Analysis of Slip Flow Heat Transfer between Asymmetrically Heated Parallel Plates
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:71211", author = "Hari Mohan Kushwaha and Santosh K. Sahu", title = "Analysis of Slip Flow Heat Transfer between Asymmetrically Heated Parallel Plates", 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.", volume = "9", number = "2", pages = "419-7", }