Enhancement in heat transfer due to hybrid nanoparticles in MHD flow of Brinkman-type fluids using Caputo fractional derivatives
Abstract The flow of fluid through porous media is of great importance in industry and other physical situations, Darcy’s law is one of the most useful laws to describe such situation, however, the flows through a dense swarm of particles or through a very high porous media cannot be elaborated by t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2022-08-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-022-18110-1 |
| _version_ | 1818517080971935744 |
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| author | Nadeem Ahmad Sheikh Dennis Ling Chuan Ching Ilyas Khan Hamzah bin Sakidin |
| author_facet | Nadeem Ahmad Sheikh Dennis Ling Chuan Ching Ilyas Khan Hamzah bin Sakidin |
| author_sort | Nadeem Ahmad Sheikh |
| collection | DOAJ |
| description | Abstract The flow of fluid through porous media is of great importance in industry and other physical situations, Darcy’s law is one of the most useful laws to describe such situation, however, the flows through a dense swarm of particles or through a very high porous media cannot be elaborated by this law. To overcome this difficulty, Brinkman proposed a new idea of Brinkman-type fluid in highly porous media. In this study, the Brinkman-type fluid flow is analyzed with hybrid nanoparticles (a hybridized mixture of clay and alumina), suspended in water taken as a base fluid under the effect of an applied magnetic field. The fluid motion is taken inside a vertical channel with heated walls. Free convection is induced due to buoyancy. The momentum and energy equations are written in dimensionless form using the non-dimensional variables. The energy equation is modified to fractional differential equations using the generalized Fourier’s law and the Caputo fractional derivatives. The fractional model is solved using the Laplace and Fourier transformation. Variations in velocity and temperature are shown for various fractional parameter values, as well as charts for the classical model. For the volume fractions of nanoparticles, the temperature distribution increases, with maximum values of hybrid nanoparticles with the highest specified volume fractions. Moreover, due to hybrid nanoparticles, the rate of heat transfer is intensified. |
| first_indexed | 2024-12-11T00:51:25Z |
| format | Article |
| id | doaj.art-8459426af5404ac99c47bbca01d38173 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-12-11T00:51:25Z |
| publishDate | 2022-08-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-8459426af5404ac99c47bbca01d381732022-12-22T01:26:37ZengNature PortfolioScientific Reports2045-23222022-08-0112111410.1038/s41598-022-18110-1Enhancement in heat transfer due to hybrid nanoparticles in MHD flow of Brinkman-type fluids using Caputo fractional derivativesNadeem Ahmad Sheikh0Dennis Ling Chuan Ching1Ilyas Khan2Hamzah bin Sakidin3Fundamental and Applied Sciences Department, Universiti Teknologi PETRONASFundamental and Applied Sciences Department, Universiti Teknologi PETRONASDepartment of Mathematics, College of Science Al-Zulfi, Majmaah UniversityFundamental and Applied Sciences Department, Universiti Teknologi PETRONASAbstract The flow of fluid through porous media is of great importance in industry and other physical situations, Darcy’s law is one of the most useful laws to describe such situation, however, the flows through a dense swarm of particles or through a very high porous media cannot be elaborated by this law. To overcome this difficulty, Brinkman proposed a new idea of Brinkman-type fluid in highly porous media. In this study, the Brinkman-type fluid flow is analyzed with hybrid nanoparticles (a hybridized mixture of clay and alumina), suspended in water taken as a base fluid under the effect of an applied magnetic field. The fluid motion is taken inside a vertical channel with heated walls. Free convection is induced due to buoyancy. The momentum and energy equations are written in dimensionless form using the non-dimensional variables. The energy equation is modified to fractional differential equations using the generalized Fourier’s law and the Caputo fractional derivatives. The fractional model is solved using the Laplace and Fourier transformation. Variations in velocity and temperature are shown for various fractional parameter values, as well as charts for the classical model. For the volume fractions of nanoparticles, the temperature distribution increases, with maximum values of hybrid nanoparticles with the highest specified volume fractions. Moreover, due to hybrid nanoparticles, the rate of heat transfer is intensified.https://doi.org/10.1038/s41598-022-18110-1 |
| spellingShingle | Nadeem Ahmad Sheikh Dennis Ling Chuan Ching Ilyas Khan Hamzah bin Sakidin Enhancement in heat transfer due to hybrid nanoparticles in MHD flow of Brinkman-type fluids using Caputo fractional derivatives Scientific Reports |
| title | Enhancement in heat transfer due to hybrid nanoparticles in MHD flow of Brinkman-type fluids using Caputo fractional derivatives |
| title_full | Enhancement in heat transfer due to hybrid nanoparticles in MHD flow of Brinkman-type fluids using Caputo fractional derivatives |
| title_fullStr | Enhancement in heat transfer due to hybrid nanoparticles in MHD flow of Brinkman-type fluids using Caputo fractional derivatives |
| title_full_unstemmed | Enhancement in heat transfer due to hybrid nanoparticles in MHD flow of Brinkman-type fluids using Caputo fractional derivatives |
| title_short | Enhancement in heat transfer due to hybrid nanoparticles in MHD flow of Brinkman-type fluids using Caputo fractional derivatives |
| title_sort | enhancement in heat transfer due to hybrid nanoparticles in mhd flow of brinkman type fluids using caputo fractional derivatives |
| url | https://doi.org/10.1038/s41598-022-18110-1 |
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