0
Research Papers

Conjugate Heat Transfer in a Microchannel Simultaneously Developing Gas Flow: A Vorticity Stream Function-Based Numerical Analysis

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

Department of Mechanical and Nuclear Engineering,
University of Sharjah,
Sharjah 27272, UAE
e-mail: kramadan@sharjah.ac.ae

Mohammed Kamil

Department of Mechanical and Nuclear Engineering,
University of Sharjah,
Sharjah 27272, UAE
e-mail: mmohammed@sharjah.ac.ae

M. S. Bataineh

Department of Mathematics,
University of Sharjah,
Sharjah 27272, UAE
e-mail: mbataineh@sharjah.ac.ae

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Thermal Science and Engineering Applications. Manuscript received January 19, 2019; final manuscript received April 3, 2019; published online May 15, 2019. Assoc. Editor: Aaron P. Wemhoff.

J. Thermal Sci. Eng. Appl 11(6), 061011 (May 15, 2019) (13 pages) Paper No: TSEA-19-1026; doi: 10.1115/1.4043468 History: Received January 19, 2019; Accepted April 03, 2019

A simultaneously developing microchannel gas flow is analyzed numerically, using the vorticity–stream function form of the Navier–Stokes equation, together with the fluid energy equation and the solid wall heat conduction equation. Rarefaction, shear work, viscous dissipation, pressure work, axial conduction, and conjugate effects on heat transfer characteristics are investigated. The shear work contribution to the wall heat flux is evaluated in both the developing and the fully developed flow regions and compared with the conductive wall heat flux. The assumption of hydrodynamically fully developed, thermally developing flow—normally used in the analysis of channel heat transfer—is assessed and compared with the simultaneously developing flow case. Analytical expressions for the fluid flow and heat transfer parameters under fully developed conditions are also derived and compared with the numerical results for verification. The analysis presented shows that the shear work and the combined viscous dissipation and pressure work result in extending the thermal entrance length by far. Heat conduction in the wall also contributes to increase the thermal entry length. The results presented also demonstrate the shear work contribution to heat transfer in the slip flow regime, although minor in the very first portion of the thermal entrance length, and it becomes progressively more significant as the flow thermal development conditions are approached and turns out to be exactly equal in magnitude to the conductive wall heat flux in the thermally fully developed region, resulting in a zero Nusselt number, as verified by both the exact and numerical solutions.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

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]
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), pp. 091401. [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(February), pp. 248–257. [CrossRef]
Nonino, C., Savino, S., Giudice, S. D., and Mansutti, L., 2009, “Conjugate Forced Convection and Heat Conduction in Circular Microchannels,” Int. 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]
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(September), pp. 87–94. [CrossRef]
Avci, M., Aydin, O., and Arici, M. E., 2012, “Conjugate Heat Transfer With Viscous Dissipation in a Microtube,” Int. J. Heat Mass Transfer, 55(19–20), pp. 5302–5308. [CrossRef]
Lelea, D., 2007, “The Conjugate Heat Transfer of the Partially Heated Microchannels,” Heat Mass Transfer, 44(33), pp. 33–41. [CrossRef]
Kabar, Y., Bessaih, R., and Rebay, M., 2013, “Conjugate Heat Transfer With Rarefaction in Parallel Plates Microchannel,” Superlattices Microstruct., 60(August), pp. 370–388. [CrossRef]
Sen, S., and Darici, S., 2017, “Transient Conjugate Heat Transfer in a Circular Microchannel Involving Rarefaction, Viscous Dissipation and Axial Conduction Effects,” Appl. Therm. Eng., 111(January), pp. 855–862. [CrossRef]
Sadeghi, A., Asgarshamsi, A., and Saidi, M. H., 2009, “Analysis of Laminar Flow in the Entrance Region of Parallel Plate Microchannels for Slip Flow,” Proceedings of the ASME 2009 7th International Conference on Nanochannels, Microchannels and Minichannels, Paper No. ICNMM2009-82012, pp. 345–352.
Groce, G., Rovenskaya, O., and D’Agaro, P., 2015, “Computational Analysis of Conjugate Heat Transfer in Gaseous Microchannels,” ASME J. Heat Transfer, 137(4), p. 041701. [CrossRef]
Wei, X., Ward, M. C. L., Lu, D., and Jiang, Zh., 2007, “Simulation of Rarefied Gas Flow in Microchannel Based on Vorticity–Stream Function Method,” Proceedings of MNC2007, Paper No. MNC2007-21120.
Pan, L. S., Liu, G. R., and Lam, K. Y., 1999, “Determination of Slip Coefficient for Rarefied Gas Flows Using Direct Simulation Monte Carlo,” J. Micromech. Microeng., 9(1), pp. 89–96. [CrossRef]
Wu, L., 2008, “A Slip Model for Rarefied Gas Flows at Arbitrary Knudsen Number,” Appl. Phys. Lett., 93(25), p. 253103. [CrossRef]
Wang, S., Lukyanov, A. A., Wang, L., Wu, Y. S., Pomerantz, A., Xu, W., and Kleinberg, R., 2017, “A Non-Empirical Gas Slippage Model for Low to Moderate Knudsen Numbers,” Phys. Fluids, 29(1), pp. 012004. [CrossRef]
Nicolas, X., Chenier, E., Tchekiken, C., and Lauriat, G., 2018, “Revisited Analysis of Gas Convection and Heat Transfer in Micro Channels: Influence of Viscous Stress Power at Wall on Nusselt Number,” Int. J. Therm. Sci., 134(December), pp. 565–584. [CrossRef]
Renksizbulut, M., Niazmand, H., and Tercan, G., 2006, “Slip-Flow and Heat Transfer in Rectangular Microchannels With Constant Wall Temperature,” Int. J. Therm. Sci., 45(9), pp. 870–881. [CrossRef]
Shah, R. K., and London, A. L., 1978, Laminar Flow Forced Convection in Ducts, Academic Press, New York.
Hadjiconstantinou, N. G., and Simek, O., 2002, “Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels,” ASME J. Heat Transfer, 124(2), pp. 356–364. [CrossRef]

Figures

Grahic Jump Location
Fig. 2

Grid sensitivity analysis: numerical solutions of the velocity components ((a) and (b)), vorticity (c), and the stream function (d) distributions in the developing region with different grid sizes at x/Dh = 0.15

Grahic Jump Location
Fig. 3

Grid sensitivity analysis: numerical solutions for the Nusselt number (a), the inner wall heat flux (b), the gas mean temperature (c), and the temperature distribution (d) in both the gas and the wall with different grid sizes

Grahic Jump Location
Fig. 4

Gas flow development with equilibrium conditions at the wall: velocity (a), vorticity (b), stream function (c), and temperature (d) distributions at various downstream locations

Grahic Jump Location
Fig. 5

Gas flow development with nonequilibrium conditions at the wall: velocity (a), vorticity (b), stream function (c), and temperature (d) distributions at various downstream locations

Grahic Jump Location
Fig. 6

Shear work relative to heat conduction at the wall and the Nusselt number variation in the developing region of gas microchannel flow: (a) effect of Brinkman number and (b) effect of Knudsen number

Grahic Jump Location
Fig. 7

A comparison of the energy equation solutions with simultaneously developing flow and HFD flow cases with equilibrium conditions at the gas–wall interface

Grahic Jump Location
Fig. 8

A comparison of the energy equation solutions with simultaneously developing flow and HFD flow cases with nonequilibrium conditions at the gas–wall interface

Grahic Jump Location
Fig. 9

Variation of the Nusselt number (a), the inner wall heat flux (b), the gas mean and inner wall temperatures (c), and the temperature distribution (d) with wall thickness, for kw/kf = 100

Grahic Jump Location
Fig. 10

Variation of the Nusselt number (a), the inner wall heat flux (b), the gas mean and inner wall temperatures (c), and the temperature distribution (d) with wall thickness, for kw/kf = 10

Grahic Jump Location
Fig. 11

Effect of wall-to-fluid thermal conductivity ratio on the local Nusselt number (a), the inner wall heat flux (b), the gas mean and inner wall temperatures (c), and the temperature distribution in the gas and the wall (d) with Ho/H = 2

Grahic Jump Location
Fig. 12

Variation of the Nusselt number (a), the inner wall heat flux (b), the gas mean and inner wall temperatures (c), and the temperature distribution (d) with Knudsen number, for kw/kf = 100 and Ho/H = 2

Grahic Jump Location
Fig. 13

Variation of the Nusselt number (a), the inner wall heat flux (b), the gas mean and inner wall temperatures (c), and the temperature distribution (d) with Brinkman number, for kw/kf = 200 and Ho/H = 2

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In