Darcy–Forchheimer MHD Couple Stress 3D Nanofluid over an Exponentially Stretching Sheet through Cattaneo–Christov Convective Heat Flux with Zero Nanoparticles Mass Flux Conditions
In the last decade, nanoparticles have provided numerous challenges in the field of science. The nanoparticles suspended in various base fluids can transform the flow of fluids and heat transfer characteristics. In this research work, the mathematical model is offered to present the 3D magnetohydrod...
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MDPI AG
2019-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/21/9/867 |
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| author | Muhammad Wakeel Ahmad Poom Kumam Zahir Shah Ali Ahmad Farooq Rashid Nawaz Abdullah Dawar Saeed Islam Phatiphat Thounthong |
| author_facet | Muhammad Wakeel Ahmad Poom Kumam Zahir Shah Ali Ahmad Farooq Rashid Nawaz Abdullah Dawar Saeed Islam Phatiphat Thounthong |
| author_sort | Muhammad Wakeel Ahmad |
| collection | DOAJ |
| description | In the last decade, nanoparticles have provided numerous challenges in the field of science. The nanoparticles suspended in various base fluids can transform the flow of fluids and heat transfer characteristics. In this research work, the mathematical model is offered to present the 3D magnetohydrodynamics Darcy–Forchheimer couple stress nanofluid flow over an exponentially stretching sheet. Joule heating and viscous dissipation impacts are also discussed in this mathematical model. To examine the relaxation properties, the proposed model of Cattaneo–Christov is supposed. For the first time, the influence of temperature exponent is scrutinized via this research article. The designed system of partial differential equations (PDE’s) is transformed to set of ordinary differential equations (ODE’s) by using similarity transformations. The problem is solved analytically via homotopy analysis technique. Effects of dimensionless couple stress, magnetic field, ratio of rates, porosity, and coefficient of inertia parameters on the fluid flow in <i>x</i>- and <i>y</i>-directions have been examined in this work. The augmented ratio of rates parameter upsurges the velocity profile in the <i>x</i>-direction. The augmented magnetic field, porosity parameter, coefficient of inertia, and couple stress parameter diminishes the velocity field along the <i>x</i>-direction. The augmented magnetic field, porosity parameter, coefficient of inertia, ratio of rates parameter, and couple stress parameter reduces the velocity field along the <i>y</i>-axis. The influences of time relaxation, Prandtl number, and temperature exponent on temperature profile are also discussed. Additionally, the influences of thermophoresis parameter, Schmidt number, Brownian motion parameter, and temperature exponent on fluid concentration are explained in this work. For engineering interests, the impacts of parameters on skin friction and Nusselt number are accessible through tables. |
| first_indexed | 2024-04-11T13:18:35Z |
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| last_indexed | 2024-04-11T13:18:35Z |
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| spelling | doaj.art-d49a0ce1e4c441a49ba248cc1fb58d3a2022-12-22T04:22:19ZengMDPI AGEntropy1099-43002019-09-0121986710.3390/e21090867e21090867Darcy–Forchheimer MHD Couple Stress 3D Nanofluid over an Exponentially Stretching Sheet through Cattaneo–Christov Convective Heat Flux with Zero Nanoparticles Mass Flux ConditionsMuhammad Wakeel Ahmad0Poom Kumam1Zahir Shah2Ali Ahmad Farooq3Rashid Nawaz4Abdullah Dawar5Saeed Islam6Phatiphat Thounthong7Department of Mathematics, Abdul Wali Khan University, Mardan 23200, PakistanKMUTT-Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandKMUTT-Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandMathematics Department, COMSATS University, Abbottabad Campus, Islamabad 22060, PakistanDepartment of Mathematics, Abdul Wali Khan University, Mardan 23200, PakistanDepartment of Mathematics, Qurtuba University of Science and Information Technology, Peshawar 25000, PakistanDepartment of Mathematics, Abdul Wali Khan University, Mardan 23200, PakistanRenewable Energy Research Centre, Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok, 1518 Pracharat 1 Road, Bangsue, Bangkok 10800, ThailandIn the last decade, nanoparticles have provided numerous challenges in the field of science. The nanoparticles suspended in various base fluids can transform the flow of fluids and heat transfer characteristics. In this research work, the mathematical model is offered to present the 3D magnetohydrodynamics Darcy–Forchheimer couple stress nanofluid flow over an exponentially stretching sheet. Joule heating and viscous dissipation impacts are also discussed in this mathematical model. To examine the relaxation properties, the proposed model of Cattaneo–Christov is supposed. For the first time, the influence of temperature exponent is scrutinized via this research article. The designed system of partial differential equations (PDE’s) is transformed to set of ordinary differential equations (ODE’s) by using similarity transformations. The problem is solved analytically via homotopy analysis technique. Effects of dimensionless couple stress, magnetic field, ratio of rates, porosity, and coefficient of inertia parameters on the fluid flow in <i>x</i>- and <i>y</i>-directions have been examined in this work. The augmented ratio of rates parameter upsurges the velocity profile in the <i>x</i>-direction. The augmented magnetic field, porosity parameter, coefficient of inertia, and couple stress parameter diminishes the velocity field along the <i>x</i>-direction. The augmented magnetic field, porosity parameter, coefficient of inertia, ratio of rates parameter, and couple stress parameter reduces the velocity field along the <i>y</i>-axis. The influences of time relaxation, Prandtl number, and temperature exponent on temperature profile are also discussed. Additionally, the influences of thermophoresis parameter, Schmidt number, Brownian motion parameter, and temperature exponent on fluid concentration are explained in this work. For engineering interests, the impacts of parameters on skin friction and Nusselt number are accessible through tables.https://www.mdpi.com/1099-4300/21/9/867MHDnanofluidsheat transfercouple stress fluidHAMCattaneo–Christov heat flux model |
| spellingShingle | Muhammad Wakeel Ahmad Poom Kumam Zahir Shah Ali Ahmad Farooq Rashid Nawaz Abdullah Dawar Saeed Islam Phatiphat Thounthong Darcy–Forchheimer MHD Couple Stress 3D Nanofluid over an Exponentially Stretching Sheet through Cattaneo–Christov Convective Heat Flux with Zero Nanoparticles Mass Flux Conditions Entropy MHD nanofluids heat transfer couple stress fluid HAM Cattaneo–Christov heat flux model |
| title | Darcy–Forchheimer MHD Couple Stress 3D Nanofluid over an Exponentially Stretching Sheet through Cattaneo–Christov Convective Heat Flux with Zero Nanoparticles Mass Flux Conditions |
| title_full | Darcy–Forchheimer MHD Couple Stress 3D Nanofluid over an Exponentially Stretching Sheet through Cattaneo–Christov Convective Heat Flux with Zero Nanoparticles Mass Flux Conditions |
| title_fullStr | Darcy–Forchheimer MHD Couple Stress 3D Nanofluid over an Exponentially Stretching Sheet through Cattaneo–Christov Convective Heat Flux with Zero Nanoparticles Mass Flux Conditions |
| title_full_unstemmed | Darcy–Forchheimer MHD Couple Stress 3D Nanofluid over an Exponentially Stretching Sheet through Cattaneo–Christov Convective Heat Flux with Zero Nanoparticles Mass Flux Conditions |
| title_short | Darcy–Forchheimer MHD Couple Stress 3D Nanofluid over an Exponentially Stretching Sheet through Cattaneo–Christov Convective Heat Flux with Zero Nanoparticles Mass Flux Conditions |
| title_sort | darcy forchheimer mhd couple stress 3d nanofluid over an exponentially stretching sheet through cattaneo christov convective heat flux with zero nanoparticles mass flux conditions |
| topic | MHD nanofluids heat transfer couple stress fluid HAM Cattaneo–Christov heat flux model |
| url | https://www.mdpi.com/1099-4300/21/9/867 |
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