Document Type

Article

Publication Date

2024

DOI

10.22105/cand.2024.443017.1090

Publication Title

Computational Algorithms and Numerical Dimensions

Volume

3

Issue

1

Pages

1-16

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.

Rights

© 2024 The Authors.

This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) License.

Original Publication Citation

Abid, M., Bibi, M., Yasin, N., & Shahid, M. (2024). A novel computational analysis of boundary-driven two-dimensional heat flow with internal heat generation. Computational Algorithms and Numerical Dimensions, 3(1), 1-16. https://doi.org/10.22105/cand.2024.443017.1090

ORCID

0009-0004-4585-8841 (Yasin)

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