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A Numerical Study of Impulsively Started External Convection at Microscale

Published online by Cambridge University Press:  22 May 2014

K. Ramadan
K. Ramadan*
Affiliation:
Department of Mechanical Engineering, Mu'tah UniversityP. O. Box 7, Karak 61710, Jordan
*
[email protected]
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Abstract

Impulsively started external convection at microscale level is studied numerically in both planar and axisymmetric geometries. Using similarity transformation, the resulting coupled partial and non-linear ordinary differential equations are simultaneously solved by finite differences together with a well established ordinary differential equation solver, over a range of problem parameters. Rarefaction effects within the slip flow regime on the thermal boundary layer response, heat transfer rate and transition time when system experiences sudden changes in surface temperature are analyzed, and a comparison between sudden surface cooling and heating is presented. The results show that the thermal boundary layer thickness, heat transfer rate and the transition time is considerably influenced by the degree of rarefaction. The transition time tends to be less sensitive with increasing rarefaction. The velocity slip and temperature jump factors are found to have opposite effects on the transition time and the heat transfer rate, with the velocity slip factor having the most profound influence on these parameters.

Keywords

MicroscaleRarefactionSlip flowVelocity slipTemperature jumpTransient convection
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 1 , February 2015 , pp. 79 - 90
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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References

REFERENCES

1.Gad-el-Hak, M., “The Fluid Mechanics of Microdevices – The Freeman Scholar Lecture,” Journal of Fluids Engineering, ASME, 121, pp. 5–33 (1999).CrossRefGoogle Scholar
2.Mueller, T. J. and DeLaurier, J. D., “Aerodynamics of Small Vehicles,” Annual Review of Fluid Mechanics, 35, pp. 89–111 (2003).CrossRefGoogle Scholar
3.Sun, Q., Boyd, I. D. and Candler, G. V., “Numerical Simulation of Gas Flow Over Microscale Airfoils,” Journal of Thermophysics and Heat Transfer, 16, pp. 171–179 (2002).CrossRefGoogle Scholar
4.Martin, M. J. and Boyd, I. D., “Blasius Boundary Layer Solution with Slip Flow Conditions,” Bartel, T. J. and Gallis, M. A. (Eds.), 22nd Rarefied Gas Dynamics Symposium, Sydney, Australia (2000).Google Scholar
5.Vedantam, N. K., “Effects of Slip on Flow Characteristics of a Laminar Flat Plate Boundary Layer,” Proceedings of the ASME Fluids Engineering Summer Meeting, Miami, FL, pp. 1551–1560 (2006).Google Scholar
6.Martin, M. J. and Boyd, I. D., “Stagnation-Point Heat Transfer Near the Continuum Limit,” AIAA Journal, 47, pp. 283–285 (2009).CrossRefGoogle Scholar
7.Martin, M. J. and Boyd, I. D., “Momentum and Heat Transfer in a Laminar Boundary Layer with Slip Flow,” Journal of Thermophysics and Heat Transfer, 20, pp. 710–719 (2006).CrossRefGoogle Scholar
8.Martin, M. J. and Boyd, I. D., “Falkner-Skan Flow over a Wedge with Slip Boundary Conditions,” Journal of Thermophysics and Heat Transfer, 24, pp. 263–270 (2010).CrossRefGoogle Scholar
9.Aziz, A., “Hydrodynamic and Thermal Slip Flow Boundary Layers over a Flat Plate with Constant Heat Flux Boundary Condition,” Communications in Nonlinear Science and Numerical Simulation, 15, pp. 573–580 (2010).CrossRefGoogle Scholar
10.Castelloes, F. V., Cardoso, C. R., Couto, P. and Cotta, R. M., “Transient Analysis of Slip Flow and Heat Transfer in Microchannels,” Heat Transfer Engineering, 28, pp. 549–558 (2007).CrossRefGoogle Scholar
11.Yang, J. and Kwok, D. Y., “Time dependent Laminar Electrokinetic Slip Flow in Infinitely Extended Rectangular Microchannels,” Journal of Chemical Physics, 118, pp. 354–363 (2003).CrossRefGoogle Scholar
12.A., Bhattacharyya, A., Masliyah, J. H. and Yang, J., “Oscillating Laminar Electrokinetic Flow in Infinitely Extended Circular Microchannels,” Journal of Colloid and Interface Science, 261, pp. 12–20 (2003).Google Scholar
13.Wiwatanapataphee, B., Wu, Y. H. and Hu, M., “Chayantrakom, K., a Study of Transient Flows of Newtonian Fluids Through Micro-Annuals with a Slip Boundary,” Journal of Physics A: Mathematical and Theoretical, 42, 065206 (2009), doi:10.1088/1751-8113/42/6/065206.CrossRefGoogle Scholar
14.Colin, S., “Rarefaction and Compressibility Effects on Steady and Transient Gas Flows in Microchannels,” Microfluidics and Nanofluidics, 1, pp. 268–279 (2005).CrossRefGoogle Scholar
15.Bestman, A. R., Ikonwa, I. O. and Mbelegodu, I. U., “Transient Slip Flow,” International Journal of Energy Research, 19, pp. 275–277 (1995).CrossRefGoogle Scholar
16.Mukhopadhyay, S., “Effects of Slip on Unsteady Mixed Convective Flow and Heat Transfer Past a Stretching Surface,” Chinese Physics Letters, 27, 124401 (2010).CrossRefGoogle Scholar
17.Bhattacharyya, K., Mukhopadhyay, S. and Layek, G. C., “Slip Effects on an Unsteady Boundary Layer Stagnation-Point Flow and Heat Transfer towards a Stretching Sheet,” Chinese Physics Letters, 28, 094702 (2011).CrossRefGoogle Scholar
18.Karniadakis, G., Beskok, A. and Aluru, N., Micro-flows and Nanoflows, Fundamentals and Simulation, Springer Science, New York (2005).Google Scholar
19.Sharipov, F., “Data on the Velocity Slip and Temperature Jump on a Gas-Solid Interface,” Journal of Physical and Chemical Reference Data, 40, 023101 (2011).CrossRefGoogle Scholar
20.Ramadan, K. and Al-Nimr, M. A., “On Impulsively Started Convection: The Case of Stagnation Point Flow,” International Journal of Thermal Sciences, 50, pp. 2355–2364 (2011).CrossRefGoogle Scholar
21.White, F. M., Viscous Fluid Flow, McGraw-Hill, New York (1974).Google Scholar
22.Colin, S., “Gas Microflows in the Slip Flow Regime: A Critical Review on Convective Heat Transfer,” Journal of Heat Transfer, ASME, 134, 020908 (2012).CrossRefGoogle Scholar
23.Hong, C. and Asako, Y., “Some Considerations on Thermal Boundary Layer Condition of Slip Flow,” International Journal of Heat and Mass Transfer, 53, pp. 3075–3079 (2010).CrossRefGoogle Scholar
24.Hong, C., Y., Asako, Y. and Lee, J-H., “Heat Transfer Characteristics of Gaseous Flows in Micro-Channel with Constant Heat Flux,” International Journal of Thermal Sciences, 46, pp. 1153–1162 (2007).CrossRefGoogle Scholar
25.Hadjiconstantinou, N. G., “Dissipation in Small Scale Gaseous Flows,” Journal of Heat Transfer, ASME, 125, pp. 944–947 (2003).CrossRefGoogle Scholar
26.Wang, C. Y., “Stagnation Slip Flow and Heat Transfer on a Moving Plate,” Chemical Engineering Science, 61, pp. 7668–7672 (2006).CrossRefGoogle Scholar