A Caputo-type fractional-order model for transient heat transfer in a longitudinal fin with functional grading
Physica Scripta, cilt.101, sa.25, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 101 Sayı: 25
- Basım Tarihi: 2026
- Doi Numarası: 10.1088/1402-4896/ae7e28
- Dergi Adı: Physica Scripta
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Chemical Abstracts Core, Compendex, INSPEC, zbMATH
- Anahtar Kelimeler: Caputo fractional derivative, Chebyshev collocation method, functionally graded materials, L1 approximation, longitudinal fin, partial differential equation
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
In this paper, we study the transient thermal behavior of a constant-area longitudinal fin composed of a functionally graded material. The longitudinal variation in thermal conductivity along the fin is modeled using four types: linear, quadratic, power, and exponential. The proposed problem is studied using a Caputo-type fractional-order model. In materials with spatially varying properties, the thermal response often exhibits nonlocal behavior that motivates the use of fractional derivatives. We derive the numerical solution to the model using the (Formula presented) (Formula presented) approximation of the Caputo derivative, while the spatial operator is treated using the Chebyshev collocation method based on the fourth kind Chebyshev polynomials. The numerical results are plotted for fins with linear, quadratic, power-law, and exponential grading at various fractional orders. Also, the functionally graded longitudinal fin efficiency and the influence of inhomogeneity parameters on the fin’s temperature distribution are shown through graphical simulations. The numerical results reveal that the transient thermal response is strongly influenced by both the fractional order and the thermal-conductivity grading profile. The fin efficiency increases with dimensionless time and asymptotically approaches a steady-state value. Increasing the convective parameter reduces the fin efficiency. The effects of linear, quadratic, power-law, and exponential thermal conductivity gradings on the thermal performance of the functionally graded fin are examined and compared.