An Application of the Finite Element Method for Heat and Mass Transfer of Boundary Layer Flow Using Variable Thermal Conductivity and Mass Diffusivity
Since mass diffusivity and thermal conductivity cannot be considered constants in practical analysis, an existing heat and mass transfer model of unsteady mixed convection flow over a stretching sheet is modified by incorporating the effects of nonlinear mixed convection variable thermal conductivit...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/7929161 |
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| author | Muhammad Shoaib Arif Kamaleldin Abodayeh Yasir Nawaz |
| author_facet | Muhammad Shoaib Arif Kamaleldin Abodayeh Yasir Nawaz |
| author_sort | Muhammad Shoaib Arif |
| collection | DOAJ |
| description | Since mass diffusivity and thermal conductivity cannot be considered constants in practical analysis, an existing heat and mass transfer model of unsteady mixed convection flow over a stretching sheet is modified by incorporating the effects of nonlinear mixed convection variable thermal conductivity and mass diffusivity and solved its dimensionless form by applying the finite element method which is the main novelty of this work. Nonlinear governing equations are created because of changing thermal conductivity and mass diffusivity. Nonlinear solutions can be achieved by employing the Galerkin finite element approach. Temperature and concentration-based thermal conductivity and mass diffusivity are considered. The model is expressed as a set of partial differential equations, and furthermore, it is reduced to a system of dimensionless ordinary differential equations. These obtained equations are solved with the finite element method with linear interpolating polynomials and numerical integration. In addition, a Matlab solver bvp4c is also considered for comparison purposes or validation of the computed results. The graphs depict the effect of various parameters on the velocity, temperature, and concentration curves. The results show that thermal and diffusive wave propagation is significantly affected by thermal conductivity and mass diffusivity changes. Results show that flow velocity escalates by rising values of thermal and solutal Grashof numbers. |
| format | Article |
| id | doaj-art-aebafd19a73b4f05bc63c9c35fbe5fe2 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-aebafd19a73b4f05bc63c9c35fbe5fe22025-08-20T03:38:59ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/7929161An Application of the Finite Element Method for Heat and Mass Transfer of Boundary Layer Flow Using Variable Thermal Conductivity and Mass DiffusivityMuhammad Shoaib Arif0Kamaleldin Abodayeh1Yasir Nawaz2Department of Mathematics and SciencesDepartment of Mathematics and SciencesDepartment of MathematicsSince mass diffusivity and thermal conductivity cannot be considered constants in practical analysis, an existing heat and mass transfer model of unsteady mixed convection flow over a stretching sheet is modified by incorporating the effects of nonlinear mixed convection variable thermal conductivity and mass diffusivity and solved its dimensionless form by applying the finite element method which is the main novelty of this work. Nonlinear governing equations are created because of changing thermal conductivity and mass diffusivity. Nonlinear solutions can be achieved by employing the Galerkin finite element approach. Temperature and concentration-based thermal conductivity and mass diffusivity are considered. The model is expressed as a set of partial differential equations, and furthermore, it is reduced to a system of dimensionless ordinary differential equations. These obtained equations are solved with the finite element method with linear interpolating polynomials and numerical integration. In addition, a Matlab solver bvp4c is also considered for comparison purposes or validation of the computed results. The graphs depict the effect of various parameters on the velocity, temperature, and concentration curves. The results show that thermal and diffusive wave propagation is significantly affected by thermal conductivity and mass diffusivity changes. Results show that flow velocity escalates by rising values of thermal and solutal Grashof numbers.http://dx.doi.org/10.1155/2022/7929161 |
| spellingShingle | Muhammad Shoaib Arif Kamaleldin Abodayeh Yasir Nawaz An Application of the Finite Element Method for Heat and Mass Transfer of Boundary Layer Flow Using Variable Thermal Conductivity and Mass Diffusivity Journal of Mathematics |
| title | An Application of the Finite Element Method for Heat and Mass Transfer of Boundary Layer Flow Using Variable Thermal Conductivity and Mass Diffusivity |
| title_full | An Application of the Finite Element Method for Heat and Mass Transfer of Boundary Layer Flow Using Variable Thermal Conductivity and Mass Diffusivity |
| title_fullStr | An Application of the Finite Element Method for Heat and Mass Transfer of Boundary Layer Flow Using Variable Thermal Conductivity and Mass Diffusivity |
| title_full_unstemmed | An Application of the Finite Element Method for Heat and Mass Transfer of Boundary Layer Flow Using Variable Thermal Conductivity and Mass Diffusivity |
| title_short | An Application of the Finite Element Method for Heat and Mass Transfer of Boundary Layer Flow Using Variable Thermal Conductivity and Mass Diffusivity |
| title_sort | application of the finite element method for heat and mass transfer of boundary layer flow using variable thermal conductivity and mass diffusivity |
| url | http://dx.doi.org/10.1155/2022/7929161 |
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