Applications of fractional derivatives to nanofluids: exact and numerical solutions
In this article the idea of time fractional derivatives in Caputo sense is used to study memory effects on the behavior of nanofluids because some physical processes complex visco-elasticity, behavior of mechatronic and rheology are impossible to described by classical models. In present attempt hea...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2018
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| Online Access: | http://umpir.ump.edu.my/id/eprint/23900/ http://umpir.ump.edu.my/id/eprint/23900/1/Applications%20of%20fractional%20derivatives%20to%20nanofluids.%20Exact%20and%20numerical%20solutions.pdf |
| _version_ | 1848821915225948160 |
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| author | Zulkhibri, Ismail Mohd Zuki, Salleh Aman, Sidra Khan, Ilyas |
| author_facet | Zulkhibri, Ismail Mohd Zuki, Salleh Aman, Sidra Khan, Ilyas |
| author_sort | Zulkhibri, Ismail |
| building | UMP Institutional Repository |
| collection | Online Access |
| description | In this article the idea of time fractional derivatives in Caputo sense is used to study memory effects on the behavior of nanofluids because some physical processes complex visco-elasticity, behavior of mechatronic and rheology are impossible to described by classical models. In present attempt heat and mass transfer of nanofluids (sodium alginate (SA) carrier fluid with graphene nanoparticles) are tackled using fractional derivative approach. Exact solutions are determined for temperature, concentration and velocity field, and Nusselt number via Laplace transform technique. The obtained solutions are then expressed in terms of wright function or its fractional derivatives. Numerical solutions for velocity, temperature, concentration and Nusselt number are obtained using finite difference scheme. It is found that these solutions are significantly controlled by the variations of parameters including thermal Grashof number, fractional parameter and nanoparticles volume fraction. It is observed that rate of heat transfer increases with increasing nanoparticles volume fraction and Caputo time fractional parameters. |
| first_indexed | 2025-11-15T02:32:56Z |
| format | Article |
| id | ump-23900 |
| institution | Universiti Malaysia Pahang |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T02:32:56Z |
| publishDate | 2018 |
| publisher | EDP Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | ump-239002019-10-18T02:34:06Z http://umpir.ump.edu.my/id/eprint/23900/ Applications of fractional derivatives to nanofluids: exact and numerical solutions Zulkhibri, Ismail Mohd Zuki, Salleh Aman, Sidra Khan, Ilyas QA Mathematics In this article the idea of time fractional derivatives in Caputo sense is used to study memory effects on the behavior of nanofluids because some physical processes complex visco-elasticity, behavior of mechatronic and rheology are impossible to described by classical models. In present attempt heat and mass transfer of nanofluids (sodium alginate (SA) carrier fluid with graphene nanoparticles) are tackled using fractional derivative approach. Exact solutions are determined for temperature, concentration and velocity field, and Nusselt number via Laplace transform technique. The obtained solutions are then expressed in terms of wright function or its fractional derivatives. Numerical solutions for velocity, temperature, concentration and Nusselt number are obtained using finite difference scheme. It is found that these solutions are significantly controlled by the variations of parameters including thermal Grashof number, fractional parameter and nanoparticles volume fraction. It is observed that rate of heat transfer increases with increasing nanoparticles volume fraction and Caputo time fractional parameters. EDP Sciences 2018 Article PeerReviewed pdf en http://umpir.ump.edu.my/id/eprint/23900/1/Applications%20of%20fractional%20derivatives%20to%20nanofluids.%20Exact%20and%20numerical%20solutions.pdf Zulkhibri, Ismail and Mohd Zuki, Salleh and Aman, Sidra and Khan, Ilyas (2018) Applications of fractional derivatives to nanofluids: exact and numerical solutions. Mathematical Modelling of Natural Phenomena, 13 (1). pp. 1-12. ISSN 0973-5348 (Print); 1760-6101 (Online). (Published) https://doi.org/10.1051/mmnp/2018013 https://doi.org/10.1051/mmnp/2018013 |
| spellingShingle | QA Mathematics Zulkhibri, Ismail Mohd Zuki, Salleh Aman, Sidra Khan, Ilyas Applications of fractional derivatives to nanofluids: exact and numerical solutions |
| title | Applications of fractional derivatives to nanofluids: exact and numerical solutions |
| title_full | Applications of fractional derivatives to nanofluids: exact and numerical solutions |
| title_fullStr | Applications of fractional derivatives to nanofluids: exact and numerical solutions |
| title_full_unstemmed | Applications of fractional derivatives to nanofluids: exact and numerical solutions |
| title_short | Applications of fractional derivatives to nanofluids: exact and numerical solutions |
| title_sort | applications of fractional derivatives to nanofluids: exact and numerical solutions |
| topic | QA Mathematics |
| url | http://umpir.ump.edu.my/id/eprint/23900/ http://umpir.ump.edu.my/id/eprint/23900/ http://umpir.ump.edu.my/id/eprint/23900/ http://umpir.ump.edu.my/id/eprint/23900/1/Applications%20of%20fractional%20derivatives%20to%20nanofluids.%20Exact%20and%20numerical%20solutions.pdf |