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A practical jointed approach to transient hyperbolic heat conduction of FGM cylinders and spheres

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Abstract

In this study, a practical jointed approach of hollow cylinder and sphere shape functionally graded material (FGM) is considered. Non-Fourier hyperbolic heat conduction method is used. The FGM materials consists of a mixture of ceramic and metallic materials that shows exponential variation in the radial direction. First, the problems are transformed to the Laplace domain form. After that complementary functions method (CFM) is preferred, yielding the solution appropriately that the Durbin’s numerical inverse Laplace transform method is used to transform to the real space. The transient dynamic responses of temperature and heat flux are examined with respect to specific inhomogeneity parameters and various relative temperature changes. Different plots are produced in order to emphasize the correlation of the temperature distribution and beside this heat flux between changing time and also material properties. In order to verify the results in this study, a comparison was made with the existing solutions obtained in the literatures.

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Abbreviations

c p :

Specific heat

K :

Thermal conductivity

Q :

Dimensionless radial component of heat flux

\(\vec q\) :

Heat flux vector

q r :

Radial component of heat flux

r :

Radial coordinate

r j :

Inner radius

r o :

Outer radius

r γ :

Relative radius

S :

Internal heat generation

s :

Laplace parameter

T :

Temperature field

T wi :

Inner temperature of the body

T wo :

Outer temperature of the body

T γ :

Relative temperature

T i :

Initial temperature

t :

Time

p, w :

Dimensionless nonhomogeneity parameters

η :

Dimensionless radial coordinate

ξ :

Dimensionless time

θ :

Dimensionless temperature field

ρ :

Density

τ :

Thermal relaxation time

Q o :

Dimensionless thermal relaxation time

κ m :

Thermal diffusivity of metal (κm = Κm/ρmcpm)

v :

Dimensionless nonhomogeneity parameter

m :

Metal

c :

Ceramic

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Authors and Affiliations

  1. Department of Mechanical Engineering, Ondokuz Mayis University, Samsun, 55139, Turkey

    Nihat Can

  2. Department of Mechanical Engineering, Samsun University, Samsun, 55139, Turkey

    Ibrahim Keles

Authors
  1. Nihat Can
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  2. Ibrahim Keles
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Correspondence to Nihat Can.

Additional information

Nihat Can completed his Master’s degree at Çukurova University, Adana, Turkey. He received his Ph.D. in Mechanical Engineering from Ondokuzmayis University Samsun National University. His research interests include functionally graded materials and composite materials.

Ibrahim Keles is a Professor of Department of Mechanical Engineering, Samsun University. He received his Ph.D. in Mechanical Engineering from Çukurova University Adana, Turkey. His research interests include solid mechanics, composite materials, finite element analysis and functionally graded materials.

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Can, N., Keles, I. A practical jointed approach to transient hyperbolic heat conduction of FGM cylinders and spheres. J Mech Sci Technol 37, 1223–1231 (2023). https://doi.org/10.1007/s12206-023-0209-z

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  • DOI: https://doi.org/10.1007/s12206-023-0209-z

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