Modelling of Thin CNTs Nanoliquid Film Flow Over a Bi-directional Stretching Surface
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Modelling of Thin CNTs Nanoliquid Film Flow Over a Bi-directional Stretching Surface R. Krishanan1 · S. Maity1 · S. K. Singh2 · B. S. Dandapat3 Accepted: 12 September 2020 © Springer Nature India Private Limited 2020
Abstract Unsteady flow of water and ethylene-glycol based carbon nanotubes (CNTs) nanoliquid film is examined on a bi-directional stretching surface under influence of transverse magnetic field and thermal radiation. Single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) are considered within the base liquid for investigation. Guiding full Navier–Stokes and energy equations were simplified using the thin film approximations and solved using the method of the asymptotic expansion. The result shows that nanoliquid thinning rate diminishes with rising values of CNTs volume fraction, Hartmann number and Biot number. The result also indicates that the thinning rate is more for MWCNTs with reference to the SWCNTs. It is seen that film thinning rate enhances for water-MWCNTs nanoliquid but reverse scenario is found for ethylene-glycol MWCNTs nanoliquid. The effect of various physical parameters on temperature profile has been discussed. Keywords Thin film · Nanoliquid · Carbon Nanotubes (CNTs) · Magnetic field · Thermal radiation · Bi-directional stretching
Introduction In recent years, nanofluids have gained the huge attention of many researchers from different fields. Nanofluid is a colloidal suspension of nanometer size metallic or non-metallic particles (average sizes of 1–100 nm) with the ordinary heat transfer fluid. The ordinary heat transfer fluids are water, oil, ethylene glycol etc. and these fluids have poor thermal performance. The heat conductivity efficiency of nanofluids is much higher than the ordinary heat transfer fluids in presence of nanoparticles. For this reason, nanoliquids are used extensively in microelectronics industries, in solar technology, in cooling towers etc. Choi [1] first reported
B
S. Maity [email protected]
1
Department of Basic and Applied Science, National Institute of Technology, Yupia, Papumpare, Arunachal Pradesh 791112, India
2
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, Jakkur 560064, India
3
Air Control Engineering Pvt. Ltd., 21 Hemanta Bose Sarani, Kolkata 700001, India 0123456789().: V,-vol
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the anomalous increase of thermal conductivity of nanofluids. Eastman et al. [2] observed the abnormal increase of thermal conductivity of ethylene-glycol-Cu nanofluid. After that, detailed mechanism for rising of thermal conductivity of the nanofluids was presented by Masuda et al. [3], Xuan and Li [4], Buongiorno [5], Kakac and Pramuanjaroenkij [6] etc. The carbon nanotubes (CNTs) are hollow cylindrical structure of carbon atoms (nanometer size diameter). They demonstrated many useful properties like higher thermal and electrical conductivities, higher mechanical strength and higher aspect ratio (length/diameter =
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