A Novel Computational Analysis of Boundary Driven Two Dimensional Heat Flow with the Internal Heat Generation
Publish Year: 1403
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_CAND-3-1_001
تاریخ نمایه سازی: 29 اردیبهشت 1403
Abstract:
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.
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Authors
Muhammad Abid
Department of Mathematics, North Carolina State University, Raleigh, ۲۷۶۹۵ NC, United States
Madiha Bibi
Rawalpindi Women University, Rawalpindi, Punjab ۴۶۳۰۰, Pakistan
Nasir Yasin
Departments of Mathematics & Statistics, Old Dominion University, VA ۲۳۵۲۹, Norfolk, USA
Muhammad Shahid
Department of Physics and Astronomy, Georgia State University, Atlanta, GA ۳۰۳۰۳, USA