A novel computational analysis of boundary-driven two-dimensional heat flow with internal heat generation
Accurate numerical solution of parabolic and elliptic partial differential equations governing two-dimensional heat transfer is critical for engineering simulations but computationally challenging.This work employs key numerical techniques finite differences, conjugate gradients, and Crank-Nicolson...
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| Format: | Article |
| Language: | English |
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REA Press
2024-03-01
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| Series: | Computational Algorithms and Numerical Dimensions |
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| Online Access: | https://www.journal-cand.com/article_190219_8c251f1bc728ca17716c1785a92b7e5c.pdf |
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| _version_ | 1832580033735032832 |
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| author | Muhammad Abid Madiha Bibi Nasir Yasin Muhammad Shahid |
| author_facet | Muhammad Abid Madiha Bibi Nasir Yasin Muhammad Shahid |
| author_sort | Muhammad Abid |
| collection | DOAJ |
| description | Accurate numerical solution of parabolic and elliptic partial differential equations governing two-dimensional heat transfer is critical for engineering simulations but computationally challenging.This work employs key numerical techniques finite differences, conjugate gradients, and Crank-Nicolson time stepping to solve the heat diffusion equation and analyze method performance.The Poisson equation is discretized using second-order central finite differences and solved with the conjugate gradient approach to determine the steady state solution. The transient heat equation is integrated in time via the Crank-Nicolson implicit scheme, also utilizing conjugate gradients.The methods effectively compute solutions matching analytical and boundary conditions. Convergence and stability are achieved while capturing transient thermal evolution. Insights are gained into discretization and iteration parameter impacts.The numerical framework demonstrates accurate and efficient simulation of two-dimensional conductive heat transfer. It provides a template for extension to more complex geometries and multiphysics phenomena, contributing to advances in computational engineering. |
| format | Article |
| id | doaj-art-b107403176c3416e80dd320fd2d817a7 |
| institution | Kabale University |
| issn | 2980-7646 2980-9320 |
| language | English |
| publishDate | 2024-03-01 |
| publisher | REA Press |
| record_format | Article |
| series | Computational Algorithms and Numerical Dimensions |
| spelling | doaj-art-b107403176c3416e80dd320fd2d817a72025-01-30T11:22:59ZengREA PressComputational Algorithms and Numerical Dimensions2980-76462980-93202024-03-013111610.22105/cand.2024.443017.1090190219A novel computational analysis of boundary-driven two-dimensional heat flow with internal heat generationMuhammad Abid0Madiha Bibi1Nasir Yasin2Muhammad Shahid3Department of Mathematics, North Carolina State University, Raleigh, 27695 NC, United StatesRawalpindi Women University, Rawalpindi, Punjab 46300, PakistanDepartments of Mathematics & Statistics, Old Dominion University, VA 23529, Norfolk, USADepartment of Physics and Astronomy, Georgia State University, Atlanta, GA 30303, USAAccurate numerical solution of parabolic and elliptic partial differential equations governing two-dimensional heat transfer is critical for engineering simulations but computationally challenging.This work employs key numerical techniques finite differences, conjugate gradients, and Crank-Nicolson time stepping to solve the heat diffusion equation and analyze method performance.The Poisson equation is discretized using second-order central finite differences and solved with the conjugate gradient approach to determine the steady state solution. The transient heat equation is integrated in time via the Crank-Nicolson implicit scheme, also utilizing conjugate gradients.The methods effectively compute solutions matching analytical and boundary conditions. Convergence and stability are achieved while capturing transient thermal evolution. Insights are gained into discretization and iteration parameter impacts.The numerical framework demonstrates accurate and efficient simulation of two-dimensional conductive heat transfer. It provides a template for extension to more complex geometries and multiphysics phenomena, contributing to advances in computational engineering.https://www.journal-cand.com/article_190219_8c251f1bc728ca17716c1785a92b7e5c.pdfcentral finite differentiatingconjugate gradient methodcrank-nicholson schemeheat generation |
| spellingShingle | Muhammad Abid Madiha Bibi Nasir Yasin Muhammad Shahid A novel computational analysis of boundary-driven two-dimensional heat flow with internal heat generation Computational Algorithms and Numerical Dimensions central finite differentiating conjugate gradient method crank-nicholson scheme heat generation |
| title | A novel computational analysis of boundary-driven two-dimensional heat flow with internal heat generation |
| title_full | A novel computational analysis of boundary-driven two-dimensional heat flow with internal heat generation |
| title_fullStr | A novel computational analysis of boundary-driven two-dimensional heat flow with internal heat generation |
| title_full_unstemmed | A novel computational analysis of boundary-driven two-dimensional heat flow with internal heat generation |
| title_short | A novel computational analysis of boundary-driven two-dimensional heat flow with internal heat generation |
| title_sort | novel computational analysis of boundary driven two dimensional heat flow with internal heat generation |
| topic | central finite differentiating conjugate gradient method crank-nicholson scheme heat generation |
| url | https://www.journal-cand.com/article_190219_8c251f1bc728ca17716c1785a92b7e5c.pdf |
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