{"title":"非定常耦合应力磁性纳米流体在具有欧姆耗散的拉伸片上流动的计算研究","authors":"Mahesh Kumar, G. J. Reddy, N. N. Kumar, O. Bég","doi":"10.1177/2397791419843730","DOIUrl":null,"url":null,"abstract":"To provide a deeper insight of the transport phenomena inherent to the manufacturing of magnetic nano-polymer materials, in the present work a mathematical model is developed for time-dependent hydromagnetic rheological nano-polymer boundary layer flow and heat transfer over a stretching sheet in the presence of a transverse static magnetic field. Joule heating (Ohmic dissipation) and viscous heating effects are included since these phenomena arise frequently in magnetic materials processing. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. The Tiwari–Das nanoscale model is adopted which permits different nanoparticles to be simulated (in this article, both copper–water and aluminium oxide–water nanofluids are considered). Similarity transformations are utilized to convert the governing partial differential conservation equations into a system of coupled, non-linear ordinary differential equations with appropriate wall and free stream boundary conditions. The shooting technique is used to solve the reduced non-linear coupled ordinary differential boundary value problem via MATLAB symbolic software. Validation with published results from the literature is included for the special cases of non-dissipative and Newtonian nanofluid flows. Fluid velocity and temperature profiles for both copper and aluminium oxide (Al2O3) nanofluids are observed to be enhanced with greater non-Newtonian couple stress parameter and magnetic parameter, whereas the opposite trend is computed with greater values of unsteadiness parameter. The boundary layer flow is accelerated with increasing buoyancy parameter, elastic sheet stretching parameter and convection parameter. Temperatures are generally increased with greater couple stress rheological parameter and are consistently higher for the aluminium oxide nanoparticle case. Temperatures are also boosted with magnetic parameter and exhibit an overshoot near the wall when magnetic parameter exceeds unity (magnetic force exceeds viscous force). A decrease in temperatures is induced with increasing sheet stretching parameter. Increasing Eckert number elevates temperatures considerably. With greater nanoparticle volume fraction, both skin friction and Nusselt number are elevated, and copper nanoparticles achieve higher magnitudes than aluminium oxide.","PeriodicalId":44789,"journal":{"name":"Proceedings of the Institution of Mechanical Engineers Part N-Journal of Nanomaterials Nanoengineering and Nanosystems","volume":"40 1","pages":"49 - 63"},"PeriodicalIF":4.2000,"publicationDate":"2019-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":"{\"title\":\"Computational study of unsteady couple stress magnetic nanofluid flow from a stretching sheet with Ohmic dissipation\",\"authors\":\"Mahesh Kumar, G. J. Reddy, N. N. Kumar, O. Bég\",\"doi\":\"10.1177/2397791419843730\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"To provide a deeper insight of the transport phenomena inherent to the manufacturing of magnetic nano-polymer materials, in the present work a mathematical model is developed for time-dependent hydromagnetic rheological nano-polymer boundary layer flow and heat transfer over a stretching sheet in the presence of a transverse static magnetic field. Joule heating (Ohmic dissipation) and viscous heating effects are included since these phenomena arise frequently in magnetic materials processing. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. The Tiwari–Das nanoscale model is adopted which permits different nanoparticles to be simulated (in this article, both copper–water and aluminium oxide–water nanofluids are considered). Similarity transformations are utilized to convert the governing partial differential conservation equations into a system of coupled, non-linear ordinary differential equations with appropriate wall and free stream boundary conditions. The shooting technique is used to solve the reduced non-linear coupled ordinary differential boundary value problem via MATLAB symbolic software. Validation with published results from the literature is included for the special cases of non-dissipative and Newtonian nanofluid flows. Fluid velocity and temperature profiles for both copper and aluminium oxide (Al2O3) nanofluids are observed to be enhanced with greater non-Newtonian couple stress parameter and magnetic parameter, whereas the opposite trend is computed with greater values of unsteadiness parameter. The boundary layer flow is accelerated with increasing buoyancy parameter, elastic sheet stretching parameter and convection parameter. Temperatures are generally increased with greater couple stress rheological parameter and are consistently higher for the aluminium oxide nanoparticle case. Temperatures are also boosted with magnetic parameter and exhibit an overshoot near the wall when magnetic parameter exceeds unity (magnetic force exceeds viscous force). A decrease in temperatures is induced with increasing sheet stretching parameter. Increasing Eckert number elevates temperatures considerably. With greater nanoparticle volume fraction, both skin friction and Nusselt number are elevated, and copper nanoparticles achieve higher magnitudes than aluminium oxide.\",\"PeriodicalId\":44789,\"journal\":{\"name\":\"Proceedings of the Institution of Mechanical Engineers Part N-Journal of Nanomaterials Nanoengineering and Nanosystems\",\"volume\":\"40 1\",\"pages\":\"49 - 63\"},\"PeriodicalIF\":4.2000,\"publicationDate\":\"2019-04-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"20\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Institution of Mechanical Engineers Part N-Journal of Nanomaterials Nanoengineering and Nanosystems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1177/2397791419843730\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"NANOSCIENCE & NANOTECHNOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Institution of Mechanical Engineers Part N-Journal of Nanomaterials Nanoengineering and Nanosystems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1177/2397791419843730","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"NANOSCIENCE & NANOTECHNOLOGY","Score":null,"Total":0}
Computational study of unsteady couple stress magnetic nanofluid flow from a stretching sheet with Ohmic dissipation
To provide a deeper insight of the transport phenomena inherent to the manufacturing of magnetic nano-polymer materials, in the present work a mathematical model is developed for time-dependent hydromagnetic rheological nano-polymer boundary layer flow and heat transfer over a stretching sheet in the presence of a transverse static magnetic field. Joule heating (Ohmic dissipation) and viscous heating effects are included since these phenomena arise frequently in magnetic materials processing. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. The Tiwari–Das nanoscale model is adopted which permits different nanoparticles to be simulated (in this article, both copper–water and aluminium oxide–water nanofluids are considered). Similarity transformations are utilized to convert the governing partial differential conservation equations into a system of coupled, non-linear ordinary differential equations with appropriate wall and free stream boundary conditions. The shooting technique is used to solve the reduced non-linear coupled ordinary differential boundary value problem via MATLAB symbolic software. Validation with published results from the literature is included for the special cases of non-dissipative and Newtonian nanofluid flows. Fluid velocity and temperature profiles for both copper and aluminium oxide (Al2O3) nanofluids are observed to be enhanced with greater non-Newtonian couple stress parameter and magnetic parameter, whereas the opposite trend is computed with greater values of unsteadiness parameter. The boundary layer flow is accelerated with increasing buoyancy parameter, elastic sheet stretching parameter and convection parameter. Temperatures are generally increased with greater couple stress rheological parameter and are consistently higher for the aluminium oxide nanoparticle case. Temperatures are also boosted with magnetic parameter and exhibit an overshoot near the wall when magnetic parameter exceeds unity (magnetic force exceeds viscous force). A decrease in temperatures is induced with increasing sheet stretching parameter. Increasing Eckert number elevates temperatures considerably. With greater nanoparticle volume fraction, both skin friction and Nusselt number are elevated, and copper nanoparticles achieve higher magnitudes than aluminium oxide.
期刊介绍:
Proceedings of the Institution of Mechanical Engineers Part N-Journal of Nanomaterials Nanoengineering and Nanosystems is a peer-reviewed scientific journal published since 2004 by SAGE Publications on behalf of the Institution of Mechanical Engineers. The journal focuses on research in the field of nanoengineering, nanoscience and nanotechnology and aims to publish high quality academic papers in this field. In addition, the journal is indexed in several reputable academic databases and abstracting services, including Scopus, Compendex, and CSA's Advanced Polymers Abstracts, Composites Industry Abstracts, and Earthquake Engineering Abstracts.