Mixed Convection Stagnation Point Flow of a Hybrid Nanofluid Past a Permeable Flat Plate with Radiation Effect

This article focuses on the stagnation point flow of hybrid nanofluid towards a flat plate. The cases when the buoyancy forces and the flow are in the opposite direction and the same direction are discussed. The effect of radiation and suction is also taken into account. The similarity transformatio...

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Autores principales:	Siti Nur Alwani Salleh, Norfifah Bachok, Ioan Pop
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	hybrid nanofluid mixed convection numerical solution permeable surface stability analysis radiation effect Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/ecc66c0a97b947229dc42537f9334880
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spelling	oai:doaj.org-article:ecc66c0a97b947229dc42537f93348802021-11-11T18:14:52ZMixed Convection Stagnation Point Flow of a Hybrid Nanofluid Past a Permeable Flat Plate with Radiation Effect10.3390/math92126812227-7390https://doaj.org/article/ecc66c0a97b947229dc42537f93348802021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2681https://doaj.org/toc/2227-7390This article focuses on the stagnation point flow of hybrid nanofluid towards a flat plate. The cases when the buoyancy forces and the flow are in the opposite direction and the same direction are discussed. The effect of radiation and suction is also taken into account. The similarity transformations are used to convert the partial differential equations into nonlinear ordinary differential equations. These equations are computed numerically via the bvp4c function in MATLAB software. A comparison with the previously published articles is carried out, where an outstanding agreement is observed. The dual solutions exist in the case of opposing flow <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>λ</mi><mo><</mo><mn>0</mn><mo>)</mo></mrow></semantics></math></inline-formula> and the suction parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>></mo><mn>0.6688</mn></mrow></semantics></math></inline-formula>. Meanwhile, only unique solutions exist in the case of assisting flow <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>λ</mi><mo>></mo><mn>0</mn><mo>)</mo></mrow></semantics></math></inline-formula>. The existence of dual solutions leads to stability analysis. From the analysis, the first solution is confirmed as a stable solution. Furthermore, the heat transmission rate increases, while the skin friction coefficient decreases as the radiation rate increases. An increase in the radiation rate from 0 (no radiation) to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.0</mn></mrow></semantics></math></inline-formula> increases the heat transmission rate by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5.01</mn><mo>%</mo></mrow></semantics></math></inline-formula> for water, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4.96</mn><mo>%</mo></mrow></semantics></math></inline-formula> for nanofluid, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4.80</mn><mo>%</mo></mrow></semantics></math></inline-formula> for hybrid nanofluid. Finally, it is worth mentioning that the present study yields new and original results. This study has also not been done by other researchers, indicating its novelty.Siti Nur Alwani SallehNorfifah BachokIoan PopMDPI AGarticlehybrid nanofluidmixed convectionnumerical solutionpermeable surfacestability analysisradiation effectMathematicsQA1-939ENMathematics, Vol 9, Iss 2681, p 2681 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	hybrid nanofluid mixed convection numerical solution permeable surface stability analysis radiation effect Mathematics QA1-939
spellingShingle	hybrid nanofluid mixed convection numerical solution permeable surface stability analysis radiation effect Mathematics QA1-939 Siti Nur Alwani Salleh Norfifah Bachok Ioan Pop Mixed Convection Stagnation Point Flow of a Hybrid Nanofluid Past a Permeable Flat Plate with Radiation Effect
description	This article focuses on the stagnation point flow of hybrid nanofluid towards a flat plate. The cases when the buoyancy forces and the flow are in the opposite direction and the same direction are discussed. The effect of radiation and suction is also taken into account. The similarity transformations are used to convert the partial differential equations into nonlinear ordinary differential equations. These equations are computed numerically via the bvp4c function in MATLAB software. A comparison with the previously published articles is carried out, where an outstanding agreement is observed. The dual solutions exist in the case of opposing flow <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>λ</mi><mo><</mo><mn>0</mn><mo>)</mo></mrow></semantics></math></inline-formula> and the suction parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>></mo><mn>0.6688</mn></mrow></semantics></math></inline-formula>. Meanwhile, only unique solutions exist in the case of assisting flow <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>λ</mi><mo>></mo><mn>0</mn><mo>)</mo></mrow></semantics></math></inline-formula>. The existence of dual solutions leads to stability analysis. From the analysis, the first solution is confirmed as a stable solution. Furthermore, the heat transmission rate increases, while the skin friction coefficient decreases as the radiation rate increases. An increase in the radiation rate from 0 (no radiation) to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.0</mn></mrow></semantics></math></inline-formula> increases the heat transmission rate by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5.01</mn><mo>%</mo></mrow></semantics></math></inline-formula> for water, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4.96</mn><mo>%</mo></mrow></semantics></math></inline-formula> for nanofluid, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4.80</mn><mo>%</mo></mrow></semantics></math></inline-formula> for hybrid nanofluid. Finally, it is worth mentioning that the present study yields new and original results. This study has also not been done by other researchers, indicating its novelty.
format	article
author	Siti Nur Alwani Salleh Norfifah Bachok Ioan Pop
author_facet	Siti Nur Alwani Salleh Norfifah Bachok Ioan Pop
author_sort	Siti Nur Alwani Salleh
title	Mixed Convection Stagnation Point Flow of a Hybrid Nanofluid Past a Permeable Flat Plate with Radiation Effect
title_short	Mixed Convection Stagnation Point Flow of a Hybrid Nanofluid Past a Permeable Flat Plate with Radiation Effect
title_full	Mixed Convection Stagnation Point Flow of a Hybrid Nanofluid Past a Permeable Flat Plate with Radiation Effect
title_fullStr	Mixed Convection Stagnation Point Flow of a Hybrid Nanofluid Past a Permeable Flat Plate with Radiation Effect
title_full_unstemmed	Mixed Convection Stagnation Point Flow of a Hybrid Nanofluid Past a Permeable Flat Plate with Radiation Effect
title_sort	mixed convection stagnation point flow of a hybrid nanofluid past a permeable flat plate with radiation effect
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/ecc66c0a97b947229dc42537f9334880
work_keys_str_mv	AT sitinuralwanisalleh mixedconvectionstagnationpointflowofahybridnanofluidpastapermeableflatplatewithradiationeffect AT norfifahbachok mixedconvectionstagnationpointflowofahybridnanofluidpastapermeableflatplatewithradiationeffect AT ioanpop mixedconvectionstagnationpointflowofahybridnanofluidpastapermeableflatplatewithradiationeffect
_version_	1718431917540376576

Mixed Convection Stagnation Point Flow of a Hybrid Nanofluid Past a Permeable Flat Plate with Radiation Effect

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