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Zero-dimensional model for the prediction of carbon nanotube (CNT) growth region in heterogeneous methane-flame environment

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Abstract

The conventional multi-scale modelling approach that predicts carbon nanotube (CNT) growth region in heterogeneous flame environment is computationally exhaustive. Thus, the present study is the first attempt to develop a zero-dimensional model based on existing multi-scale model where mixture fraction z and the stoichiometric mixture fraction \(z_{st}\) are employed to correlate burner operating conditions and CNT growth region for diffusion flames. Baseline flame models for inverse and normal diffusion flames are first established with satisfactory validation of the flame temperature and growth region prediction at various operating conditions. Prior to developing the correlation, investigation on the effects of \(z_{st}\) on CNT growth region is carried out for 17 flame conditions with \(z_{st}\) of 0.05 to 0.31. The developed correlation indicates linear (\(z_{lb}\)=1.54\(z_{st}\)+0.11) and quadratic (\(z_{hb}\)=\(z_{st}\)(7-13\(z_{st}\))) models for the \(z_{lb}\) and \(z_{hb}\) corresponding to the low and high boundaries of mixture fraction, respectively, where both parameters dictate the range of CNT growth rate (GR) in the mixture fraction space. Based on the developed correlations, the CNT growth in mixture fraction space is optimum in the flame with medium-range \(z_{st}\) conditions between 0.15 and 0.25. The stronger relationship between growth-region mixture-fraction (GRMF) and \(z_{st}\) at the near field region close to the flame sheet compared to that of the far field region away from the flame sheet is due to the higher temperature gradient at the former region compared to that of the latter region. The developed models also reveal three distinct regions that are early expansion, optimum, and reduction of GRMF at varying \(z_{st}\).

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Acknowledgements

This research was supported by Ministry of Education (MOE) through the Fundamental Research Grant Scheme (FRGS/1/2020/TK0/UTM/02/54) with cost center number R.J130000.7851.5F377. The research is also funded by Universiti Teknologi Malaysia (UTM) through UTM Fundamental Research (UTMFR: PY/2019/01657) grant with cost center number Q.J130 0 0 0.2551.21H10.

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Author notes

  1. Muhammad Thalhah Zainal, Norikhwan Hamzah, Mazlan Abdul Wahid, Natrah Kamaruzaman, Cheng Tung Chong, Mohd Hanafi Ani, Shokri Amzin, Tarit Das and Mohd Fairus Mohd Yasin are contributed equally to this work.

Authors and Affiliations

  1. Department of Thermo-Fluids, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310, Skudai, Malaysia

    Norikhwan Hamzah, Mazlan Abdul Wahid, Natrah Kamaruzaman, Tarit Das & Mohd Fairus Mohd Yasin

  2. China-UK Low Carbon College, Shanghai Jiao Tong University, Lingang, Shanghai, 201306, China

    Cheng Tung Chong

  3. Department of Manufacturing and Materials, Kuliyyah of Engineering, International Islamic University Malaysia, P. O. Box 10, 50728, Kuala Lumpur, Malaysia

    Mohd Hanafi Ani

  4. Department of Mechanical and Marine Engineering, Western Norway University of Applied Sciences (HVL), N5020, Bergen, Norway

    Shokri Amzin

  5. High Speed Reacting Flow Laboratory (HiREF), Universiti Teknologi Malaysia, 81310, Skudai, Malaysia

    Muhammad Thalhah Zainal, Norikhwan Hamzah, Mazlan Abdul Wahid, Natrah Kamaruzaman & Mohd Fairus Mohd Yasin

  6. Malaysia – Japan International Institute of Technology (MJIIT), Universiti Teknologi Malaysia, Jalan Sultan Yahya Petra (Jalan Semarak), 54100, Kuala Lumpur, Malaysia

    Muhammad Thalhah Zainal

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  1. Muhammad Thalhah Zainal
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Zainal, M.T., Hamzah, N., Abdul Wahid, M. et al. Zero-dimensional model for the prediction of carbon nanotube (CNT) growth region in heterogeneous methane-flame environment. Carbon Lett. 33, 2199–2210 (2023). https://doi.org/10.1007/s42823-023-00579-z

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