Heat transfer analysis: convective-radiative moving exponential porous fins with internal heat generation

Zia Ud Din; Amir Ali; Zareen A. Khan; Gul Zaman; Zia Ud Din; Amir Ali; Zareen A. Khan; Gul Zaman

doi:10.3934/mbe.2022535

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 11: 11491-11511. doi: 10.3934/mbe.2022535

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Research article

Heat transfer analysis: convective-radiative moving exponential porous fins with internal heat generation

1.
Department of Mathematics, University of Malakand Chakdara Dir(L), Khyber Pakhtunkhwa, Pakistan
2.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Academic Editor: Yang Kuang

Received: 25 June 2022 Revised: 27 July 2022 Accepted: 07 August 2022 Published: 11 August 2022

The efficiency, temperature distribution, and temperature at the tip of straight rectangular, growing and decaying moving exponential fins are investigated in this article. The influence of internal heat generation, surface and surrounding temperatures, convection-conduction, Peclet number and radiation-conduction is studied numerically on the efficiency, temperature profile, and temperature at the tip of the fin. Differential transform method is used to investigate the problem. It is revealed that thermal and thermo-geometric characteristics have a significant impact on the performance, temperature distribution, and temperature of the fin's tip.The results show that the temperature distribution of decaying exponential and rectangular fins is approximately $ 15 $ and $ 7\% $ higher than growing exponential and rectangular fins respectively. It is estimated that the temperature distribution of the fin increases by approximately $ 6\% $ when the porosity parameter is increased from $ 0.1 $ to $ 0.5 $. It is also observed that the decay exponential fin has better efficiency compared to growing exponential fin which offers significant advantages in mechanical engineering.
- convection,
- convective boundary conditions,
- exponential porous fins,
- mathematical model,
- radiation
Citation: Zia Ud Din, Amir Ali, Zareen A. Khan, Gul Zaman. Heat transfer analysis: convective-radiative moving exponential porous fins with internal heat generation[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11491-11511. doi: 10.3934/mbe.2022535

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Abstract

The efficiency, temperature distribution, and temperature at the tip of straight rectangular, growing and decaying moving exponential fins are investigated in this article. The influence of internal heat generation, surface and surrounding temperatures, convection-conduction, Peclet number and radiation-conduction is studied numerically on the efficiency, temperature profile, and temperature at the tip of the fin. Differential transform method is used to investigate the problem. It is revealed that thermal and thermo-geometric characteristics have a significant impact on the performance, temperature distribution, and temperature of the fin's tip.The results show that the temperature distribution of decaying exponential and rectangular fins is approximately $ 15 $ and $ 7\% $ higher than growing exponential and rectangular fins respectively. It is estimated that the temperature distribution of the fin increases by approximately $ 6\% $ when the porosity parameter is increased from $ 0.1 $ to $ 0.5 $. It is also observed that the decay exponential fin has better efficiency compared to growing exponential fin which offers significant advantages in mechanical engineering.

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