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Title: | Analytical solution of thermally developing microtube heat transfer including axial conduction, viscous dissipation, and rarefaction effects | Authors: | Barışık, Murat Yazıcıoğlu, Almıla Güvenç Çetin, Barbaros Kakaç, Sadık |
Keywords: | Extended Graetz problem Axial conduction Micropipe heat transfer Rarefaction effect Slip flow Viscous dissipation |
Publisher: | Elsevier Ltd. | Source: | Barışık, M., Yazıcıoğlu, A.G., Çetin, B., and Kakaç, S. (2015). Analytical solution of thermally developing microtube heat transfer including axial conduction, viscous dissipation, and rarefaction effects. International Communications in Heat and Mass Transfer, 67, 81-88. doi:10.1016/j.icheatmasstransfer.2015.05.004 | Abstract: | 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. | URI: | https://doi.org/10.1016/j.icheatmasstransfer.2015.05.004 http://hdl.handle.net/11147/5840 |
ISSN: | 0735-1933 0735-1933 |
Appears in Collections: | Mechanical Engineering / Makina Mühendisliği Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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