Analytical Study of the Energy Loss Reduction during Three-Dimensional Engine Oil-Based Hybrid Nanofluid Flow by Using Cattaneo–Christov Model
In this work, we analyzed the hybrid nanofluid (Ag+CuO+kerosene oil) flow past a bidirectionally extendable surface in the presence of a variable magnetic field. The hybrid nanofluid flow considered is electrically conductive and steady. For the simulation of the problem, the Cattaneo–Christov doubl...
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MDPI AG
2023-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/1/166 |
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| author | Ramadan A. ZeinEldin Asad Ullah Hamiden Abd El-Wahed Khalifa Muhammad Ayaz |
| author_facet | Ramadan A. ZeinEldin Asad Ullah Hamiden Abd El-Wahed Khalifa Muhammad Ayaz |
| author_sort | Ramadan A. ZeinEldin |
| collection | DOAJ |
| description | In this work, we analyzed the hybrid nanofluid (Ag+CuO+kerosene oil) flow past a bidirectionally extendable surface in the presence of a variable magnetic field. The hybrid nanofluid flow considered is electrically conductive and steady. For the simulation of the problem, the Cattaneo–Christov double-diffusion (CCDD) model was considered, which generalizes Fourier’s and Fick’s laws. The impact of the Hall current produced was taken into account. The physical problem was transformed into a mathematical form with the help of suitable transformations to reduce the complexity of the problem. The transformed system of coupled ordinary differential equations (ODEs) was solved with the semi-analytical method. The results are plotted in comparison with the ordinary nanofluid (CuO+kerosene oil) and hybrid nanofluid (Ag+CuO+kerosene oil). The impact of various parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>P</mi><mi>r</mi><mo>,</mo><mi>S</mi><mi>c</mi><mo>,</mo><msub><mi>γ</mi><mn>0</mn></msub><mo>,</mo><mi>m</mi><mo>,</mo><mi>M</mi><mo>,</mo><mi>N</mi><mi>b</mi><mo>,</mo><mi>N</mi><mi>t</mi><mo>,</mo><msub><mi>ϵ</mi><mn>1</mn></msub><mo>,</mo><msub><mi>ϵ</mi><mn>2</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula> on the state variables is described. The velocity gradient under the impact of the mass flux and magnetic parameter shows a decreasing behavior, while the Hall parameter and the stretching ratio show an increasing behavior. Moreover, the skin friction, rate of heat, and mass transfer are numerically displayed through tables. In this work, we found that the thermal and concentration relaxation coefficients showed a decreasing behavior for their increasing trends. For the validation of the implemented technique, the squared residuals are computed in Table 2, which shows that the increasing number of iterations decreases the squared residual error. The results show that Ag+CuO+kerosene oil has good performance in the reduction of the heat transfer rate. |
| first_indexed | 2024-03-09T11:07:44Z |
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| id | doaj.art-037b74a792484a0ca9bda691c80704bb |
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| last_indexed | 2024-03-09T11:07:44Z |
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| spelling | doaj.art-037b74a792484a0ca9bda691c80704bb2023-12-01T00:52:53ZengMDPI AGSymmetry2073-89942023-01-0115116610.3390/sym15010166Analytical Study of the Energy Loss Reduction during Three-Dimensional Engine Oil-Based Hybrid Nanofluid Flow by Using Cattaneo–Christov ModelRamadan A. ZeinEldin0Asad Ullah1Hamiden Abd El-Wahed Khalifa2Muhammad Ayaz3Deanship of Scientific Research, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, PakistanDepartment of Operations and Management Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, EgyptDepartment of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Khyber Pakhtunkhwa, PakistanIn this work, we analyzed the hybrid nanofluid (Ag+CuO+kerosene oil) flow past a bidirectionally extendable surface in the presence of a variable magnetic field. The hybrid nanofluid flow considered is electrically conductive and steady. For the simulation of the problem, the Cattaneo–Christov double-diffusion (CCDD) model was considered, which generalizes Fourier’s and Fick’s laws. The impact of the Hall current produced was taken into account. The physical problem was transformed into a mathematical form with the help of suitable transformations to reduce the complexity of the problem. The transformed system of coupled ordinary differential equations (ODEs) was solved with the semi-analytical method. The results are plotted in comparison with the ordinary nanofluid (CuO+kerosene oil) and hybrid nanofluid (Ag+CuO+kerosene oil). The impact of various parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>P</mi><mi>r</mi><mo>,</mo><mi>S</mi><mi>c</mi><mo>,</mo><msub><mi>γ</mi><mn>0</mn></msub><mo>,</mo><mi>m</mi><mo>,</mo><mi>M</mi><mo>,</mo><mi>N</mi><mi>b</mi><mo>,</mo><mi>N</mi><mi>t</mi><mo>,</mo><msub><mi>ϵ</mi><mn>1</mn></msub><mo>,</mo><msub><mi>ϵ</mi><mn>2</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula> on the state variables is described. The velocity gradient under the impact of the mass flux and magnetic parameter shows a decreasing behavior, while the Hall parameter and the stretching ratio show an increasing behavior. Moreover, the skin friction, rate of heat, and mass transfer are numerically displayed through tables. In this work, we found that the thermal and concentration relaxation coefficients showed a decreasing behavior for their increasing trends. For the validation of the implemented technique, the squared residuals are computed in Table 2, which shows that the increasing number of iterations decreases the squared residual error. The results show that Ag+CuO+kerosene oil has good performance in the reduction of the heat transfer rate.https://www.mdpi.com/2073-8994/15/1/166symmetric flowhybrid nanofluidenergy lossheat and mass transferCattaneo–Christov modelstretching surface |
| spellingShingle | Ramadan A. ZeinEldin Asad Ullah Hamiden Abd El-Wahed Khalifa Muhammad Ayaz Analytical Study of the Energy Loss Reduction during Three-Dimensional Engine Oil-Based Hybrid Nanofluid Flow by Using Cattaneo–Christov Model Symmetry symmetric flow hybrid nanofluid energy loss heat and mass transfer Cattaneo–Christov model stretching surface |
| title | Analytical Study of the Energy Loss Reduction during Three-Dimensional Engine Oil-Based Hybrid Nanofluid Flow by Using Cattaneo–Christov Model |
| title_full | Analytical Study of the Energy Loss Reduction during Three-Dimensional Engine Oil-Based Hybrid Nanofluid Flow by Using Cattaneo–Christov Model |
| title_fullStr | Analytical Study of the Energy Loss Reduction during Three-Dimensional Engine Oil-Based Hybrid Nanofluid Flow by Using Cattaneo–Christov Model |
| title_full_unstemmed | Analytical Study of the Energy Loss Reduction during Three-Dimensional Engine Oil-Based Hybrid Nanofluid Flow by Using Cattaneo–Christov Model |
| title_short | Analytical Study of the Energy Loss Reduction during Three-Dimensional Engine Oil-Based Hybrid Nanofluid Flow by Using Cattaneo–Christov Model |
| title_sort | analytical study of the energy loss reduction during three dimensional engine oil based hybrid nanofluid flow by using cattaneo christov model |
| topic | symmetric flow hybrid nanofluid energy loss heat and mass transfer Cattaneo–Christov model stretching surface |
| url | https://www.mdpi.com/2073-8994/15/1/166 |
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