Double solutions and stability analysis of slip flow past a stretching/shrinking sheet in a carbon nanotube

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dc.citation.epage824
dc.citation.issue4
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage816
dc.contributor.affiliationУніверситет Путра Малайзія
dc.contributor.affiliationUniversiti Putra Malaysia
dc.contributor.authorНорзавари, Н. Х. А.
dc.contributor.authorБачок, Н.
dc.contributor.authorАлі, Ф. М.
dc.contributor.authorРахмін, Н. А. А.
dc.contributor.authorNorzawary, N. H. A.
dc.contributor.authorBachok, N.
dc.contributor.authorAli, F. M.
dc.contributor.authorRahmin, N. A. A.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-24T09:14:11Z
dc.date.created2022-02-28
dc.date.issued2022-02-28
dc.description.abstractУ цій статті досліджується потік через точку застою поверхні, що розтягується/стискається, у вуглецевих нанотрубках (ВНТ) з ефектами ковзання. Застосовуючи перетворення подібності, основні диференціальні рівняння в частинних похідних модифікуються, щоб отримати нелінійні звичайні диференціальні рівняння. Потім вони чисельно розв’язуються в Matlab за допомогою розв’язувача bvp4c. Застосовуються одностінні та багатостінні ВНТ; вода слугує базовою рідиною. Досліджено вплив параметрів потоку, який продемонстровано у вигляді графіків і фізично оцінено для таких величин: безрозмірна швидкість, температура, поверхневе тертя та числа Нуссельта. Згідно з отриманими даними, однозначні розв’язки існують для листів, що розтягуються, тоді як для листів, що стискаються, отримано неоднозначні розв’язки. Аналіз стійкості застосовується, щоб визначити, який розв’язок є стійким.
dc.description.abstractA stagnation point flow past a stretching/shrinking surface in carbon nanotubes (CNTs) with slip effects is investigated in this paper. Applying transformations of similarity, the governing partial differential equations are modified to the nonlinear ordinary differential equations. Afterward, they are numerically solved in Matlab by the bvp4c solver. The single-wall CNTs and multi-wall CNTs are used, including water as a base fluid. The effects of the flow parameters are investigated, shown in the form of graphs, and physically evaluated for the dimensionless velocity, temperature, skin friction, and Nusselt numbers. According to our findings, the unique solution exists for stretching sheets, whereas non-unique solutions are obtainable for shrinking sheets. The stability analysis is utilized to discover which solution is stable.
dc.format.extent816-824
dc.format.pages9
dc.identifier.citationDouble solutions and stability analysis of slip flow past a stretching/shrinking sheet in a carbon nanotube / N. H. A. Norzawary, N. Bachok, F. M. Ali, N. A. A. Rahmin // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 4. — P. 816–824.
dc.identifier.citationenDouble solutions and stability analysis of slip flow past a stretching/shrinking sheet in a carbon nanotube / N. H. A. Norzawary, N. Bachok, F. M. Ali, N. A. A. Rahmin // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 4. — P. 816–824.
dc.identifier.doidoi.org/10.23939/mmc2022.04.816
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/64239
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 4 (9), 2022
dc.relation.ispartofMathematical Modeling and Computing, 4 (9), 2022
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dc.relation.references[16] Othman M. N., Jedi A., Bakar N. A. A. MHD Stagnation Point on Nanofluid Flow and Heat Transfer of Carbon Nanotube over a Shrinking Surface with Heat Sink Effect. Molecules. 26 (24), 7441 (2021).
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dc.relation.references[23] Bachok N., Ishak A., Pop I. Stagnation-point flow over a stretching/shrinking sheet in a nanofluid. Nanoscale Research Letters. 6, 623 (2011).
dc.relation.references[24] Oztop H. F., Abu–Nada E. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International Journal of Heat and Fluid Flow. 29 (5), 1326–1336 (2008).
dc.relation.references[25] Xue Q. Z. Model of thermal conductivity of carbon nanotube-based composites. Physica B: Condensed Matter. 368 (1–4), 302–307 (2005).
dc.relation.references[26] Anuar N. S., Bachok N., Arifin N. M., Rosali H. MHD flow past a nonlinear stretching/shrinking sheet in carbon nanotubes: Stability analysis. Chinese Journal of Physics. 65, 436–446 (2020).
dc.relation.references[27] Anuar N. S., Bachok N., Turkyilmazoglu M., Arifin N. M., Rosali H. Analytical and stability analysis of MHD flow past a nonlinearly deforming vertical surface in Carbon Nanotubes. Alexandria Engineering Journal. 59 (1), 497–507 (2020).
dc.relation.references[28] Banerjee A., Bhattacharyya K., Mahato S. K., Chamka A. J. Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H2O nanofluid on a flat surface in a porous medium: A stability analysis. Chinese Physics B. 31 (4), 044701 (2022).
dc.relation.references[29] Weidman P. D., Kubitschek D. G., Davis A. M. J. The effect of transpiration on self-similiar boundary layer flow over moving surfaces. International Journal of Engineering Science. 44 (11–12), 730–737 (2006).
dc.relation.references[30] Harris S. D., Ingham D. B., Pop I. Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transport in Porous Media. 77, 267–285 (2009).
dc.relation.referencesen[1] Hiemenz K. Die Grenzchicht an einem in den gleichfromigen Flussigkeitsstrom eingetauchten geraden Kreiszylinder. Dingler’s Polytech J. 326, 321–324 (1911).
dc.relation.referencesen[2] Homann F. Der Einfluß grosser Z¨ahigkeit bei der Str¨omung um den Zylinder und um die Kugel. Zeutschrift f¨ur Angewandte Mathematik und Mechanik. 16, 153–164 (1936).
dc.relation.referencesen[3] Mahapatra T. R., Gupta A. S. Heat transfer in stagnation-point flow towards a stretching sheet. Heat Mass Transfer. 38, 517–521 (2002).
dc.relation.referencesen[4] Mahapatra T. R., Gupta A. S. Stagnation-point flow towards a stretching surface. The Canadian Journal of Chemical Engineering. 81 (2), 258–263 (2003).
dc.relation.referencesen[5] Crane L. J. Flow Past a Stretching Plate. Zeitschrift f¨ur angewandte Mathematik und Physik. 21, 645–647 (1970).
dc.relation.referencesen[6] Khan A. V., Pop I. Boundary-layer flow of a nanofluid past a stretching sheet. International Journal of Heat and Mass Transfer. 53 (11–12), 2477–2483 (2010).
dc.relation.referencesen[7] Nadeem S., Khan M. R., Khan A. U. MHD oblique stagnation point flow of nanofluid over an oscillatory stretching/shrinking sheet: existence of dual solutions. Physica Scripta. 94 (7), 075204 (2019).
dc.relation.referencesen[8] Nadeem S., Rehman M. I., Saleem S., Bonyah E. Dual solutions in MHD stagnation point flow of nanofluid induced by porous stretching/shrinking sheet with anisotropic slip. AIP Advances. 10 (6), 065207 (2020).
dc.relation.referencesen[9] Zainal N. A., Nazar R., Naganthran K., Pop I. Unsteady Stagnation Point Flow of Hybrid Nanofluid Past a Convectively Heated Stretching/Shrinking Sheet with Velocity Slip. Mathematics. 8 (10), 1649 (2020).
dc.relation.referencesen[10] Choi S. U. S., Eastman J. A. Enhancing thermal conductivity of fluids with nanoparticles. ASME Publ.-Fed. 231, 99–106 (1995).
dc.relation.referencesen[11] Choi S. U. S., Zhang Z. G., Yu W., Lockwood F. E., Grulke E. A. Anomalous thermal conductivity enhancement in nanotube suspensions. Applied Physics Letters. 79 (14), 2252–2254 (2001).
dc.relation.referencesen[12] Mare T., Halelfadl S., Sow O., Estelle P., Duret S., Bazantay F. Comparison of the thermal performances of two nanofluids at low temperature in a plate heat exchanger. Experimental Thermal and Fluid Science. 35 (8), 1535–1543 (2011).
dc.relation.referencesen[13] Liu M. S., Lin M. C. C., Huang I. T., Wang C. C. Enhancement of thermal conductivity with carbon nanotube for nanofluids. International Communications in
dc.relation.referencesen[14] Sreedevi P., Reddy P. S., Chamka A. J. Magneto-hydrodynamics heat and mass transfer analysis of single and multi-wall carbon nanotubes over vertical cone with convective boundary condition. International Journal of Mechanical Sciences. 135, 646–655 (2018).
dc.relation.referencesen[15] Norzawary N. H. A., Bachok N., Ali F. M. Stagnation Point Flow over a Stretching/Shrinking Sheet in a Carbon Nanotubes with Suction/Injection Effects. CFD Letters. 20 (2), 106–114 (2020).
dc.relation.referencesen[16] Othman M. N., Jedi A., Bakar N. A. A. MHD Stagnation Point on Nanofluid Flow and Heat Transfer of Carbon Nanotube over a Shrinking Surface with Heat Sink Effect. Molecules. 26 (24), 7441 (2021).
dc.relation.referencesen[17] Bhattacharyya K., Mukhopadhyay S., Layek G. C. Steady boundary layer slip flow and heat transfer over a flat porous plate embedded in a porous media. Journal of Petroleum Science and Engineering. 78 (2), 304–309 (2011).
dc.relation.referencesen[18] Bhattacharyya K., Layek G. C., Gorla R. S. R. Slip effect on boundary layer flow on a moving flat plate in a parallel free stream. International Journal of Fluid Mechanics Research. 39 (5), 438–447 (2012).
dc.relation.referencesen[19] Khan W. A., Khan Z. H., Rahi M. Fluid flow and heat transfer of carbon nanotubes along a flat plate with Navier slip boundary. Applied Nanoscience. 4, 633–641 (2014).
dc.relation.referencesen[20] Bachok N., Najib N., Ariffin N. M., Senu N. Stability of dual solutions in boundary layer flow and heat transfer on a moving plate in a copper-water nanofluid with slip effect. WSEAS Transactions on Fluid Mechanics. 11, 151–158 (2016).
dc.relation.referencesen[21] Najib N., Bachok N., Ariffin N. M., Senu N. Boundary layer flow and heat transfer of nanofluids over a moving plate with partial slip and thermal convective boundary condition:stability analysis. International Journal of Mechanic. 11, 18–24 (2016).
dc.relation.referencesen[22] Anuar N. S., Bachok N., Pop I. A stability analysis of solutions in boundary layer flow and heat transfer of carbon nanotubes over a moving plate with slip effect. Energies. 11 (12), 3243 (2018).
dc.relation.referencesen[23] Bachok N., Ishak A., Pop I. Stagnation-point flow over a stretching/shrinking sheet in a nanofluid. Nanoscale Research Letters. 6, 623 (2011).
dc.relation.referencesen[24] Oztop H. F., Abu–Nada E. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International Journal of Heat and Fluid Flow. 29 (5), 1326–1336 (2008).
dc.relation.referencesen[25] Xue Q. Z. Model of thermal conductivity of carbon nanotube-based composites. Physica B: Condensed Matter. 368 (1–4), 302–307 (2005).
dc.relation.referencesen[26] Anuar N. S., Bachok N., Arifin N. M., Rosali H. MHD flow past a nonlinear stretching/shrinking sheet in carbon nanotubes: Stability analysis. Chinese Journal of Physics. 65, 436–446 (2020).
dc.relation.referencesen[27] Anuar N. S., Bachok N., Turkyilmazoglu M., Arifin N. M., Rosali H. Analytical and stability analysis of MHD flow past a nonlinearly deforming vertical surface in Carbon Nanotubes. Alexandria Engineering Journal. 59 (1), 497–507 (2020).
dc.relation.referencesen[28] Banerjee A., Bhattacharyya K., Mahato S. K., Chamka A. J. Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H2O nanofluid on a flat surface in a porous medium: A stability analysis. Chinese Physics B. 31 (4), 044701 (2022).
dc.relation.referencesen[29] Weidman P. D., Kubitschek D. G., Davis A. M. J. The effect of transpiration on self-similiar boundary layer flow over moving surfaces. International Journal of Engineering Science. 44 (11–12), 730–737 (2006).
dc.relation.referencesen[30] Harris S. D., Ingham D. B., Pop I. Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transport in Porous Media. 77, 267–285 (2009).
dc.rights.holder© Національний університет “Львівська політехніка”, 2022
dc.subjectвуглецеві нанотрубки
dc.subjectподвійні розв’язки
dc.subjectпотік точки застою
dc.subjectрозтягування/стискання листа
dc.subjectефекти ковзання
dc.subjectаналіз стійкості
dc.subjectcarbon nanotube
dc.subjectdual solutions
dc.subjectstagnation point flow
dc.subjectstretching/shrinking sheet
dc.subjectslip effects
dc.subjectstability analysis
dc.titleDouble solutions and stability analysis of slip flow past a stretching/shrinking sheet in a carbon nanotube
dc.title.alternativeПодвійні розв’язки та аналіз стійкості ковзаючого обтікання листа, що розтягується/стискається, у вуглецевих нанотрубках
dc.typeArticle

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Mathematical Modeling And Computing. – 2022. – Vol. 9, No. 4