Research Papers

Numerical Analysis of Conjugated Convection-Conduction Heat Transfer in a Microtube Gas Flow

[+] Author and Article Information
K. M. Ramadan

Mechanical Engineering Department,
University of Sharjah,
Sharjah 27272, United Arab Emirates

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received March 28, 2018; final manuscript received July 13, 2018; published online September 17, 2018. Assoc. Editor: Samuel Sami.

J. Thermal Sci. Eng. Appl 11(1), 011004 (Sep 17, 2018) (11 pages) Paper No: TSEA-18-1159; doi: 10.1115/1.4040991 History: Received March 28, 2018; Revised July 13, 2018

Numerical solutions for conjugate heat transfer of a hydro-dynamically fully developed, thermally developing, steady, incompressible laminar gas flow in a microtube with uniform wall heat flux boundary condition are presented. The mathematical model takes into account effects of rarefaction, viscous dissipation, flow work, shear work, and axial conduction in both the wall and the fluid. The effect of the tube wall thickness, the wall-to-fluid thermal conductivity ratio, as well as other factors on heat transfer parameters is investigated, and comparisons with the case of zero wall thickness are presented as appropriate. The results illustrate the significance of heat conduction in the tube wall on convective heat transfer and disclose the significant deviation from those with no conjugated effects. Increasing the wall thickness lowers the local Nusselt number. Increasing the wall-to-fluid thermal conductivity ratio also results in lower Nusselt number. In relatively long and thick microtubes with high wall-to-fluid thermal conductivity ratio, the local Nusselt number exhibits minimum values in the entrance regions and at the end sections due to axial conduction effects. The analysis presented also demonstrate the significance of rarefaction, shear work, axial conduction, as well as the combined viscous dissipation and flow work effects on heat transfer parameters in a microtube gas flow. The combined flow work and viscous dissipation effects on heat transfer parameters are significant and result in a reduction in the Nusselt number. The shear work lowers the Nusselt number when heat is added to the fluid.

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Cole, K. D. , Cetin, B. , and Brettmann, L. , 2014, “ Microchannel Heat Transfer With Slip Flow and Wall Effects,” J. Thermophys. Heat Transfer, 28(3), pp. 455–461. [CrossRef]
Vocale, P. G. , Morini, L. , Spiga, M. , and Colin, S. , 2017, “ Shear Work Contribution to Convective Heat Transfer of Dilute Gases in Slip Flow Regime,” Eur. J. Mech. B/Fluids, 64, pp. 60–68. [CrossRef]
Knupp, D. C. , Cotta, R. M. , and Naveira-Cotta, C. P. , 2012, “ Theoretical Analysis of Conjugated Heat Transfer With a Single Domain Formulation and Integral Transforms,” Int. Commun. Heat Mass Transfer, 39(3), pp. 355–362. [CrossRef]
Knupp, D. C. , Cotta, R. M. , and Naveira-Cotta, C. P. , 2013, “ Conjugated Convection-Conduction Analysis in Microchannels With Axial Diffusion Effects and a Single Domain Formulation,” ASME J. Heat Transfer, 135(9), p. 091401. [CrossRef]
Nonino, C. , Savino, S. , Giudice, S. D. , and Mansutti, L. , 2009, “ Conjugate Forced Convection and Heat Conduction in Circular Microchannels,” Intl. J. Heat Fluid Flow, 30(5), pp. 823–830. [CrossRef]
Zhang, S.-X. , He, Y.-L. , Lauriat, G. , and Tao, W.-Q. , 2010, “ Numerical Studies of Simultaneously Developing Laminar Flow and Heat Transfer in Microtubes With Thick Wall and Constant Outside Wall Temperature,” Int. J. Heat Mass Transfer, 53(19–20), pp. 3977–3989. [CrossRef]
Avcı, M. , Aydın, O. , and Arıcı, M. E. , 2012, “ Conjugate Heat Transfer With Viscous Dissipation in a Microtube,” Intl. J. Heat Mass Transfer, 55(19–20), pp. 5302–5308. [CrossRef]
Rahimi, M. , and Mehryar, R. , 2012, “ Numerical Study of Axial Heat Conduction Effects on the Local Nusselt Number at the Entrance and Ending Regions of a Circular Microchannel,” Int. J. Therm. Sci., 59, pp. 87–94. [CrossRef]
Kabar, Y. , Bessaih, R. , and Rebay, M. , 2013, “ Conjugate Heat Transfer With Rarefaction in Parallel Plates Microchannel,” Superlattices Microstruct., 60, pp. 370–388. [CrossRef]
Lelea, D. , 2007, “ The Conjugate Heat Transfer of the Partially Heated Microchannels,” Heat Mass Transfer, 44(1), pp. 33–41. [CrossRef]
Knupp, D. C. , Cotta, R. M. , Naveira-Cotta, C. P. , and Kakac, S. , 2015, “ Transient Conjugated Heat Transfer in Microchannels: Integral Transforms With Single Domain Formulation,” Int. J. Therm. Sci., 88, pp. 248–257. [CrossRef]
Ramadan, K. M. , 2017, “ Effects of Pressure Work, Viscous Dissipation, Shear Work and Axial Conduction on Convective Heat Transfer in a Microtube,” Case Stud. Therm. Eng., 10, pp. 370–381. [CrossRef]
Ramadan, K. , and Tlili, I. , 2016, “ Shear Work, Viscous Dissipation and Axial Conduction Effects on Microchannel Heat Transfer With a Constant Wall Temperature,” Proc IMechE Part C, 230(14), pp. 2496–2507. [CrossRef]
Ramadan, K. M. , 2017, “ Pressure Work and Viscous Dissipation Effects on Heat Transfer in a Parallel–Plate Microchannel Gas Flow,” J. Mech., (epub).


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Fig. 1

Problem geometry and boundary conditions

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Fig. 2

The computational domain

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Fig. 5

Significance of flow work on heat transfer characteristics

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Fig. 6

Effect of wall to fluid thermal conductivity ratio on the local Nusselt number with L/Di=20

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Fig. 7

Effect of wall to fluid thermal conductivity ratio on the local Nusselt number with L/Di=40

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Fig. 8

Temperature distribution in the fluid and the wall for kw/kf=10 (a) and kw/kf=500 (b)

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Fig. 9

Effect of tube wall thickness on the local Nusselt number with zero viscous dissipation, flow work, and no rarefaction

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Fig. 10

Effect of tube wall thickness on the local Nusselt number including viscous dissipation, flow work, and rarefaction effects

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Fig. 11

Effect of rarefaction on Nusselt number (a), inner wall and mean temperatures (b), fluid temperature at the wall (c), and temperature distribution at different axial locations (d)

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Fig. 12

Effect of viscous dissipation and pressure work with rarefaction on Nusselt number (a), gas mean temperatures (b), inner wall temperature and gas temperatures at the wall (c), and radial temperature distribution at different axial locations (d)

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Fig. 3

Code verification: Grid independent solution

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Fig. 4

Code verification: Comparison of present study with previous studies



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