.cej.2005.06.009
[10]	M. H. Siegel, J. C. Merchuk, K. Schugerl, Air-Lift Reactor Analysis: Interrelationships between riser, downcomer, and gas-liquid separator behavior including gas recirculation effects, AIChE J., 32 (1986), 1585-1595.
[11]	K. I. Kikuchi, H. Takahashi, Y. Takeda, F. Sugawara, Hydrodynamic behavior of single particles in a draft-tube bubble column, Can. J. Chem. Eng., 77 (1999), 573-578. doi: 10.1002/cjce.5450770319
[12]	C. D. Ho, P. C. Lee, J. W. Tu, Mass transfer enhancement in double-pass parallel-plate mass exchangers under asymmetric wall fluxes, Chem. Eng. Technol., 32 (2009), 1567-1577. doi: 10.1002/ceat.200900121
[13]	C. D. Ho, H. M. Yeh, J. J. Guo, An analytical study on the enrichment of heavy water in the continuous thermal diffusion column with external refluxes, Sep. Sci. Technol., 37 (2002), 3129-3153. doi: 10.1081/SS-120005664
[14]	C. Heinen, G. Guthausen, H. Buggisch, Determination of the power law exponent from magnetic resonance imaging (MRI) flow data, Chem. Eng. Technol., 25 (2002), 873-877. doi: 10.1002/1521-4125(20020910)25:9<873::AID-CEAT873>3.0.CO;2-T
[15]	R. P. Bharti, R. P. Chhabra, V. Eswaran, Steady forced convection heat transfer from a heated circular cylinder to power-law fluids, Int. J. Heat Mass Transfer, 50 (2007), 977-990. doi: 10.1016/j.ijheatmasstransfer.2006.08.008
[16]	A. Carezzato, M. R. Alcantara, J. Telis-Romero, C. C. Tadini, J. A. W. Gut, Non-Newtonian heat transfer on a plate heat exchanger with generalized configurations, Chem. Eng. Technol., 32 (2007), 21-26.
[17]	C. D. Ho, G. G. Lin, W. H. Lan, Analytical and experimental studies of power-law fluids in double-pass heat exchangers for improved device performance under uniform heat fluxes, Int. J. Heat Mass Transfer, 61 (2013), 464-474. doi: 10.1016/j.ijheatmasstransfer.2013.02.007
[18]	A. A. Delouei, M. Nazari, M. H. Kayhani, G. Ahmadi, Direct-forcing immersed boundary—non-Newtonian lattice Boltzmann method for transient non-isothermal sedimentation, J. Aerosol. Sci., 104 (2017), 106-122. doi: 10.1016/j.jaerosci.2016.09.002
[19]	A. A. Delouei, M. Nazari, M. H. Kayhani, S. K. Kang, S. Succi, Non-Newtonian particulate flow simulation: A direct-forcing immersed boundary-lattice Boltzmann approach, Phys. A Statist. Mech. Appl., 447 (2016), 1-20. doi: 10.1016/j.physa.2015.11.032
[20]	A. A. Delouei, M. Nazari, M. H. Kayhani, S. Succi, Non-Newtonian unconfined flow and heat transfer over a heated cylinder using the direct-forcing immersed boundary-thermal lattice Boltzmann method, Phys. Rev. E, 89 (2014), 053312.
[21]	A. Jalali, A. A. Delouei, M. Khorashadizadeh, A. M. Golmohamadi, S. Karimnejad, Mesoscopic simulation of forced convective heat transfer of Carreau-Yasuda fluid flow over an inclined square: Temperature-dependent viscosity, J. Appl. Comput. Mech., 6 (2020), 307-319.
[22]	A. A. Delouei, M. Nazari, M. H. Kayhani, S. Succi, Immersed boundary—thermal lattice Boltzmann methods for non-newtonian flows over a heated cylinder: A comparative study, Comm. Comput. Phys., 18 (2015), 489-515. doi: 10.4208/cicp.060414.220115a
[23]	A. A. Delouei, M. Nazari, M. H. Kayhani, G. Ahmadi, A non-Newtonian direct numerical study for stationary and moving objects with various shapes: An immersed boundary—Lattice Boltzmann approach, J. Aerosol Sci., 93 (2016), 45-62. doi: 10.1016/j.jaerosci.2015.11.006
[24]	V. D. Zimparov, A. K. da Silva, A. Bejan, Thermodynamic optimization of treeshaped flow geometries with constant channel wall temperature, Int. J. Heat Mass Transfer, 49 (2006), 4839-4849. doi: 10.1016/j.ijheatmasstransfer.2006.05.024
[25]	B. Weigand, D. Lauffer, The extended Graetz problem with piecewise constant wall temperature for pipe and channel flows, Int. J. Heat Mass Transfer, 47 (2004), 5303-5312. doi: 10.1016/j.ijheatmasstransfer.2004.06.027
[26]	A. Behzadmehr, N. Galanis, A. Laneville, Low Reynolds number mixed convection in vertical tubes with uniform wall heat flux, Int. J. Heat Mass Transfer, 46 (2003), 4823-4833. doi: 10.1016/S0017-9310(03)00323-5
[27]	O. Manca, S. Nardini, Experimental investigation on natural convection in horizontal channels with the upper wall at uniform heat flux, Int. J. Heat Mass Transfer, 50 (2007), 1075-1086. doi: 10.1016/j.ijheatmasstransfer.2006.07.038
[28]	M. Ghalambaz, J. Zhang, Conjugate solid-liquid phase change heat transfer in heatsink filled with phase change material-metal foam, Int. J. Heat Mass Transfer, 146 (2020), 118832-118849. doi: 10.1016/j.ijheatmasstransfer.2019.118832
[29]	M. Ghalambaz, S. M. H. Zadeh, S. A. M. Mehryan, I. Pop, D. S. Wen, Analysis of melting behavior of PCMs in a cavity subject to a non-uniform magnetic field using a moving grid technique, Appl. Math. Model., 77 (2020), 1936-1953. doi: 10.1016/j.apm.2019.09.015
[30]	C. J. Ho, Y. C. Liu, M. Ghalambaz, W. M. Yan, Forced convection heat transfer of nano-encapsulated phase change material (NEPCM) suspension in a mini-channel heatsink, Int. J. Heat Mass Transfer, 155 (2020), 119858-119870. doi: 10.1016/j.ijheatmasstransfer.2020.119858
[31]	S. A. M. Mehryan, L. S. Gargari, A. Hajjar, M. Sheremet, Natural convection flow of a suspension containing nano-encapsulated phase change particles in an eccentric annulus, J. Energy Storage, 28 (2020), 101236-101273. doi: 10.1016/j.est.2020.101236
[32]	M. Ghalambaz, S. A. M. Mehryan, A. Hajjar, A. Veismoradi, Unsteady natural convection flow of a suspension comprising nano-encapsulated phase change materials (NEPCMs) in a porous medium, Adv. Powder Technol., 31 (2020), 954-966. doi: 10.1016/j.apt.2019.12.010
[33]	C. J. Hsu, Heat transfer in a round tube with sinusoidal wall heat flux distribution, AIChE J., 11 (1965), 690-695. doi: 10.1002/aic.690110423
[34]	A. Barletta, E. Rossi di Schio, Effects of viscous dissipation on laminar forced convection with axially periodic wall heat flux, Heat Mass Transfer, 35 (1999), 9-16.
[35]	D. K. Choi, D. H. Choi, Developing mixed convection flow in a horizontal tube under circumferentially non-uniform heating, Int. J. Heat Mass Transfer, 35 (1994), 1899-1913.
[36]	D. Y. Lee, S. J. Park, S. T. Ro, Heat transfer by oscillating flow in a circular pipe with a sinusoidal wall temperature distribution, Int. J. Heat Mass Transfer, 38 (1995), 2529-2537. doi: 10.1016/0017-9310(95)00020-A
[37]	C. D. Ho, J. W. Tu, C. M. Yang, Conjugated heat transfer in double-pass laminar counterflow concentric-tube heat exchangers with sinusoidal wall fluxes, Int. J. Heat Mass Transfer, 61 (2009), 464-474.
[38]	D. Murkerjee, E. J. Davis, Direct-contact heat transfer immiscible fluid layers in laminar flow, AIChE J., 18 (1972), 94-101. doi: 10.1002/aic.690180118
[39]	E. J. Davis, S. Venkatesh, The solution of conjugated multiphase heat and mass transfer problems, Chem. Eng. J., 34 (1979), 775-787. doi: 10.1016/0009-2509(79)85133-7
[40]	R. W. Hanks, K. M. Larsen, The flow of power-law non-Newtonian fluids in concentric annuli, Ind. Eng. Chem. Fundam., 18 (1979), 33-35. doi: 10.1021/i160069a008
[41]	A. Barletta, E. Zanchini, Laminar forced convection with sinusoidal wall heat flux distribution: axially periodic regime, Heat Mass Transfer, 31 (1995), 41-48. doi: 10.1007/BF02537420
[42]	J. O. Wilkes, Fluid mechanics for chemical engineers, Prentice-Hall PTR, New Jersey, 1999.
[43]	J. R. Welty, C. E. Wicks, R. E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer, third ed. John Wiley & Sons, New York, 1984.

Reader Comments

Your name:*

Email:*
© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)