Heat Transfer of Hybrid Nanomaterials Base Maxwell Micropolar Fluid Flow over an Exponentially Stretching Surface
A numerical investigation of three-dimensional hybrid nanomaterial micropolar fluid flow across an exponentially stretched sheet is performed. Recognized similarity transformations are adopted to convert governing equations from PDEs into the set ODEs. The dimensionless system is settled by the oper...
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MDPI AG
2022-04-01
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| Series: | Nanomaterials |
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| Online Access: | https://www.mdpi.com/2079-4991/12/7/1207 |
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| author | Piyu Li Faisal Z. Duraihem Aziz Ullah Awan A. Al-Zubaidi Nadeem Abbas Daud Ahmad |
| author_facet | Piyu Li Faisal Z. Duraihem Aziz Ullah Awan A. Al-Zubaidi Nadeem Abbas Daud Ahmad |
| author_sort | Piyu Li |
| collection | DOAJ |
| description | A numerical investigation of three-dimensional hybrid nanomaterial micropolar fluid flow across an exponentially stretched sheet is performed. Recognized similarity transformations are adopted to convert governing equations from PDEs into the set ODEs. The dimensionless system is settled by the operating numerical approach bvp4c. The impacts of the nanoparticle volume fraction, dimensionless viscosity ratio, stretching ratio parameter, and dimensionless constant on fluid velocity, micropolar angular velocity, fluid temperature, and skin friction coefficient in both <i>x</i>-direction and <i>y</i>-direction are inspected. Graphical outcomes are shown to predict the features of the concerned parameters into the current problem. These results are vital in the future in the branches of technology and industry. The micropolar function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo> </mo><mi>R</mi><mfenced><mi>η</mi></mfenced></mrow></semantics></math></inline-formula> increases for higher values of the micropolar parameter and nanoparticle concentration. Micropolar function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mfenced><mi>η</mi></mfenced></mrow></semantics></math></inline-formula> declines for higher values of the micropolar parameter and nanoparticle concentration. Temperature function is enhanced for higher values of solid nanoparticle concentration. Temperature function declines for higher values of the micropolar parameter. The range of the physical parameters are presented as: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.005</mn><mo><</mo><msub><mi>ϕ</mi><mn>2</mn></msub><mo><</mo><mn>0.09</mn><mo>,</mo><mo> </mo><mi>P</mi><mi>r</mi><mo>=</mo><mn>6.2</mn><mo>,</mo><mo> </mo><mn>0</mn><mo><</mo><mi>K</mi><mo><</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>0</mn><mo><</mo><mi>a</mi><mo><</mo><mn>2.0</mn><mo>,</mo><mo> </mo><msub><mi>ϕ</mi><mn>1</mn></msub><mo>=</mo><mn>0.1</mn><mo>,</mo><mo> </mo><mi>and</mi><mo> </mo><mn>0</mn><mo><</mo><mi>c</mi><mo><</mo><mn>1.5</mn></mrow></semantics></math></inline-formula>. |
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| spelling | doaj.art-3fef90f33d1c4f60bfe5bcf698f2d2882023-11-30T23:46:01ZengMDPI AGNanomaterials2079-49912022-04-01127120710.3390/nano12071207Heat Transfer of Hybrid Nanomaterials Base Maxwell Micropolar Fluid Flow over an Exponentially Stretching SurfacePiyu Li0Faisal Z. Duraihem1Aziz Ullah Awan2A. Al-Zubaidi3Nadeem Abbas4Daud Ahmad5School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221018, ChinaDepartment of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, University of the Punjab, Lahore 54590, PakistanDepartment of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi ArabiaDepartment of Mathematics, Quaid-I-Azam University Islamabad 44000, PakistanDepartment of Mathematics, University of the Punjab, Lahore 54590, PakistanA numerical investigation of three-dimensional hybrid nanomaterial micropolar fluid flow across an exponentially stretched sheet is performed. Recognized similarity transformations are adopted to convert governing equations from PDEs into the set ODEs. The dimensionless system is settled by the operating numerical approach bvp4c. The impacts of the nanoparticle volume fraction, dimensionless viscosity ratio, stretching ratio parameter, and dimensionless constant on fluid velocity, micropolar angular velocity, fluid temperature, and skin friction coefficient in both <i>x</i>-direction and <i>y</i>-direction are inspected. Graphical outcomes are shown to predict the features of the concerned parameters into the current problem. These results are vital in the future in the branches of technology and industry. The micropolar function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo> </mo><mi>R</mi><mfenced><mi>η</mi></mfenced></mrow></semantics></math></inline-formula> increases for higher values of the micropolar parameter and nanoparticle concentration. Micropolar function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mfenced><mi>η</mi></mfenced></mrow></semantics></math></inline-formula> declines for higher values of the micropolar parameter and nanoparticle concentration. Temperature function is enhanced for higher values of solid nanoparticle concentration. Temperature function declines for higher values of the micropolar parameter. The range of the physical parameters are presented as: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.005</mn><mo><</mo><msub><mi>ϕ</mi><mn>2</mn></msub><mo><</mo><mn>0.09</mn><mo>,</mo><mo> </mo><mi>P</mi><mi>r</mi><mo>=</mo><mn>6.2</mn><mo>,</mo><mo> </mo><mn>0</mn><mo><</mo><mi>K</mi><mo><</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>0</mn><mo><</mo><mi>a</mi><mo><</mo><mn>2.0</mn><mo>,</mo><mo> </mo><msub><mi>ϕ</mi><mn>1</mn></msub><mo>=</mo><mn>0.1</mn><mo>,</mo><mo> </mo><mi>and</mi><mo> </mo><mn>0</mn><mo><</mo><mi>c</mi><mo><</mo><mn>1.5</mn></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2079-4991/12/7/1207boundary layer flowmicropolar hybrid nanofluidexponential stretching surfacenumerical technique |
| spellingShingle | Piyu Li Faisal Z. Duraihem Aziz Ullah Awan A. Al-Zubaidi Nadeem Abbas Daud Ahmad Heat Transfer of Hybrid Nanomaterials Base Maxwell Micropolar Fluid Flow over an Exponentially Stretching Surface Nanomaterials boundary layer flow micropolar hybrid nanofluid exponential stretching surface numerical technique |
| title | Heat Transfer of Hybrid Nanomaterials Base Maxwell Micropolar Fluid Flow over an Exponentially Stretching Surface |
| title_full | Heat Transfer of Hybrid Nanomaterials Base Maxwell Micropolar Fluid Flow over an Exponentially Stretching Surface |
| title_fullStr | Heat Transfer of Hybrid Nanomaterials Base Maxwell Micropolar Fluid Flow over an Exponentially Stretching Surface |
| title_full_unstemmed | Heat Transfer of Hybrid Nanomaterials Base Maxwell Micropolar Fluid Flow over an Exponentially Stretching Surface |
| title_short | Heat Transfer of Hybrid Nanomaterials Base Maxwell Micropolar Fluid Flow over an Exponentially Stretching Surface |
| title_sort | heat transfer of hybrid nanomaterials base maxwell micropolar fluid flow over an exponentially stretching surface |
| topic | boundary layer flow micropolar hybrid nanofluid exponential stretching surface numerical technique |
| url | https://www.mdpi.com/2079-4991/12/7/1207 |
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