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Turkish Journal of Mathematics

Author ORCID Identifier

HÜSEYİN DEMİR: 0000-0003-3606-878X

İNCİ ÇİLİNGİR SÜNGÜ: 0000-0001-7788-181X

İBRAHİM KELEŞ: 0000-0001-8252-2635

DOI

10.55730/1300-0098.3551

Abstract

The present study assumes that the material properties of the fin vary by a force rule in the axial direction, with the exception of the thermal relaxation coefficient, which is assumed to be constant. The temperature distribution in the longitudinal fin with homogeneous cross-section exposed to the laser heat source is numerically investigated. This is because these constraints lead to a linear differential equation with partial solutions that can't be analytically resolved using conventional methods, except for a few elementary order functions. Consequently, a linear or non-linear system of equations as a function of time is obtained by transforming a differential equation attained with one or more independent factors using the highly efficient, potent and practical semi-analytical method known as the Chebyshev Pseudospectral Method. Temperature distributions in the fin are then examined in terms of different homogeneity factors and time-varying heat source capacity. Furthermore, the numerical solutions' convergence is emphasised, and the results are confirmed using homogenous solutions from the literature.

Keywords

Transient heat transfer, functionally graded materials, laser heat source, Chebyshev pseudospectral method

First Page

941

Last Page

954

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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