Numerical Solutions of Heat Diffusion Equation Over One Dimensional Rod Region

Makhtoumi, Mehran

doi:10.48550/arxiv.1807.09588

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“…Dülk and Kovácsházy [2] solved a steady-state heat equation in a two-layer medium problem and then showed that multilayered media can be represented as a hierarchy of two-layered media. Adaptive methods for analytical and numerical solutions of heat diffusion in one-dimension thin rod was investigated by Makhtoumi [3] a comprehensive analysis was carried out between the two methods. Kaushik [4] solved a steady 2-D heat equation with constant thermal conductivity numerically using TDMA technique, a comparison was made between Gauss-Seidel and TDMA.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Steady State Heat Conduction in a Rectangular Plate and Comparison with the Numerical Finite Difference Method

2022

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The medium of heat conduction is seemingly important in the world today and needs to be well understood. This paper looks at the steady state heat conduction in a rectangular plate characterized by Dirichlet boundary conditions. The steady state heat model is formulated based on some assumptions governing this phenomenon. The model which is an elliptic partial differential equation is solved using both analytic and numerical methods. The separable variable method which is an analytic method gives rise to a closed form solution. A comparative study was made by comparing the accuracy of the Finite Difference Method (FDM) and the separable variable method and the relative errors determined. The results obtained from the separable variable method were close to the numerical method. The FDM gives approximate solution with less time and fitting resilience. It is thus concluded that the FDM method allows control over mensurable error.

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Section: Introductionmentioning

confidence: 99%

Analytical Solution of Steady State Heat Conduction in a Rectangular Plate and Comparison with the Numerical Finite Difference Method

2022

View full text Add to dashboard Cite

show abstract

Numerical Solutions of Heat Diffusion Equation Over One Dimensional Rod Region

Cited by 1 publication

References 0 publications

Analytical Solution of Steady State Heat Conduction in a Rectangular Plate and Comparison with the Numerical Finite Difference Method

Analytical Solution of Steady State Heat Conduction in a Rectangular Plate and Comparison with the Numerical Finite Difference Method

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