Abstract
This paper investigates the isothermal calendering process for Sutterby fluid model. Lubrication approximation theory (LAT) is used for the simplification of the governing equations. The perturbation technique is utilized to find the system solution. The zeroth-order and first-order solutions of velocity profile, sheet thickness, pressure gradient and pressure are obtained while numerical solution of other mechanical quantities is evaluated. The values of the parameters influencing the different flow and engineering parameters are obtained through graphs and in a tabular manner. It is observed that the material parameter mainly controls the sheet thickness, roll separating force, flow rate, power input, exiting sheet thickness, and pressure distribution. It is to be noted from the results that with the increase in the material parameter, the sheet thickness and power input increase while roll separating force decreases.
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
1. Gaskell, R. E. The calendering of plastic materials. J. Appl. Mech. 1950, 17, 334–336. https://doi.org/10.1115/1.4010136.Search in Google Scholar
2. McKelvey, J. M. Polymer Processing; Wiley: New York, 1962. Chap. 9.Search in Google Scholar
3. Brazinsky, I., Cosway, H. F., Valle, C. F.Jr, Jones, R. C., Story, V. A theoretical study of liquid-film spread heights in the calendering of Newtonian and power law fluids. J. Appl. Polym. Sci. 1970, 14, 2771–2784. https://doi.org/10.1002/app.1970.070141111.Search in Google Scholar
4. Alston, W. W.Jr, Astill, K. N. An analysis for the calendering of non-Newtonian fluids. J. Appl. Polym. Sci. 1973, 17, 3157–3174. https://doi.org/10.1002/app.1973.070171018.Search in Google Scholar
5. Gruber, U., Mewes, D. Theoretische Untersuchung des Kalandrierens von Polymeren/Theoretical examination of the calendering of polymers. Appl. Rheol. 1991, 1, 152–159. https://doi.org/10.2478/arh-1991-010308.Search in Google Scholar
6. Middleman, S. Fundamentals of Polymer Processing; McGraw-Hill: New York, 1977.Search in Google Scholar
7. Tadmor, Z., Gogos, C. G. Principles of Polymer Processing; Wiley: New York, 2013.Search in Google Scholar
8. Yu, J. S., Lee, J. W., Lee, K. J. Analysis and simulation of calendering process of non-Newtonian polymeric fluids. Kor. J. Chem. Eng. 1984, 1, 173–180. https://doi.org/10.1007/bf02697450.Search in Google Scholar
9. Zheng, R., Tanner, R. I. A numerical analysis of calendering. J. Non-Newtonian Fluid Mech. 1988, 28, 149–170. https://doi.org/10.1016/0377-0257(88)85037-7.Search in Google Scholar
10. Sofou, S., Mitsoulis, E. Calendering of pseudoplastic and viscoplastic sheets of finite thickness. J. Plastic Film Sheeting 2004, 20, 185–222. https://doi.org/10.1177/8756087904047660.Search in Google Scholar
11. Mitsoulis, E., Sofou, S. Calendering pseudoplastic and viscoplastic fluids with slip at the roll surface. J. Appl. Mech. 2006, 73, 291–299. https://doi.org/10.1115/1.2083847.Search in Google Scholar
12. Méndez, F. Variable viscosity effects on calendering viscoplastic fluids. Mec. Comput. 2010, 29, 5449–5460.Search in Google Scholar
13. Arcos, J. C., Bautista, O., Méndez, F., Bautista, E. G. Theoretical analysis of the calendered exiting thickness of viscoelastic sheets. J. Non-Newtonian Fluid Mech. 2012, 177, 29–36. https://doi.org/10.1016/j.jnnfm.2012.04.004.Search in Google Scholar
14. Hernández, A., Arcos, J., Méndez, F., Bautista, O. Effect of pressure-dependent viscosity on the exiting sheet thickness in the calendering of Newtonian fluids. Appl. Math. Model. 2013, 37, 6952–6963.10.1115/IMECE2012-87725Search in Google Scholar
15. Sajid, M., Siddique, H., Ali, N., Javed, M. A. Calendering of non-isothermal Rabinowitsch fluid. J. Polym. Eng. 2018, 38, 83–92. https://doi.org/10.1515/polyeng-2016-0294.Search in Google Scholar
16. Ali, N., Atif, H. M., Javed, M. A., Sajid, M. A mathematical model of the calendered exiting thickness of micropolar sheet. Polym. Eng. Sci. 2018, 58, 327–334. https://doi.org/10.1002/pen.24578.Search in Google Scholar
17. Khaliq, S., Abbas, Z. A theoretical analysis of roll-over-web coating assessment of viscous nanofluid containing Cu-water nanoparticles. J. Plastic Film Sheeting 2020, 36, 55–75. https://doi.org/10.1177/8756087919866485.Search in Google Scholar
18. Abbas, Z., Khaliq, S. Calendering analysis of non-isothermal viscous nanofluid containing Cu-water nanoparticles using two counter-rotating rolls. J. Plastic Film Sheeting 2021, 37, 182–204. https://doi.org/10.1177/8756087920951614.Search in Google Scholar
19. Khaliq, S., Abbas, Z. Analysis of calendering process of non-isothermal flow of non-Newtonian fluid: a perturbative and numerical study. J. Plastic Film Sheeting 2021, 37, 338–366. https://doi.org/10.1177/8756087920979024.Search in Google Scholar
20. Javed, M. A., Ali, N., Arshad, S., Shamshad, S. Numerical approach for the calendering process using Carreau-Yasuda fluid model. J. Plastic Film Sheeting 2021, 37, 312–337. https://doi.org/10.1177/8756087920988748.Search in Google Scholar
21. Khaliq, S., Abbas, Z. Non-isothermal blade coating analysis of viscous fluid with temperature-dependent viscosity using lubrication approximation theory. J. Polym. Eng. 2021, 41, 705–716. https://doi.org/10.1515/polyeng-2021-0087.Search in Google Scholar
22. Abbas, Z., Khaliq, S. Numerical study of non-isothermal analysis of exiting sheet thickness in the calendering of micropolar-Casson fluid. J. Plastic Film Sheeting 2022, 38, 105–129. https://doi.org/10.1177/87560879211025080.Search in Google Scholar
23. Akbar, N. S., Nadeem, S. Nano Sutterby fluid model for the peristaltic flow in small intestines. J. Comput. Theor. Nanosci. 2013, 10, 2491–2499. https://doi.org/10.1166/jctn.2013.3238.Search in Google Scholar
24. Azhar, E., Iqbal, Z., Maraj, E. N. Impact of entropy generation on stagnation-point flow of sutterby nanofluid: a numerical analysis. Z. Naturforsch. 2016, 71, 837–848. https://doi.org/10.1515/zna-2016-0188.Search in Google Scholar
25. Hayat, T., Zahir, H., Mustafa, M., Alsaedi, A. Peristaltic flow of Sutterby fluid in a vertical channel with radiative heat transfer and compliant walls: a numerical study. Res. Phy. 2016, 6, 805–810. https://doi.org/10.1016/j.rinp.2016.10.015.Search in Google Scholar
26. Hayat, T., Alsaedi, A., Rafiq, M., Ahmad, B. Joule heating and thermal radiation effects on peristalsis in curved configuration. Res. Phy. 2016, 6, 1088–1095. https://doi.org/10.1016/j.rinp.2016.11.044.Search in Google Scholar
27. Hayat, T., Masood, F., Qayyum, S., Alsaedi, A. Sutterby fluid flow subject to homogeneous–heterogeneous reactions and nonlinear radiation. Phys. A 2020, 544, 123439. https://doi.org/10.1016/j.physa.2019.123439.Search in Google Scholar
28. Imran, N., Javed, M., Sohail, M., Thounthong, P., Abdelmalek, Z. Theoretical exploration of thermal transportation with chemical reactions for sutterby fluid model obeying peristaltic mechanism. J. Mater. Res. Technol. 2020, 9, 7449–7459. https://doi.org/10.1016/j.jmrt.2020.04.071.Search in Google Scholar
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