Analytical solution of thermally developing microtube heat transfer including axial conduction, viscous dissipation, and rarefaction effects

2015-10
Barışık, Murat
Yazıcıoğlu, Almıla Güvenç
Çetin, Barbaros
Kakaç, Sadık
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The solution of extended Graetz problem for micro-scale gas flows is performed by coupling of rarefaction, axial conduction and viscous dissipation at slip flow regime. The analytical coupling achieved by using Gram-Schmidt orthogonalization technique provides interrelated appearance of corresponding effects through the variation of non-dimensional numbers. The developing temperature field is determined by solving the energy equation locally together with the fully developed flow profile. Analytical solutions of local temperature distribution, and local and fully developed Nusselt number are obtained in terms of dimensionless parameters: Peclet number, Knudsen number, Brinkman number, and the parameter Kappa accounting temperature-jump. The results indicate that the Nusselt number decreases with increasing Knudsen number as a result of the increase of temperature jump at the wall. For low Peclet number values, temperature gradients and the resulting temperature jump at the pipe wall cause Knudsen number to develop higher effect on flow. Axial conduction should not be neglected for Peclet number values less than 100 for all cases without viscous dissipation, and for short pipes with viscous dissipation. The effect of viscous heating should be considered even for small Brinkman number values with large length over diameter ratios. For a fixed Kappa value, the deviation from continuum increases with increasing rarefaction, and Nusselt number values decrease with an increase in Knudsen number.
Atomic and Molecular Physics, and Optics, General Chemical Engineering, Condensed Matter Physics, Extended Graetz problem, Micropipe heat transfer, Slip flow, Rarefaction effect, Axial conduction, Viscous dissipation
https://hdl.handle.net/11511/52341
International Communications in Heat and Mass Transfer
Department of Mechanical Engineering, Article

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Citation Formats
M. Barışık, A. G. Yazıcıoğlu, B. Çetin, and S. Kakaç, “Analytical solution of thermally developing microtube heat transfer including axial conduction, viscous dissipation, and rarefaction effects,” International Communications in Heat and Mass Transfer, pp. 81–88, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52341.
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