Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-06T06:56:43.271Z Has data issue: false hasContentIssue false
  • English
  • Français

A Numerical Study of the Extended Graetz Problem in a Microchannel with Constant Wall Heat Flux: Shear Work Effects on Heat Transfer

Published online by Cambridge University Press:  18 May 2015

K. Ramadan  and
I. Tlili
K. Ramadan
Affiliation:
Department of Mechanical Engineering, Mu’tah University, Karak, Jordan
I. Tlili
Affiliation:
Department of Mechanical Engineering, Majmaah University, Majmaah, Saudi Arabia
Get access

Abstract

Heat convection of a microchannel gas flow with constant wall heat flux boundary condition is investigated numerically, considering viscous dissipation and axial conduction. The shear work due to the slipping fluid at the wall is incorporated in the analysis. An analytical solution for fully developed conditions is also derived. The effect of the shear work on heat transfer is quantified through a comparative analysis in both the entrance- and the fully developed- regions. The analysis shows that the shear work effect on heat transfer is considerable, and neglecting this term leads to an overestimation of the Nusselt number in gas heating and an underestimation in gas cooling. The over/under estimation of the Nusselt number is dependent on both the Knudsen number and the Brinkman number. The results presented also demonstrate the significance of the shear work in the developing flow region. It is shown that in the developing flow region the Nusselt number is less sensitive to viscous dissipation when the shear work is neglected. It can be concluded from this study that the shear work effect is significant and neglecting it can lead to considerable errors in microchannel flow heat transfer.

Keywords

Microchannel flowVelocity slipTemperature jumpShear work
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 6 , December 2015 , pp. 733 - 743
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Gad-el-Hak, M. (Editor), MEMS, Introduction and Fundamentals, 2nd Edition, Taylor & Francis Group, Boca Raton, Florida (2006).Google Scholar
2.Maslen, H. S., “On Heat Transfer in Slip Flow,” Journal of the Aeronautical Sciences, 25, pp. 400–401 (1958).Google Scholar
3.Sparrow, E. M. and Lin, S. H., “Laminar Heat Transfer in Tubes Under Slip-Flow Conditions,” Journal of Heat Transfer, 84, pp. 363–369 (1962).CrossRefGoogle Scholar
4.Inman, R. M., “Laminar Slip Flow Heat Transfer in a Parallel Plate Channel or Round Tube with Uniform Wall Heating,” National Aeronautics and Space Administration, Washington, D. C., Technical Note D-2393 (1964).Google Scholar
5.Hong, C. and Asako, Y., “Some Considerations on Thermal Boundary Condition of Slip Flow,” International Journal of Heat and Mass Transfer, 53, pp. 3075–3079 (2010).Google Scholar
6.Hadjiconstantinou, N. G., “Dissipation in Small Scale Gaseous Flows,” Journal of Heat Transfer, 125, pp. 944–947 (2003).Google Scholar
7.Colin, S., “Gas Microflows in the Slip Flow Regime: A. Critical Review on Convective Heat Transfer,” Journal of Heat Transfer, 134, p. 020908 (2012).Google Scholar
8.Shi, W., Miyamoto, M., Katoh, Y. and Kurima, J., “Choked Flow of Low Density Gas in a Narrow Parallel-Plate Channel with Adiabatic Walls,” International Journal of Heat and Mass Transfer, 44, pp. 2555–2565 (2001).Google Scholar
9.Miyamoto, M., Shi, W., Katoh, Y. and Kurima, J., “Choked Flow and Heat Transfer of Low Density Gas in a Narrow Parallel-Plate Channel with Uniformly Heating Walls,” International Journal of Heat and Mass Transfer, 46, pp. 2685–2693 (2003).Google Scholar
10.Myong, R. S., Lockerby, D. A. and Reese, J. M., “The Effect of Gaseous Slip on Microscale Heat Transfer: An Extended Graetz Problem,” International Journal of Heat and Mass Transfer, 49, pp. 2502–2513 (2006).Google Scholar
11.Chen, C.-H., “Slip-Flow Heat Transfer in a Micro-channel with Viscous Dissipation,” Heat and Mass Transfer, 42, pp. 853–860 (2006).CrossRefGoogle Scholar
12.Tunc, G. and Bayazitoglu, Y., “Heat Transfer in Rectangular Microchannels,” International Journal of Heat and Mass Transfer, 45, pp. 2395–2403 (2002).Google Scholar
13.Tunc, G. and Bayazitoglu, Y., “Heat Transfer in Microtubes with Viscous Dissipation,” International Journal of Heat and Mass Transfer, 44, pp. 2395–2403 (2001).Google Scholar
14.Knupp, D. C., Cotta, R. M., Naveira-Cotta, C. P. and Kakac, S. “Transient Conjugated Heat Transfer in Microchannels: Integral Transforms with Single Domain Formulation,” International Journal of Thermal Sciences, 88, pp. 248–257 (2015).Google Scholar
15.Zade, A. Q., Renksizbulut, M. and Friedman, J., “Heat Transfer Characteristics of Developing Gaseous Slip-Flow in Rectangular Microchannels with Variable Physical Properties,” International Journal of Heat and Fluid Flow, 32, pp. 117–127 (2011).Google Scholar
16.Rij, J. V., Ameel, T. and Harmann, T., “The Effect of Viscous Dissipation and Rarefaction on Rectangular Microchannel Convective Heat Transfer,” International Journal of Thermal Sciences, 48, pp. 271–281 (2009).Google Scholar
17.Sun, W., Kakac, S. and Yazicioglu, A. G., “A Numerical Study of Single-Phase Convective Heat Transfer in Microtubes for Slip Flow,” International Journal of Thermal Sciences, 46, pp. 1084–1094 (2007).Google Scholar
18.Rij, J. V., Harmann, T. and Ameel, T., “The Effect of Creep Flow on Two-Dimensional Isoflux Micro-channels,” International Journal of Thermal Sciences, 46, pp. 1095–1103 (2007).Google Scholar
19.Niazman, H. and Rahimi, B., “Mixed Convective Slip Flows in a Vertical Parallel Plate Microchannel with Symmetric and Asymmetric Wall Heat Fluxes,” Transactions of the Canadian Society for Mechanical Engineering, 36, pp. 207–218 (2012).Google Scholar
20.Renksizbulut, M., Niazman, H. and Tercan, G., “Slip-Flow and Heat Transfer in Rectangular Microchannels with Constant Wall Temperature,” International Journal of Thermal Sciences, 45, pp. 870–881 (2006).Google Scholar
21.Kabar, Y., Bessaih, R. and Rebay, M., “Conjugate Heat Transfer with Rarefaction in Parallel Plates Microchannel,” Superlattices and Microstructures, 60, pp. 370–388 (2013).Google Scholar
22.Loussif, N. and Orfi, J., “Simultaneously Developing Laminar Flow in an Isothermal Micro-Tube with Slip Flow Models,” Heat and Mass Transfer, 50, pp. 573–582.Google Scholar
23.Aziz, A. and Niedbalski, N., “Thermally Developing Microtube Gas Flow with Axial Conduction and Viscous Dissipation,” International Journal of Thermal Sciences, 50, pp. 332–340 (2011).CrossRefGoogle Scholar
24.Cetin, B., Yazicioglu, A. G. and Kakac, S., “Fluid Flow in Microtubes with Axial Conduction Including Rarefaction and Viscous Dissipation,” International Communications in Heat and Mass Transfer, 35, pp. 535–544 (2008).Google Scholar
25.Aydin, O. and Avi, M., “Analysis of Micro-Graetz Problem in a Microtube,” Nanoscale and Microscale Thermophysical Engineering, 10, pp. 345–358 (2006).CrossRefGoogle Scholar
26.Esmaeilnejad, A., Aminfar, H. and Neistanak, M. S. “Numerical Investigation of Forced Convection Heat Transfer Through Microchannels with Non-Newtonian Nanofluids,” International Journal of Thermal Sciences, 75, pp. 76–86 (2014).Google Scholar
27.Satapathy, A. K., “Slip Flow Heat Transfer in an Infinite Microtube with Axial Conduction,” International Journal of Thermal Sciences, 49, pp. 153–160 (2010).Google Scholar
28.Xiao, N., Elsnab, J. and Ameel, T., “Microtube Gas Flows with Second-Order Slip Flow and Temperature Jump Boundary Conditions,” International Journal of Thermal Sciences, 48, pp. 243–251 (2009).Google Scholar
29.Cetin, B., Yazicioglu, A. G. and Kakac, S., “Slip-Flow Heat Transfer in Microtubes with Axial Conduction and Viscous Dissipation - An Extended Graetz Problem,” International Journal of Thermal Sciences, 48, pp. 1673–1678 (2009).Google Scholar
30.Jeong, H.-E. and Jeong, J.-T., “Extended Graetz Problem Including Streamwise Conduction and Viscous Dissipation In Microchannel,” International Journal of Heat and Mass Transfer, 49, pp. 2151–2157 (2006).Google Scholar
31.Jeong, H.-E. and Jeong, J.-T., “Extended Graetz Problem Including Axial Conduction and Viscous Dissipation in Microtube,” Journal of Mechanical Science and Technology, 20, pp. 158–188 (2006).Google Scholar
32.Liu, H-L., Shao, X-D. and Jia, J-Y., “Effects of Axial Heat Conduction and Viscous Dissipation on Heat Transfer in Circular Micro-Channels,” International Journal of Thermal Sciences, 66, pp. 34–41 (2013).Google Scholar
33.Zhu, X. and Liao, Q., “Heat Transfer for Laminar Slip Flow in a Microchannel of Arbitrary Cross Section with Complex Thermal Boundary Conditions,” Applied Thermal Engineering, 26, pp. 1246–1256 (2006).Google Scholar
34.Valko, P. P., “Solution of the Graetz-Brinkman problem with the Laplace transform Galerkin method,” International Journal of Heat and Mass Transfer, 48, pp, 1874–1882 (2005).CrossRefGoogle Scholar
35.Minkowycz, W. J., Sparrow, E. M. and Murthy, J. Y., Handbook of Numerical Heat Transfer, John Wiley & Sons, New Jersey, (2006).Google Scholar
36.Schmidt, F. W. and Zeldin, B., “Laminar Heat Transfer in the Entrance Region of Ducts,” Applied Scientific Research, 23, pp. 73–94 (1970).Google Scholar