Application of fractional differential equations to heat transfer in hybrid nanofluid: modeling and solution via integral transforms

Abstract This article deals with the generalization of natural convection flow of Cu−Al2O3−H2O $Cu - Al_{2}O_{3} - H_{2}O$ hybrid nanofluid in two infinite vertical parallel plates. To demonstrate the flow phenomena in two parallel plates of hybrid nanofluids, the Brinkman type fluid model together...
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Autor*in:	Muhammad Saqib [verfasserIn] Ilyas Khan [verfasserIn] Sharidan Shafie [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Applications of fractional derivatives Heat transfer problem Modeling and simulation Hybrid nanofluid

Übergeordnetes Werk:	In: Advances in Difference Equations - SpringerOpen, 2006, (2019), 1, Seite 18
Übergeordnetes Werk:	year:2019 ; number:1 ; pages:18

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1186/s13662-019-1988-5

Katalog-ID:	DOAJ038687909

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allfields	10.1186/s13662-019-1988-5 doi (DE-627)DOAJ038687909 (DE-599)DOAJ26365e5db0bf4bc89b59abae520804d0 DE-627 ger DE-627 rakwb eng QA1-939 Muhammad Saqib verfasserin aut Application of fractional differential equations to heat transfer in hybrid nanofluid: modeling and solution via integral transforms 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This article deals with the generalization of natural convection flow of Cu−Al2O3−H2O $Cu - Al_{2}O_{3} - H_{2}O$ hybrid nanofluid in two infinite vertical parallel plates. To demonstrate the flow phenomena in two parallel plates of hybrid nanofluids, the Brinkman type fluid model together with the energy equation is considered. The Caputo–Fabrizio fractional derivative and the Laplace transform technique are used to developed exact analytical solutions for velocity and temperature profiles. The general solutions for velocity and temperature profiles are brought into light through numerical computation and graphical representation. The obtained results show that the velocity and temperature profiles show dual behaviors for 0<α<1 $0 < \alpha < 1$ and 0<β<1 $0 < \beta < 1$ where α and β are the fractional parameters. It is noticed that, for a shorter time, the velocity and temperature distributions decrease with increasing values of the fractional parameters, whereas the trend reverses for a longer time. Moreover, it is found that the velocity and temperature profiles oppositely behave for the volume fraction of hybrid nanofluids. Applications of fractional derivatives Heat transfer problem Modeling and simulation Hybrid nanofluid Mathematics Ilyas Khan verfasserin aut Sharidan Shafie verfasserin aut In Advances in Difference Equations SpringerOpen, 2006 (2019), 1, Seite 18 (DE-627)377755699 (DE-600)2132815-8 16871847 nnns year:2019 number:1 pages:18 https://doi.org/10.1186/s13662-019-1988-5 kostenfrei https://doaj.org/article/26365e5db0bf4bc89b59abae520804d0 kostenfrei http://link.springer.com/article/10.1186/s13662-019-1988-5 kostenfrei https://doaj.org/toc/1687-1847 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 1 18
spelling	10.1186/s13662-019-1988-5 doi (DE-627)DOAJ038687909 (DE-599)DOAJ26365e5db0bf4bc89b59abae520804d0 DE-627 ger DE-627 rakwb eng QA1-939 Muhammad Saqib verfasserin aut Application of fractional differential equations to heat transfer in hybrid nanofluid: modeling and solution via integral transforms 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This article deals with the generalization of natural convection flow of Cu−Al2O3−H2O $Cu - Al_{2}O_{3} - H_{2}O$ hybrid nanofluid in two infinite vertical parallel plates. To demonstrate the flow phenomena in two parallel plates of hybrid nanofluids, the Brinkman type fluid model together with the energy equation is considered. The Caputo–Fabrizio fractional derivative and the Laplace transform technique are used to developed exact analytical solutions for velocity and temperature profiles. The general solutions for velocity and temperature profiles are brought into light through numerical computation and graphical representation. The obtained results show that the velocity and temperature profiles show dual behaviors for 0<α<1 $0 < \alpha < 1$ and 0<β<1 $0 < \beta < 1$ where α and β are the fractional parameters. It is noticed that, for a shorter time, the velocity and temperature distributions decrease with increasing values of the fractional parameters, whereas the trend reverses for a longer time. Moreover, it is found that the velocity and temperature profiles oppositely behave for the volume fraction of hybrid nanofluids. Applications of fractional derivatives Heat transfer problem Modeling and simulation Hybrid nanofluid Mathematics Ilyas Khan verfasserin aut Sharidan Shafie verfasserin aut In Advances in Difference Equations SpringerOpen, 2006 (2019), 1, Seite 18 (DE-627)377755699 (DE-600)2132815-8 16871847 nnns year:2019 number:1 pages:18 https://doi.org/10.1186/s13662-019-1988-5 kostenfrei https://doaj.org/article/26365e5db0bf4bc89b59abae520804d0 kostenfrei http://link.springer.com/article/10.1186/s13662-019-1988-5 kostenfrei https://doaj.org/toc/1687-1847 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 1 18
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author	Muhammad Saqib
spellingShingle	Muhammad Saqib misc QA1-939 misc Applications of fractional derivatives misc Heat transfer problem misc Modeling and simulation misc Hybrid nanofluid misc Mathematics Application of fractional differential equations to heat transfer in hybrid nanofluid: modeling and solution via integral transforms
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topic_title	QA1-939 Application of fractional differential equations to heat transfer in hybrid nanofluid: modeling and solution via integral transforms Applications of fractional derivatives Heat transfer problem Modeling and simulation Hybrid nanofluid
topic	misc QA1-939 misc Applications of fractional derivatives misc Heat transfer problem misc Modeling and simulation misc Hybrid nanofluid misc Mathematics
topic_unstemmed	misc QA1-939 misc Applications of fractional derivatives misc Heat transfer problem misc Modeling and simulation misc Hybrid nanofluid misc Mathematics
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title	Application of fractional differential equations to heat transfer in hybrid nanofluid: modeling and solution via integral transforms
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title_full	Application of fractional differential equations to heat transfer in hybrid nanofluid: modeling and solution via integral transforms
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title_sort	application of fractional differential equations to heat transfer in hybrid nanofluid: modeling and solution via integral transforms
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title_auth	Application of fractional differential equations to heat transfer in hybrid nanofluid: modeling and solution via integral transforms
abstract	Abstract This article deals with the generalization of natural convection flow of Cu−Al2O3−H2O $Cu - Al_{2}O_{3} - H_{2}O$ hybrid nanofluid in two infinite vertical parallel plates. To demonstrate the flow phenomena in two parallel plates of hybrid nanofluids, the Brinkman type fluid model together with the energy equation is considered. The Caputo–Fabrizio fractional derivative and the Laplace transform technique are used to developed exact analytical solutions for velocity and temperature profiles. The general solutions for velocity and temperature profiles are brought into light through numerical computation and graphical representation. The obtained results show that the velocity and temperature profiles show dual behaviors for 0<α<1 $0 < \alpha < 1$ and 0<β<1 $0 < \beta < 1$ where α and β are the fractional parameters. It is noticed that, for a shorter time, the velocity and temperature distributions decrease with increasing values of the fractional parameters, whereas the trend reverses for a longer time. Moreover, it is found that the velocity and temperature profiles oppositely behave for the volume fraction of hybrid nanofluids.
abstractGer	Abstract This article deals with the generalization of natural convection flow of Cu−Al2O3−H2O $Cu - Al_{2}O_{3} - H_{2}O$ hybrid nanofluid in two infinite vertical parallel plates. To demonstrate the flow phenomena in two parallel plates of hybrid nanofluids, the Brinkman type fluid model together with the energy equation is considered. The Caputo–Fabrizio fractional derivative and the Laplace transform technique are used to developed exact analytical solutions for velocity and temperature profiles. The general solutions for velocity and temperature profiles are brought into light through numerical computation and graphical representation. The obtained results show that the velocity and temperature profiles show dual behaviors for 0<α<1 $0 < \alpha < 1$ and 0<β<1 $0 < \beta < 1$ where α and β are the fractional parameters. It is noticed that, for a shorter time, the velocity and temperature distributions decrease with increasing values of the fractional parameters, whereas the trend reverses for a longer time. Moreover, it is found that the velocity and temperature profiles oppositely behave for the volume fraction of hybrid nanofluids.
abstract_unstemmed	Abstract This article deals with the generalization of natural convection flow of Cu−Al2O3−H2O $Cu - Al_{2}O_{3} - H_{2}O$ hybrid nanofluid in two infinite vertical parallel plates. To demonstrate the flow phenomena in two parallel plates of hybrid nanofluids, the Brinkman type fluid model together with the energy equation is considered. The Caputo–Fabrizio fractional derivative and the Laplace transform technique are used to developed exact analytical solutions for velocity and temperature profiles. The general solutions for velocity and temperature profiles are brought into light through numerical computation and graphical representation. The obtained results show that the velocity and temperature profiles show dual behaviors for 0<α<1 $0 < \alpha < 1$ and 0<β<1 $0 < \beta < 1$ where α and β are the fractional parameters. It is noticed that, for a shorter time, the velocity and temperature distributions decrease with increasing values of the fractional parameters, whereas the trend reverses for a longer time. Moreover, it is found that the velocity and temperature profiles oppositely behave for the volume fraction of hybrid nanofluids.
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title_short	Application of fractional differential equations to heat transfer in hybrid nanofluid: modeling and solution via integral transforms
url	https://doi.org/10.1186/s13662-019-1988-5 https://doaj.org/article/26365e5db0bf4bc89b59abae520804d0 http://link.springer.com/article/10.1186/s13662-019-1988-5 https://doaj.org/toc/1687-1847
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up_date	2024-07-03T19:20:14.704Z
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Application of fractional differential equations to heat transfer in hybrid nanofluid: modeling and solution via integral transforms

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