Taguchi Method and Numerical Simulation for Variable Viscosity and Non-Linear Boussinesq Effects on Natural Convection over a Vertical Truncated Cone in Porous Media
This study uses an optimization approach representation and numerical solution for the variable viscosity and non-linear Boussinesq effects on the free convection over a vertical truncated cone in porous media. The surface of the vertical truncated cone is maintained at uniform wall temperature and...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-01-01
|
| Series: | Energies |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1996-1073/13/2/504 |
| _version_ | 1811186092465979392 |
|---|---|
| author | Ken Ming Tu Kuo Ann Yih Fu I Chou Jyh Horng Chou |
| author_facet | Ken Ming Tu Kuo Ann Yih Fu I Chou Jyh Horng Chou |
| author_sort | Ken Ming Tu |
| collection | DOAJ |
| description | This study uses an optimization approach representation and numerical solution for the variable viscosity and non-linear Boussinesq effects on the free convection over a vertical truncated cone in porous media. The surface of the vertical truncated cone is maintained at uniform wall temperature and uniform wall concentration (UWT/UWC). The viscosity of the fluid varies inversely to a linear function of the temperature. The partial differential equation is transformed into a non-similar equation and solved by Keller box method (KBM). Compared with previously published articles, the results are considered to be very consistent. Numerical results for the local Nusselt number and local Sherwood number with the six parameters (1) dimensionless streamwise coordinate ξ, (2) buoyancy ratio N, (3) Lewis number Le, (4) viscosity-variation parameter <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">θ</mi> <mi mathvariant="normal">r</mi> </msub> </mrow> </semantics> </math> </inline-formula> , (5) non-linear temperature parameter <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">δ</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> </inline-formula>, and (6) non-linear concentration parameter <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">δ</mi> <mn>2</mn> </msub> </mrow> </semantics> </math> </inline-formula> are expressed in figures and tables. The Taguchi method was used to predict the best point of the maxima of the local Nusselt (Sherwood) number of 3.8636 (5.1156), resulting in ξ (4), N (10), Le (0.5), <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">θ</mi> <mi mathvariant="normal">r</mi> </msub> </mrow> </semantics> </math> </inline-formula> (−2), <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">δ</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> </inline-formula> (2), <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">δ</mi> <mn>2</mn> </msub> </mrow> </semantics> </math> </inline-formula> (2) and ξ (4), N (10), Le (2), <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">θ</mi> <mi mathvariant="normal">r</mi> </msub> </mrow> </semantics> </math> </inline-formula> (−2), <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">δ</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> </inline-formula> (2), <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">δ</mi> <mn>2</mn> </msub> </mrow> </semantics> </math> </inline-formula> (2), respectively. |
| first_indexed | 2024-04-11T13:39:52Z |
| format | Article |
| id | doaj.art-763f2576a56e4cd1862afb8c2a1a16ac |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-04-11T13:39:52Z |
| publishDate | 2020-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-763f2576a56e4cd1862afb8c2a1a16ac2022-12-22T04:21:18ZengMDPI AGEnergies1996-10732020-01-0113250410.3390/en13020504en13020504Taguchi Method and Numerical Simulation for Variable Viscosity and Non-Linear Boussinesq Effects on Natural Convection over a Vertical Truncated Cone in Porous MediaKen Ming Tu0Kuo Ann Yih1Fu I Chou2Jyh Horng Chou3Department of Electrical Engineering, National Kaohsiung University of Science and Technology, No. 415, Jiangong Rd., Sanmin Dist., Kaohsiung City 8077, TaiwanDepartment of Aircraft Engineering, Air Force Institute of Technology, No. 1, Julun Rd., Gangshan Dist., Kaohsiung City 82063, TaiwanDepartment of Automation Engineering, National Formosa University, No. 64, Wunhua Rd., Huwei Township, Yunlin County 632, TaiwanDepartment of Electrical Engineering, National Kaohsiung University of Science and Technology, No. 415, Jiangong Rd., Sanmin Dist., Kaohsiung City 8077, TaiwanThis study uses an optimization approach representation and numerical solution for the variable viscosity and non-linear Boussinesq effects on the free convection over a vertical truncated cone in porous media. The surface of the vertical truncated cone is maintained at uniform wall temperature and uniform wall concentration (UWT/UWC). The viscosity of the fluid varies inversely to a linear function of the temperature. The partial differential equation is transformed into a non-similar equation and solved by Keller box method (KBM). Compared with previously published articles, the results are considered to be very consistent. Numerical results for the local Nusselt number and local Sherwood number with the six parameters (1) dimensionless streamwise coordinate ξ, (2) buoyancy ratio N, (3) Lewis number Le, (4) viscosity-variation parameter <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">θ</mi> <mi mathvariant="normal">r</mi> </msub> </mrow> </semantics> </math> </inline-formula> , (5) non-linear temperature parameter <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">δ</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> </inline-formula>, and (6) non-linear concentration parameter <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">δ</mi> <mn>2</mn> </msub> </mrow> </semantics> </math> </inline-formula> are expressed in figures and tables. The Taguchi method was used to predict the best point of the maxima of the local Nusselt (Sherwood) number of 3.8636 (5.1156), resulting in ξ (4), N (10), Le (0.5), <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">θ</mi> <mi mathvariant="normal">r</mi> </msub> </mrow> </semantics> </math> </inline-formula> (−2), <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">δ</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> </inline-formula> (2), <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">δ</mi> <mn>2</mn> </msub> </mrow> </semantics> </math> </inline-formula> (2) and ξ (4), N (10), Le (2), <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">θ</mi> <mi mathvariant="normal">r</mi> </msub> </mrow> </semantics> </math> </inline-formula> (−2), <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">δ</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> </inline-formula> (2), <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="sans-serif">δ</mi> <mn>2</mn> </msub> </mrow> </semantics> </math> </inline-formula> (2), respectively.https://www.mdpi.com/1996-1073/13/2/504taguchi experimental methodvariable viscositynon-linear boussinesqfree convectionvertical truncated coneporous media |
| spellingShingle | Ken Ming Tu Kuo Ann Yih Fu I Chou Jyh Horng Chou Taguchi Method and Numerical Simulation for Variable Viscosity and Non-Linear Boussinesq Effects on Natural Convection over a Vertical Truncated Cone in Porous Media Energies taguchi experimental method variable viscosity non-linear boussinesq free convection vertical truncated cone porous media |
| title | Taguchi Method and Numerical Simulation for Variable Viscosity and Non-Linear Boussinesq Effects on Natural Convection over a Vertical Truncated Cone in Porous Media |
| title_full | Taguchi Method and Numerical Simulation for Variable Viscosity and Non-Linear Boussinesq Effects on Natural Convection over a Vertical Truncated Cone in Porous Media |
| title_fullStr | Taguchi Method and Numerical Simulation for Variable Viscosity and Non-Linear Boussinesq Effects on Natural Convection over a Vertical Truncated Cone in Porous Media |
| title_full_unstemmed | Taguchi Method and Numerical Simulation for Variable Viscosity and Non-Linear Boussinesq Effects on Natural Convection over a Vertical Truncated Cone in Porous Media |
| title_short | Taguchi Method and Numerical Simulation for Variable Viscosity and Non-Linear Boussinesq Effects on Natural Convection over a Vertical Truncated Cone in Porous Media |
| title_sort | taguchi method and numerical simulation for variable viscosity and non linear boussinesq effects on natural convection over a vertical truncated cone in porous media |
| topic | taguchi experimental method variable viscosity non-linear boussinesq free convection vertical truncated cone porous media |
| url | https://www.mdpi.com/1996-1073/13/2/504 |
| work_keys_str_mv | AT kenmingtu taguchimethodandnumericalsimulationforvariableviscosityandnonlinearboussinesqeffectsonnaturalconvectionoveraverticaltruncatedconeinporousmedia AT kuoannyih taguchimethodandnumericalsimulationforvariableviscosityandnonlinearboussinesqeffectsonnaturalconvectionoveraverticaltruncatedconeinporousmedia AT fuichou taguchimethodandnumericalsimulationforvariableviscosityandnonlinearboussinesqeffectsonnaturalconvectionoveraverticaltruncatedconeinporousmedia AT jyhhorngchou taguchimethodandnumericalsimulationforvariableviscosityandnonlinearboussinesqeffectsonnaturalconvectionoveraverticaltruncatedconeinporousmedia |