Duality Solutions in Hydromagnetic Flow of SWCNT-MWCNT/Water Hybrid Nanofluid over Vertical Moving Slender Needle

Recently, the topic of convection of heat transfer has created an interest among researchers because of its numerous applications in the daily life. The objective of this paper was to study theoretically the problem of mixed convection boundary layer flow and heat transfer of single-wall carbon nano...

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Autores principales:	Nur Adilah Liyana Aladdin, Norfifah Bachok
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	hybrid nanofluid MHD mixed convection flow moving slender needle dual solutions Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/1a5ac9aa799b4f448106d2f6613a55fd
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institution	DOAJ
collection	DOAJ
language	EN
topic	hybrid nanofluid MHD mixed convection flow moving slender needle dual solutions Mathematics QA1-939
spellingShingle	hybrid nanofluid MHD mixed convection flow moving slender needle dual solutions Mathematics QA1-939 Nur Adilah Liyana Aladdin Norfifah Bachok Duality Solutions in Hydromagnetic Flow of SWCNT-MWCNT/Water Hybrid Nanofluid over Vertical Moving Slender Needle
description	Recently, the topic of convection of heat transfer has created an interest among researchers because of its numerous applications in the daily life. The objective of this paper was to study theoretically the problem of mixed convection boundary layer flow and heat transfer of single-wall carbon nanotube (SWCNT) and multi-wall carbon nanotube (MWCNT) in presence of hydromagnetic effects. The problem was initiated by formulating a mathematical model in partial differential equation (PDE) for the hybrid nanofluid flow with appropriate boundary conditions. The similarity equation was used to transform the PDE into an ordinary differential equation (ODE) and solved using bvp4c in MATLAB. The graphical results on variation of skin friction coefficient, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>C</mi><mi>f</mi></msub></mrow></semantics></math></inline-formula>, local Nusselt number, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><msub><mi>u</mi><mi>x</mi></msub></mrow></semantics></math></inline-formula>, shear stress, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>f</mi><mo>″</mo></msup><mfenced><mi>c</mi></mfenced></mrow></semantics></math></inline-formula> and local heat flux, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><msup><mi>θ</mi><mo>′</mo></msup><mfenced><mi>c</mi></mfenced></mrow></semantics></math></inline-formula> with the effects of magnetic, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mo>,</mo></mrow></semantics></math></inline-formula> size of needle, c, mixed convection parameter, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula> and volume fraction of nanoparticles, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula> were presented and discussed in detail. The study revealed that duality of solutions appears when the buoyance force is in opposing flow of the fluid motion, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo><</mo><mn>0</mn></mrow></semantics></math></inline-formula>. The presence of <i>M</i> in hybrid nanofluid reduced the skin friction coefficient and heat transfer. On the other hand, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>C</mi><mi>f</mi></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><msub><mi>u</mi><mi>x</mi></msub></mrow></semantics></math></inline-formula> increased as different concentrations of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>φ</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> and c were added. It gives an insight into the medical field, especially in treating cancer cells. By means, it reveals that CNTs hybrid nanofluid shows high potential in reaching the site of tumors faster compared with nanofluid. A stability analysis has to be carried out. It is noticed that the first solution was stable and physically realizable.
format	article
author	Nur Adilah Liyana Aladdin Norfifah Bachok
author_facet	Nur Adilah Liyana Aladdin Norfifah Bachok
author_sort	Nur Adilah Liyana Aladdin
title	Duality Solutions in Hydromagnetic Flow of SWCNT-MWCNT/Water Hybrid Nanofluid over Vertical Moving Slender Needle
title_short	Duality Solutions in Hydromagnetic Flow of SWCNT-MWCNT/Water Hybrid Nanofluid over Vertical Moving Slender Needle
title_full	Duality Solutions in Hydromagnetic Flow of SWCNT-MWCNT/Water Hybrid Nanofluid over Vertical Moving Slender Needle
title_fullStr	Duality Solutions in Hydromagnetic Flow of SWCNT-MWCNT/Water Hybrid Nanofluid over Vertical Moving Slender Needle
title_full_unstemmed	Duality Solutions in Hydromagnetic Flow of SWCNT-MWCNT/Water Hybrid Nanofluid over Vertical Moving Slender Needle
title_sort	duality solutions in hydromagnetic flow of swcnt-mwcnt/water hybrid nanofluid over vertical moving slender needle
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/1a5ac9aa799b4f448106d2f6613a55fd
work_keys_str_mv	AT nuradilahliyanaaladdin dualitysolutionsinhydromagneticflowofswcntmwcntwaterhybridnanofluidoververticalmovingslenderneedle AT norfifahbachok dualitysolutionsinhydromagneticflowofswcntmwcntwaterhybridnanofluidoververticalmovingslenderneedle
_version_	1718411366054756352
spelling	oai:doaj.org-article:1a5ac9aa799b4f448106d2f6613a55fd2021-11-25T18:17:15ZDuality Solutions in Hydromagnetic Flow of SWCNT-MWCNT/Water Hybrid Nanofluid over Vertical Moving Slender Needle10.3390/math92229272227-7390https://doaj.org/article/1a5ac9aa799b4f448106d2f6613a55fd2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2927https://doaj.org/toc/2227-7390Recently, the topic of convection of heat transfer has created an interest among researchers because of its numerous applications in the daily life. The objective of this paper was to study theoretically the problem of mixed convection boundary layer flow and heat transfer of single-wall carbon nanotube (SWCNT) and multi-wall carbon nanotube (MWCNT) in presence of hydromagnetic effects. The problem was initiated by formulating a mathematical model in partial differential equation (PDE) for the hybrid nanofluid flow with appropriate boundary conditions. The similarity equation was used to transform the PDE into an ordinary differential equation (ODE) and solved using bvp4c in MATLAB. The graphical results on variation of skin friction coefficient, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>C</mi><mi>f</mi></msub></mrow></semantics></math></inline-formula>, local Nusselt number, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><msub><mi>u</mi><mi>x</mi></msub></mrow></semantics></math></inline-formula>, shear stress, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>f</mi><mo>″</mo></msup><mfenced><mi>c</mi></mfenced></mrow></semantics></math></inline-formula> and local heat flux, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><msup><mi>θ</mi><mo>′</mo></msup><mfenced><mi>c</mi></mfenced></mrow></semantics></math></inline-formula> with the effects of magnetic, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mo>,</mo></mrow></semantics></math></inline-formula> size of needle, c, mixed convection parameter, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula> and volume fraction of nanoparticles, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula> were presented and discussed in detail. The study revealed that duality of solutions appears when the buoyance force is in opposing flow of the fluid motion, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo><</mo><mn>0</mn></mrow></semantics></math></inline-formula>. The presence of <i>M</i> in hybrid nanofluid reduced the skin friction coefficient and heat transfer. On the other hand, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>C</mi><mi>f</mi></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><msub><mi>u</mi><mi>x</mi></msub></mrow></semantics></math></inline-formula> increased as different concentrations of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>φ</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> and c were added. It gives an insight into the medical field, especially in treating cancer cells. By means, it reveals that CNTs hybrid nanofluid shows high potential in reaching the site of tumors faster compared with nanofluid. A stability analysis has to be carried out. It is noticed that the first solution was stable and physically realizable.Nur Adilah Liyana AladdinNorfifah BachokMDPI AGarticlehybrid nanofluidMHDmixed convection flowmoving slender needledual solutionsMathematicsQA1-939ENMathematics, Vol 9, Iss 2927, p 2927 (2021)

Duality Solutions in Hydromagnetic Flow of SWCNT-MWCNT/Water Hybrid Nanofluid over Vertical Moving Slender Needle

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