A computational time integrator for heat and mass transfer modeling of boundary layer flow using fuzzy parameters
Engineering and industrial applications depend on boundary layer flow, the thin fluid layer near a solid surface with significant viscosity. It is imperative to comprehend the mechanics of heat and mass transfer to enhance aeronautical technology, forecast weather, and design thermal systems that ar...
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125000415 |
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| author | Muhammad Shoaib Arif Wasfi Shatanawi Yasir Nawaz |
| author_facet | Muhammad Shoaib Arif Wasfi Shatanawi Yasir Nawaz |
| author_sort | Muhammad Shoaib Arif |
| collection | DOAJ |
| description | Engineering and industrial applications depend on boundary layer flow, the thin fluid layer near a solid surface with significant viscosity. It is imperative to comprehend the mechanics of heat and mass transfer to enhance aeronautical technology, forecast weather, and design thermal systems that are more efficient. Modelling and simulating these flows with precision is indispensable. Numerous models presume that fluid characteristics are continuous. Viscosity and thermal conductivity are dramatically affected by pressure and temperature. Complex computational methodologies are necessary to address this issue. A computational exponential integrator is modified for solving fuzzy partial differential equations. The scheme is explicit and provides second-order accuracy in time. The space discretization is performed with the existing compact scheme with sixth-order accuracy on internal grid points. The stability and convergence of the scheme are rigorously analyzed, and the results demonstrate superior performance compared to traditional first- and second-order methods, particularly at specific time step sizes. Stability and convergence analyses show that the method provides a 15 % improvement in accuracy compared to first-order methods and a 10 % improvement over second-order methods, particularly at time step sizes of Δt=0.01. Numerical experiments validate the accuracy and efficiency of the approach, showing significant improvements in modelling the influence of uncertainty on heat and mass transfer. The Hartmann number, Eckert number, and reaction rate parameters are selected as fuzzified parameters in the dimensionless model of partial differential equations. In addition, the scheme is compared with the existing first and second orders in time. The calculated results demonstrate that it works better than these old schemes on particular time step sizes. In addition, the scheme is compared with existing first- and second-order methods in time, demonstrating a 20 % reduction in computational time for large-scale simulations. The computational framework allows flexible examination of complex fluid flow issues with uncertainty and improves simulation stability and accuracy. This method enhances scientific and engineering models by employing fuzzy logic in computational fluid dynamics. |
| format | Article |
| id | doaj-art-dd6dc2c13b7c4728af389172353701d9 |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-dd6dc2c13b7c4728af389172353701d92025-02-10T04:34:59ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101113A computational time integrator for heat and mass transfer modeling of boundary layer flow using fuzzy parametersMuhammad Shoaib Arif0Wasfi Shatanawi1Yasir Nawaz2Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia; Corresponding author.Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia; Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, JordanDepartment of Mathematics, Air University, PAF Complex E-9, Islamabad 44000, PakistanEngineering and industrial applications depend on boundary layer flow, the thin fluid layer near a solid surface with significant viscosity. It is imperative to comprehend the mechanics of heat and mass transfer to enhance aeronautical technology, forecast weather, and design thermal systems that are more efficient. Modelling and simulating these flows with precision is indispensable. Numerous models presume that fluid characteristics are continuous. Viscosity and thermal conductivity are dramatically affected by pressure and temperature. Complex computational methodologies are necessary to address this issue. A computational exponential integrator is modified for solving fuzzy partial differential equations. The scheme is explicit and provides second-order accuracy in time. The space discretization is performed with the existing compact scheme with sixth-order accuracy on internal grid points. The stability and convergence of the scheme are rigorously analyzed, and the results demonstrate superior performance compared to traditional first- and second-order methods, particularly at specific time step sizes. Stability and convergence analyses show that the method provides a 15 % improvement in accuracy compared to first-order methods and a 10 % improvement over second-order methods, particularly at time step sizes of Δt=0.01. Numerical experiments validate the accuracy and efficiency of the approach, showing significant improvements in modelling the influence of uncertainty on heat and mass transfer. The Hartmann number, Eckert number, and reaction rate parameters are selected as fuzzified parameters in the dimensionless model of partial differential equations. In addition, the scheme is compared with the existing first and second orders in time. The calculated results demonstrate that it works better than these old schemes on particular time step sizes. In addition, the scheme is compared with existing first- and second-order methods in time, demonstrating a 20 % reduction in computational time for large-scale simulations. The computational framework allows flexible examination of complex fluid flow issues with uncertainty and improves simulation stability and accuracy. This method enhances scientific and engineering models by employing fuzzy logic in computational fluid dynamics.http://www.sciencedirect.com/science/article/pii/S2666818125000415Exponential integrator computational schemeStability: convergenceFuzzy fluid modelFuzzy parametersHeat and mass transferuncertainty modelling |
| spellingShingle | Muhammad Shoaib Arif Wasfi Shatanawi Yasir Nawaz A computational time integrator for heat and mass transfer modeling of boundary layer flow using fuzzy parameters Partial Differential Equations in Applied Mathematics Exponential integrator computational scheme Stability: convergence Fuzzy fluid model Fuzzy parameters Heat and mass transfer uncertainty modelling |
| title | A computational time integrator for heat and mass transfer modeling of boundary layer flow using fuzzy parameters |
| title_full | A computational time integrator for heat and mass transfer modeling of boundary layer flow using fuzzy parameters |
| title_fullStr | A computational time integrator for heat and mass transfer modeling of boundary layer flow using fuzzy parameters |
| title_full_unstemmed | A computational time integrator for heat and mass transfer modeling of boundary layer flow using fuzzy parameters |
| title_short | A computational time integrator for heat and mass transfer modeling of boundary layer flow using fuzzy parameters |
| title_sort | computational time integrator for heat and mass transfer modeling of boundary layer flow using fuzzy parameters |
| topic | Exponential integrator computational scheme Stability: convergence Fuzzy fluid model Fuzzy parameters Heat and mass transfer uncertainty modelling |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125000415 |
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