Analysis of Slip Flow Heat Transfer between Asymmetrically Heated Parallel Plates

Authors: Hari Mohan Kushwaha, Santosh K. Sahu

Abstract:

In the present study, analysis of heat transfer is carried out in the slip flow region for the fluid flowing between two parallel plates by employing the asymmetric heat fluxes at surface of the plates. The flow is assumed to be hydrodynamically and thermally fully developed for the analysis. The second order velocity slip and viscous dissipation effects are considered for the analysis. Closed form expressions are obtained for the Nusselt number as a function of Knudsen number and modified Brinkman number. The limiting condition of the present prediction for Kn = 0, Kn2 = 0, and Brq1 = 0 is considered and found to agree well with other analytical results.

Keywords: Knudsen Number, Modified Brinkman Number, Slip Flow, Velocity Slip.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1338488

References:

[1] G. E., Karniadakis, and A. Beskok, Micro Flows: Fundamentals and Simulation. Springer-Verlag, New York 2002, pp. 1-70.
[2] M. Gad-el-Hak, (Ed.), The MEMS Handbook, CRC Press, New York 2001, pp 64-101.
[3] S. G. Kandlikar, S. Colin, Y. Peles, S. Garimella, R.F. Pease, J.J. Brandner, and D.B. Tuckerman, Heat Transfer in Microchannels-2012 Status and Research Needs, J. Heat Transf., vol. 135, 2013, pp. 091001- 1.
[4] C.P. Tso, and S.P. Mahulikar, “The use of the Brinkman number for single phase forced convective heat transfer in microchannels,” Int. J. Heat Mass Transf., vol. 41, 1998, pp. 1759–1769.
[5] O. Aydin, and M. Avci, “Viscous dissipation effects on the heat transfer in a Poiseuille flow,” Appl. Energy, vol. 83, 2006, pp. 495–512.
[6] J. Koo, and C. Kleinstreuer, “Viscous dissipation effects in microtubes and microchannels,” Int. J. Heat Mass Transf., vol. 47, 2004, pp. 3159– 3169.
[7] T. Zhang, L. Jia, L. Yang, and Y. Jaluria, “Effect of viscous heating on heat transfer performance in microchannel slip flow region”, Int. J. Heat Mass Transf., vol. 46, 2010, pp. 4927-4934.
[8] X. Zhu, “Analysis of heat transfer between two unsymmetrically heated parallel plates with micro-spacing in the slip flow regime,” Microscale Thermophys. Eng. vol. 6, 2003, pp. 287–301.
[9] J.S. Francisca, and C.P. Tso, “Viscous dissipation effects on parallel plates with constant heat flux boundary conditions,” Int. Commun. Heat Mass Transf., vol. 36, 2009, pp. 249–254
[10] A. Sadeghi, and M.H. Saidi, “Viscous dissipation and rarefaction effects on laminar forced convection in microchannels,” J. Heat Transf., vol. 132, 2010 pp. 072401-12.
[11] S. Colin, P. Lalonde, and R. Caen, “Validation of a second-order slip flow model in rectangular microchannels,” Heat Transf. Eng. Vol. 25, 2010, pp. 23-30.
[12] J. Maurer, P. Tabeling, P. Joseph, and H. Willaime, “Second-order slip laws in microchannels for helium and nitrogen,” Phys. Fluids, vol. 15, 2003, pp. 2613-2621.
[13] H.M. Kushwaha, and S.K. Sahu, “Analysis of gaseous flow between parallel plates by second order velocity slip and temperature jump boundary conditions,” Heat Transf.-Asian Res., vol. 43, 2014, pp. 734- 748.
[14] H.M. Kushwaha, and S.K. Sahu, “Analysis of gaseous flow in a micropipe with second order velocity slip and temperature jump boundary conditions,” Heat Mass Transf. vol. 50, 2014, pp. 1649-1659.
[15] H.M. Kushwaha, and S.K. Sahu, “Analysis of heat transfer in the slip flow region between parallel plates,” 5th International and 41st National conference on Fluid Mechanics and Fluid Power, Indian Institute of Technology Kanpur, India, Dec.12-14, 2014, to be published.
[16] H.M. Kushwaha, and S.K. Sahu, “Effect of viscous dissipation and rarefaction on parallel plates with constant heat flux boundary conditions,” Chem. Eng. Technol. vol. 38, 2015, pp. 1-12.