In this paper, the radial deformation and the corresponding stresses in a homogeneous annular fin for an isotropic material has been investigated. A numerical technique is proposed to obtain the solution of the transient coupled thermoelasticity in an annular fin cylinder with it’s base suddenly subject to a heat flux of a decayed exponential function of time. The system of fundamental equations is solved by using an implicit finite-difference method. The present method is a second-order accurate in time and space and unconditionally stable. A numerical method is used to calculate the temperature, displacement and the components of stresses with time t and through the radial of the annular fin cylinder. The results indicate that the effect of coupled thermoelasticity on temperature, stresses and displacement is very pronounced. Comparison is made with the results predicted by the theory of thermoelasticity in the absence of coupled thermoelasticity.
Coupled problem thermoelasticity Implicit finite difference method Stresses Annular fin problem
Inner and outer radii of the fin.
Specific heat of material of the fin.
Young’s modulus of material of the fin.
Heat transfer coefficient.
Is the coefficient of the thermal conductivity.
Dimensionless outer radius.
Heat flux from the base of the fin.
Dimension and dimensionless radial coordinate.
Dimension and dimensionless time.
Dimension and dimensionless radial component of displacement.
Linear thermal expansion coefficient of material of the fin.
Dimension, dimensionless and ambient temperature.
Thickness of the fin.
It is a parameter of the thermo mechanical coupling.
Exponent of the decayed heat flux.
Density of material of the fin.
Dimension and dimensionless radial stress.
Dimension and dimensionless circumferential stress.
Poisson’s ratio of material of the fin.
Dimensionless exponent of the decayed heat flux.
This is a preview of subscription content, log in to check access
Takeuti Y, Furukawa T (1981) Some considerations on thermal shock problems in a plate. J Appl Mech 48:113–118
Prevost JH, Tao D (1983) Finite element analysis of dynamic coupled thermoelasticity problems with relaxation time. ASME J Appl Mech 50:817–822
Chen CK, Chen HT (1988) Application of hybrid Laplace transform finite-difference method to transient heat conduction problem. Numer Heat Transf 14:343–356
Yang YC, Chen CK (1986) Thermoelastic transient response of an infinitely long annular cylinder composed of two different materials. Int J Eng Sci 24:569–581
Sherief HH, Anwar MN (1989) A problem in generalized thermoelasticity for an infinitely long annular cylinder composed of two different materials. J Therm Stresses 12:529–543
Wagner P (1994) Fundamental matrix of the system of dynamic linear thermoelasticity. J Therm Stresses 17:549–569
Jane KC, Lee ZY (1999) Thermoelastic transient response of an infinitely long annular multilayered cylinder. Mech Res Commun 26:709–718
Eslami MR, Shakeri M, Ohadi AR, Shiari B (1999) Coupled thermoelasticity of shells of revolution: effect of normal stress and coupling. AIAA J 37:496–504
Tehrani PH, Eslami MR (1998) Two-D time harmonic dynamic coupled thermoelasticity analysis by BEM formulation. Eng Anal Bound Elem 22:245–250
Abd-Alla AM, Abd-Alla AN, Zeidan NA (2000) Thermal stresses in a non-homogeneous orthotropic elastic multilayered cylinder. J Therm Stresses 23:413–428
El-Naggar AM, Abd-Alla AB, Fahmy MA, Ahmed SM (2002) Thermal stresses in a rotating non-homogeneous orthotropic hollow cylinder. Heat Mass Transf 39:41–46
Abd-Alla AM, El-Naggar AM, Fahmy MA (2003) Magneto-thermoelastic problem in non-homogeneous isotropic cylinder. Heat Mass Transf 39:625–629
Lee HL, Yang YC (2001) Inverse problem of coupled thermoelasticity for prediction of heat flux and thermal stresses an annular cylinder. Int Commun Heat Mass Transf 28:661–670
Chen CK, Hung CI, Lee ZY (2001) Transient thermal stresses analysis of multilayered hollow cylinder. Acta Mech 151:75–88
Abd-El-Salam MR, Abd-Alla AM, Hosham Hany A (2007) A numerical solution of magneto-thermoelastic problem in non-homogenous isotropic cylinder by the finite difference method. Appl Math Model 31(8):1662–1670
Jabbari M, Dehbani H, Eslami MR (2010) An exact solution for classic coupled thermoelasticity in spherical coordinates. J Press Vessel Technol 132:1–11
Yang YC, Chu SS (2001) Transient coupled thermoelastic analysis of an annular fin. Int Commun Heat Mass Transf 28:1103–1114
Hung CI, Chen CK, Lee ZY (2001) Thermoelastic transient response of multilayered hollow cylinder with initial interface pressure. J Therm Stresses 24:987–1006
Lee H, Yang Y, Chu S (2002) Transient thermoelastic analysis of an annular fin with coupling effect and variable heat transfer coefficient. J Therm Stresses 25(12):1105–1120
Manoach E, Ribeiro P (2004) Coupled, thermoelastic, large amplitude vibrations of Timoshenko beams. Int J Mech Sci 46:1589–1606
Noda N, Hetnarski RB, Tanigawa Y (2000) Thermal stresses. Lastran, New York
Wachtman JB, Tefft WE, Stinchfied RP (1960) Elastic constants of synthetic crystal corundum at room temperature. J Res Natl Bur Stand, Phys Chem 64A:211–228
Abd-Alla AM, Mahmoud SR (2010) Magneto-thermoelastic problem in rotating non-homogeneous orthotropic hollow cylinder under the hyperbolic heat conduction model. Meccanica 45(4):451–462
Shih W, Chang S, Tsai H (2010) Thermal prediction for transient coupled thermoelastic problem of a two-layer composite material exposed to radiation. J Therm Stresses 33(6):577–594
Bagri A, Eslami MR (2008) Generalized thermoelasticity of functionally graded annular disk considering the Lord-Shulman theory. Compos Struct 83:168–179
Yang YC, Chu SS (2001) Transient coupled thermoelastic analysis of an annular fin. Int Commun Heat Mass Transf 28(8):1103–1114
Bahtui A, Eslami MR (2007) Coupled thermoelasticity of functionally graded cylindrical shells. Mech Res Commun 34:1–18
Bakhshi M, Bagri A, Eslami MR (2006) Coupled thermoelasticity of functionally graded disk. Mech Adv Mat Struct 13:214–225
Hetnarski RB, Eslami MR (2009) Thermal stresses-advanced theory and applications. Solid mechanics and its applications, vol XXXIV. Springer, New York
Chapra CS (2004) Applied numerical methods with MATLAB for engineering and science. McGraw-Hill, New York