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GASEOUS SLIP FLOW FORCED CONVECTION IN A MICROPIPE AND PARALLEL-PLATE MICROCHANNEL WITH A PIECEWISE UNIFORM WALL HEAT FLUX AND AXIAL HEAT CONDUCTION

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Abstract

A forced convective heat transfer problem inside a micropipe as well as inside a microchannel with parallel walls in the laminar gaseous slip flow regime, a with finite heating region and a prescribed wall heat flux, including the axial heat conduction effect, is analytically investigated. The temperature field and Nusselt number are derived under the assumption that the flow is hydrodynamically fully developed in the finite-length heating region. The solution is found by applying the functional analysis method, by decomposing the energy equation into a pair of first-order partial differential equations. The first-order slip boundary conditions are imposed at the gas–wall interface. The analytical solution is compared with available calculations. The results show that the thermal characteristics in the heating region are significantly affected by the axial heat conduction, rarefaction effects, and finite length of the heating region.

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REFERENCES

  1. C. Karniadakis, A. Beskok, and N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation (Springer, New York, 2005), pp. 60 and 400.

  2. J. M. Ha and G. P. Peterson, “The Heat Transport Capacity of Micro Heat Pipe," J. Heat Transfer 120, 1064–1071 (1998).

  3. B. Weigand, Analytical Methods for Heat Transfer and Fluid Flow Problems (Springer, Berlin–Heidelberg, 2015), p. 149.

  4. E. Papoutsakis, D. Ramkrishna, and H. C. Lim, “The Extended Graetz Problem with Dirichlet Wall Boundary Conditions," Appl. Sci. Res.36, 13–34 (1980).

  5. E. Papoutsakis, D. Ramkrishna, and H. C. Lim, “The Extended Graetz Problem with Prescribed Wall Flux," AIChE J. 26. 779–787 (1980).

  6. B. Weigand, M. Kanzamar, and H. Beer, “The Extended Graetz Problem with Piecewise Constant Wall Heat Flux for Pipe and Channel Flows," Int. J. Heat Mass Transfer 44, 3941–3952 (2001).

  7. B. Weigand and D. Lauffer, “The Extended Graetz Problem with Piecewise Constant Wall Temperature for Pipe and Channel Flows," Int. J. Heat Mass Transfer 47, 5303–5312 (2004).

  8. J. Lahjomri, K. Zniber, A. Oubarra, and A. Alemany, “Heat Transfer by Hartmann Flow in Thermal Entrance Region with Uniform Heat Flux: The Graetz Problem Extended," Energy Conv. Manag.44, 11–34 (2003).

  9. S. Colin, “Gas Microflows in the Slip Flow Regime: A Critical Review on Convective Heat Transfer," Trans. ASME, J. Heat Transfer 134, 020908 (2012).

  10. Y. Haddout and J. Lahjomri, “The Extended Graetz Problem for a Gaseous Slip Flow in Micropipe and Parallel-Plate Microchannel with Heating Section of Finite Length: Effects of Axial Conduction, Viscous Dissipation and Pressure Work," Int. J. Heat Mass Transfer80, 673–687 (2015).

  11. Y. Haddout, E. Essaghir, A. Oubarra, and J. Lahjomri, “Convective Heat Transfer for a Gaseous Slip Flow in Micropipe and Parallel-Plate Microchannel with Uniform Wall Heat Flux: Effect of Axial Heat Conduction," Indian J. Phys. 92, 741–755 (2018).

  12. O. Aydın and O. Avcı, “Analysis of Laminar Heat Transfer in Micro Poiseuille Flow," Int. J. Thermal Sci. 46, 30–37 (2007).

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Authors and Affiliations

  1. ERMAM, Ibn Zohr University, 638, Ouarzazate, Morocco

    Y. Haddout

  2. Hassan II University, 20100, Casablanca, Morocco

    A. Oubarra & J. Lahjomri

Authors
  1. Y. Haddout
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  2. A. Oubarra
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  3. J. Lahjomri
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Correspondence to Y. Haddout.

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Haddout, Y., Oubarra, A. & Lahjomri, J. GASEOUS SLIP FLOW FORCED CONVECTION IN A MICROPIPE AND PARALLEL-PLATE MICROCHANNEL WITH A PIECEWISE UNIFORM WALL HEAT FLUX AND AXIAL HEAT CONDUCTION. J Appl Mech Tech Phy 61, 945–954 (2020). https://doi.org/10.1134/S0021894420060061

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  • DOI: https://doi.org/10.1134/S0021894420060061

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