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Adomian decomposition sumudu transform method for solving a solid and porous fin with temperature dependent internal
Trushit Patel1, Ramakanta Meher1
1Department of Applied Mathematics and Humanities, SVNIT, Icchanath Circle, Surat, 395007 India.
Springerplus
|May 25, 2016
Summary
The Adomian decomposition sumudu transform method accurately solves fractional heat transfer problems in fins. This fractional calculus approach validates well against numerical solutions for temperature distribution.
Area of Science:
- Heat Transfer
- Fractional Calculus
- Mathematical Modeling
Background:
- Analyzing temperature distribution in fins is crucial for thermal management.
- Fractional energy balance equations offer a more comprehensive model for heat transfer.
- Internal heat generation dependent on temperature complicates fin analysis.
Purpose of the Study:
- To introduce and apply the Adomian decomposition sumudu transform method (ADSTM) for solving fractional heat transfer problems.
- To investigate temperature distribution in solid and porous fins with temperature-dependent internal heat generation.
- To validate the ADSTM by comparing its results with numerical solutions.
Main Methods:
- Adomian decomposition sumudu transform method (ADSTM)
- Modeling heat transfer in porous media using Darcy's model
- Solving fractional order energy balance equations
Main Results:
- The ADSTM effectively determines temperature distribution in both solid and porous fins.
- Results show good agreement between the ADSTM and direct numerical solutions.
- The study analyzes the impact of various parameters on fin temperature distribution.
Conclusions:
- The ADSTM is a reliable and accurate method for solving fractional heat transfer problems in fins.
- The findings contribute to a better understanding of thermal behavior in fin systems.
- The method's accuracy is confirmed through comparison with numerical simulations.
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