Simulation of Dissipative Hybrid Nanofluid (PEG-Water + ZrO<sub>2</sub> + MgO) Flow by a Curved Shrinking Sheet with Thermal Radiation and Higher Order Chemical Reaction
The heat transmission capabilities of hybrid nanofluids are superior to those of mono nanofluids. In addition to solar collectors and military equipment, they may be found in a number of areas including heat exchanger, automotive industry, transformer cooling and electronic cooling. The purpose of t...
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| Format: | Article |
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/10/1706 |
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| author | Gopinath Veeram Pasam Poojitha Harika Katta Sanakkayala Hemalatha Macherla Jayachandra Babu Chakravarthula S. K. Raju Nehad Ali Shah Se-Jin Yook |
| author_facet | Gopinath Veeram Pasam Poojitha Harika Katta Sanakkayala Hemalatha Macherla Jayachandra Babu Chakravarthula S. K. Raju Nehad Ali Shah Se-Jin Yook |
| author_sort | Gopinath Veeram |
| collection | DOAJ |
| description | The heat transmission capabilities of hybrid nanofluids are superior to those of mono nanofluids. In addition to solar collectors and military equipment, they may be found in a number of areas including heat exchanger, automotive industry, transformer cooling and electronic cooling. The purpose of this study was to evaluate the significance of the higher order chemical reaction parameter on the radiative flow of hybrid nanofluid (polyethylene glycol (PEG)–water combination: base fluid and zirconium dioxide, magnesium oxide: nanoparticles) via a curved shrinking sheet with viscous dissipation. Flow-driven equations were transformed into nonlinear ODEs using appropriate similarity transmutations, and then solved using the bvp4c solver (MATLAB built-in function). The results of two scenarios, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>E</mi><mi>G</mi><mo>−</mo><mi>W</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mo>+</mo><mi>Z</mi><mi>r</mi><msub><mi>O</mi><mn>2</mn></msub><mo>+</mo><mi>M</mi><mi>g</mi><mi>O</mi></mrow></semantics></math></inline-formula> (hybrid nanofluid) and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>E</mi><mi>G</mi><mo>−</mo><mi>W</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mo>+</mo><mi>Z</mi><mi>r</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>, (nanofluid) are reported. In order to draw important inferences about physical features, such as heat transfer rate, a correlation coefficient was used. The main findings of this study were that curvature parameter lowers fluid velocity, and Eckert number increases the temperature of fluid. It was observed that the volume fraction of nanoparticles enhances the skin friction coefficient and curvature parameter lessens the same. It was noticed that when curvature parameter (<i>K</i>) takes input in the range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.5</mn><mo>≤</mo><mi>K</mi><mo>≤</mo><mn>2.5</mn></mrow></semantics></math></inline-formula>, the skin friction coefficient decreases at a rate of 1.46633 (i.e., 146.633%) (in the case of hybrid nanofluid) and 1.11236 (i.e., 111.236%) (in the case of nanofluid) per unit value of curvature parameter. Increasing rates in the skin friction parameter were 3.481179 (i.e., 348.1179%) (in the case of hybrid nanofluid) and 2.745679 (in the case of nanofluid) when the volume fraction of nanoparticle (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ϕ</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>) takes input in the range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>≤</mo><msub><mi>ϕ</mi><mn>1</mn></msub><mo>≤</mo><mn>0.2</mn></mrow></semantics></math></inline-formula>. It was detected that, when Eckert number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><msub><mi>E</mi><mrow><mi>c</mi><mi>k</mi></mrow></msub></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula> increases, Nusselt number decreases. The decrement rates were observed as 1.41148 (i.e., 141.148%) (in the case of hybrid nanofluid) and 1.15337 (i.e., 153.337%) (in the case of nanofluid) when Eckert number takes input in the range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>≤</mo><msub><mi>E</mi><mrow><mi>c</mi><mi>k</mi></mrow></msub><mo>≤</mo><mn>0.2</mn></mrow></semantics></math></inline-formula>. In case of hybrid nanofluid, it was discovered that the mass transfer rate increases at a rate of 1.497214 (i.e., 149.7214%) when chemical reaction <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><mi>K</mi><mi>r</mi></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula> takes input in the range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>≤</mo><mi>K</mi><mi>r</mi><mo>≤</mo><mn>0.2</mn></mrow></semantics></math></inline-formula>. In addition, we checked our findings against those of other researchers and discovered a respectable degree of agreement. |
| first_indexed | 2024-03-10T03:28:46Z |
| format | Article |
| id | doaj.art-31b504d363f549019859d315132cab33 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:28:46Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-31b504d363f549019859d315132cab332023-11-23T12:01:13ZengMDPI AGMathematics2227-73902022-05-011010170610.3390/math10101706Simulation of Dissipative Hybrid Nanofluid (PEG-Water + ZrO<sub>2</sub> + MgO) Flow by a Curved Shrinking Sheet with Thermal Radiation and Higher Order Chemical ReactionGopinath Veeram0Pasam Poojitha1Harika Katta2Sanakkayala Hemalatha3Macherla Jayachandra Babu4Chakravarthula S. K. Raju5Nehad Ali Shah6Se-Jin Yook7Department of Mathematics, Chinthalapati Satyavathi Devi St. Theresa’s College for Women (A), Eluru 534003, Andhra Pradesh, IndiaDepartment of Mathematics, Chinthalapati Satyavathi Devi St. Theresa’s College for Women (A), Eluru 534003, Andhra Pradesh, IndiaDepartment of Mathematics, Chinthalapati Satyavathi Devi St. Theresa’s College for Women (A), Eluru 534003, Andhra Pradesh, IndiaDepartment of Mathematics, Sir Cattamanchi Ramalinga Reddy College, Eluru 534007, Andhra Pradesh, IndiaDepartment of Mathematics, Swamy Vidyaprakasananda Government College, Srikalahasti 517644, Andhra Pradesh, IndiaSchool of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, KoreaDepartment of Mechanical Engineering, Sejong University, Seoul 05006, KoreaSchool of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, KoreaThe heat transmission capabilities of hybrid nanofluids are superior to those of mono nanofluids. In addition to solar collectors and military equipment, they may be found in a number of areas including heat exchanger, automotive industry, transformer cooling and electronic cooling. The purpose of this study was to evaluate the significance of the higher order chemical reaction parameter on the radiative flow of hybrid nanofluid (polyethylene glycol (PEG)–water combination: base fluid and zirconium dioxide, magnesium oxide: nanoparticles) via a curved shrinking sheet with viscous dissipation. Flow-driven equations were transformed into nonlinear ODEs using appropriate similarity transmutations, and then solved using the bvp4c solver (MATLAB built-in function). The results of two scenarios, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>E</mi><mi>G</mi><mo>−</mo><mi>W</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mo>+</mo><mi>Z</mi><mi>r</mi><msub><mi>O</mi><mn>2</mn></msub><mo>+</mo><mi>M</mi><mi>g</mi><mi>O</mi></mrow></semantics></math></inline-formula> (hybrid nanofluid) and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>E</mi><mi>G</mi><mo>−</mo><mi>W</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mo>+</mo><mi>Z</mi><mi>r</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>, (nanofluid) are reported. In order to draw important inferences about physical features, such as heat transfer rate, a correlation coefficient was used. The main findings of this study were that curvature parameter lowers fluid velocity, and Eckert number increases the temperature of fluid. It was observed that the volume fraction of nanoparticles enhances the skin friction coefficient and curvature parameter lessens the same. It was noticed that when curvature parameter (<i>K</i>) takes input in the range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.5</mn><mo>≤</mo><mi>K</mi><mo>≤</mo><mn>2.5</mn></mrow></semantics></math></inline-formula>, the skin friction coefficient decreases at a rate of 1.46633 (i.e., 146.633%) (in the case of hybrid nanofluid) and 1.11236 (i.e., 111.236%) (in the case of nanofluid) per unit value of curvature parameter. Increasing rates in the skin friction parameter were 3.481179 (i.e., 348.1179%) (in the case of hybrid nanofluid) and 2.745679 (in the case of nanofluid) when the volume fraction of nanoparticle (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ϕ</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>) takes input in the range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>≤</mo><msub><mi>ϕ</mi><mn>1</mn></msub><mo>≤</mo><mn>0.2</mn></mrow></semantics></math></inline-formula>. It was detected that, when Eckert number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><msub><mi>E</mi><mrow><mi>c</mi><mi>k</mi></mrow></msub></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula> increases, Nusselt number decreases. The decrement rates were observed as 1.41148 (i.e., 141.148%) (in the case of hybrid nanofluid) and 1.15337 (i.e., 153.337%) (in the case of nanofluid) when Eckert number takes input in the range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>≤</mo><msub><mi>E</mi><mrow><mi>c</mi><mi>k</mi></mrow></msub><mo>≤</mo><mn>0.2</mn></mrow></semantics></math></inline-formula>. In case of hybrid nanofluid, it was discovered that the mass transfer rate increases at a rate of 1.497214 (i.e., 149.7214%) when chemical reaction <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><mi>K</mi><mi>r</mi></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula> takes input in the range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>≤</mo><mi>K</mi><mi>r</mi><mo>≤</mo><mn>0.2</mn></mrow></semantics></math></inline-formula>. In addition, we checked our findings against those of other researchers and discovered a respectable degree of agreement.https://www.mdpi.com/2227-7390/10/10/1706hybrid nanofluidcurved shrinking sheetthermal radiationEckert numbercorrelation coefficientchemical reaction |
| spellingShingle | Gopinath Veeram Pasam Poojitha Harika Katta Sanakkayala Hemalatha Macherla Jayachandra Babu Chakravarthula S. K. Raju Nehad Ali Shah Se-Jin Yook Simulation of Dissipative Hybrid Nanofluid (PEG-Water + ZrO<sub>2</sub> + MgO) Flow by a Curved Shrinking Sheet with Thermal Radiation and Higher Order Chemical Reaction Mathematics hybrid nanofluid curved shrinking sheet thermal radiation Eckert number correlation coefficient chemical reaction |
| title | Simulation of Dissipative Hybrid Nanofluid (PEG-Water + ZrO<sub>2</sub> + MgO) Flow by a Curved Shrinking Sheet with Thermal Radiation and Higher Order Chemical Reaction |
| title_full | Simulation of Dissipative Hybrid Nanofluid (PEG-Water + ZrO<sub>2</sub> + MgO) Flow by a Curved Shrinking Sheet with Thermal Radiation and Higher Order Chemical Reaction |
| title_fullStr | Simulation of Dissipative Hybrid Nanofluid (PEG-Water + ZrO<sub>2</sub> + MgO) Flow by a Curved Shrinking Sheet with Thermal Radiation and Higher Order Chemical Reaction |
| title_full_unstemmed | Simulation of Dissipative Hybrid Nanofluid (PEG-Water + ZrO<sub>2</sub> + MgO) Flow by a Curved Shrinking Sheet with Thermal Radiation and Higher Order Chemical Reaction |
| title_short | Simulation of Dissipative Hybrid Nanofluid (PEG-Water + ZrO<sub>2</sub> + MgO) Flow by a Curved Shrinking Sheet with Thermal Radiation and Higher Order Chemical Reaction |
| title_sort | simulation of dissipative hybrid nanofluid peg water zro sub 2 sub mgo flow by a curved shrinking sheet with thermal radiation and higher order chemical reaction |
| topic | hybrid nanofluid curved shrinking sheet thermal radiation Eckert number correlation coefficient chemical reaction |
| url | https://www.mdpi.com/2227-7390/10/10/1706 |
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