Analytical and numerical analysis of heat transfer from radial extended surface
The nonlinear governing equation of heat diffusion through a radial fin of rectangular profile made of aluminum alloy (A319) is solved using two approaches to predict the temperature distribution, the heat flow, and the efficiency. The first approach is analytical, adopting Kirchhoff’s method. The s...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-04-01
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| Series: | Open Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/eng-2025-0112 |
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| Summary: | The nonlinear governing equation of heat diffusion through a radial fin of rectangular profile made of aluminum alloy (A319) is solved using two approaches to predict the temperature distribution, the heat flow, and the efficiency. The first approach is analytical, adopting Kirchhoff’s method. The second approach is numerical, employing the finite volume method. The novelty of this article is the accurate solution of nonlinear heat transfer through a radial fin of variable thermal conductivity subjected to a mixed mode of radiation and convection heat dissipation along its surface. Both approaches assume that the surrounding air is kept at a constant temperature, and the tip and base of the fin are subjected to Neumann’s and Dirichlet boundary conditions, respectively. In addition, the second approach assumes the arithmetic average model to evaluate the thermal conductivity at the intersection of two neighbor control volumes. Three cases are studied. In the first case, constant thermal conductivity is applied. In the second and third cases, temperature-dependent thermal conductivity is applied. In the first and second cases, the radiation heat loss is ignored, and it is considered in the third. The effect of changing the fin aspect ratio and raising the temperature difference between the fin base and the environment on fin efficiency was studied. The results of both approaches are almost identical, with a maximum error of less than (0.1%) and a maximum error of less than (2.36%) when validated with experimental measuring of a previously published article. The forward and central difference finite volume schemes showed an accurate model to estimate the temperature gradient at the west face of each control volume when predicting the conducted heat transfer at the base of the fin and along its length, respectively. It was found that the mixed convection and radiation heat dissipation value was (19.94%) greater than dissipating heat by convection only. Also, the fin tip temperature decreases (4.57%) when radiation heat loss is considered, and it increases (0.4835%) when assuming the fin material of temperature-dependent thermal conductivity. In addition, the radiation heat loss is (28.2%) greater when the temperature difference between the base and the environment is increased from (75℃) to (275℃), and it will increase to 44.483% when this temperature difference is increased to 475℃ and will reduce the fin efficiency by 0.9291. Furthermore, decreasing the aspect ratio of the fin will decrease its efficiency. |
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| ISSN: | 2391-5439 |