Abstract
In this article, transient heat conduction in a cylindrical shell of functionally graded material is studied by using analytical method. The shell is assumed to be in axisymmetry conditions. The material properties are considered to be nonlinear with a power law distribution through the thickness. The temperature distribution is derived analytically by using the Bessel functions. To verify the proposed method the obtained numerical results are compared with the published results. The comparisons of temperature distribution between various time and material properties are presented.
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Abbreviations
- a :
-
inner radius
- b :
-
outer radius
- B1, B2:
-
constant coefficients
- B1i , B2i :
-
constant coefficients
- C (kJ/kg K):
-
specific heat
- h (W/m2 K):
-
heat convection coefficients
- k (W/m K):
-
heat conductivity
- \(\bar{k}\) :
-
nondimentional heat conduction coefficient
- k 0 :
-
material constant
- m1, m2:
-
material constant
- N:
-
number of eigenvalues
- r (m):
-
radius
- \(\bar{r}\) :
-
nondimensional radius
- t :
-
time
- \(\bar{t}\) :
-
nondimensional time
- T (° K):
-
temperature distribution
- \(\bar{t}\) :
-
nondimensional temperature distribution
- T0 (°K):
-
constant temperature
- ρc c (Kj/m3 K):
-
the product of density and specific heat of ceramic
- ρc 0 :
-
material constant
- \(\rho \bar{c}\) :
-
nondimensional
- ρ (kg/m3):
-
density
- θ (°C):
-
temperature of shell body
- θ1 (°C):
-
temperature of fluid
- γ, γ i :
-
eigenvalues
- λ:
-
constant value
References
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Hosseini, S.M., Akhlaghi, M. & Shakeri, M. Transient heat conduction in functionally graded thick hollow cylinders by analytical method. Heat Mass Transfer 43, 669–675 (2007). https://doi.org/10.1007/s00231-006-0158-y
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DOI: https://doi.org/10.1007/s00231-006-0158-y