Skip to main content
SpringerLink
Log in

Magneto-thermoelastic problem in rotating non-homogeneous orthotropic hollow cylinder under the hyperbolic heat conduction model

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

In this paper, we proposed a model of generalized magneto-thermoelastic for orthotropic hollow cylinder whose surfaces are subjected to a thermal relaxation under the effect of rotation with one relaxation time. The system of fundamental equations is solved by using an implicit finite-difference scheme. A numerical method is used to calculate the temperature, displacement and the components of stresses with time and through the radial of the cylinder. Numerical results are given and illustrated graphically for each case considered. The results indicate that the effect of rotation, inhomogeneity and magnetic field are very pronounced. Comparison made with the results predicted by the theory of generalized magneto-thermoelasticity with one relaxation time in the absence of rotation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

u i :

are the components of the displacement tensor

T 0 :

is a reference temperature

k 1 :

is the thermal diffusivity

k 2 :

is the thermal conductivity

Q :

is the intensity

α i :

are the thermal expansion coefficients

H 0 :

is the constant magnetic field

τ :

is the thermal relaxation time

\(\,\hat{}\) :

is dimensionless variables

ν :

is the Poisson’s ratio

ρ :

is the mass density

Ω:

is the uniform angular velocity

c ij :

are the elastic constants

e ij :

are the strain

σ ij :

are the stress components

μ ′ :

is the magnetic permeability

τ rr :

is the Maxwell’s stress

t :

is the time

E :

is the Young’s modulus

T :

is the temperature

References

  1. Lord H, Shulman Y (1967) A generalized dynamical theory of thermoelasticity. J Mech Phys Solids 15:299–309

    Article  MATH  ADS  Google Scholar 

  2. Green AE, Lindsay KA (1972) Thermoelasticity. J Elast 2:1–7

    Article  MATH  Google Scholar 

  3. Green AE, Nagdhi PM (1991) A re-examination of the basic postulate of thermo mechanics. Proc R Soc Lond 432:171–194

    Article  MATH  ADS  Google Scholar 

  4. Green AE, Nagdhi PM (1992) On undamped heat wave in an elastic solid. J Therm Stresses 15:253–264

    Article  ADS  Google Scholar 

  5. Green AE, Nagdhi PM (1993) Thermoelasticity without energy dissipation. J Elast 31:189–208

    Article  MATH  Google Scholar 

  6. Das NC, Bhakta PC, Datta S (1988) Eigenfunction expansion method to thermoelastic and magneto-thermoelastic problems. Indian J Pure Appl Math 19:697–712

    MATH  Google Scholar 

  7. Zibdeh HS, Al Farran JM (1995) Stress analysis in composite hollow cylinders due to an symmetric temperature distribution. J Press Vessel Technol 117:59–65

    Article  Google Scholar 

  8. Noda N, Ashida F (1986) A three-dimensional treatment of transient thermal stresses semi-infinite circular subjected to an symmetric temperature on the cylindrical surface. Acta Mech 58:175–191

    Article  MATH  Google Scholar 

  9. Tsai YM (1993) Thermal stress in a transversely isotropic medium containing a penny-shaped crack. ASME J Appl Mech 50:24–28

    Article  Google Scholar 

  10. Chandrasekharaiah DS, Keshavan HR (1991) Thermoelastic plane waves in a transversely isotropic body. Acta Mech 87:11–22

    Article  MATH  MathSciNet  Google Scholar 

  11. El-Naggar AM, Abd-Alla AM, Fahmy MA, Ahmed SM (2002) Thermal stresses in a rotating non-homogeneous orthotropic hollow cylinder. J Heat Mass Transfer 39:41–46

    Article  ADS  Google Scholar 

  12. Misra JC, Samanta SC, Chakrabarty AK, Misra SC (1991) Magnetothermoelastic inter-action in an infinite elastic continuum with a cylindrical hole subjected to ramp-type heating. Int J Eng Sci 29:1505–1514

    Article  MATH  Google Scholar 

  13. Misra JC, Samanta SC, Chakrabarty AK (1991) Magneto-thermoelastic interaction in an aeolotropic solid cylinder subjected to a ramp-type heating. Int J Eng Sci29:1065–1075

    Article  MATH  Google Scholar 

  14. 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

    Article  Google Scholar 

  15. Abd-Alla AM, El-Naggar AM, Fahmy MA (2003) Magneto-thermoelastic problem in non-homogeneous isotropic cylinder. J Heat Mass Transfer 39:625–629

    Article  ADS  Google Scholar 

  16. Ding DJ, Wang HM, Chen WQ (2003) A solutions of a non-homogeneous orthotropic cylindrical shell for axisymmetric plane strain dynamic thermoelastic problems. J Sound Vib 263:815–829

    Article  ADS  Google Scholar 

  17. Abd-El-Salam MR, Abd-Alla AM, Hosham HA (2007) A numerical solution of magneto-thermoelastic problem in non-homogeneous isotropic cylinder by the finite difference method. Appl Math Model 31:1662–1670

    Article  MATH  Google Scholar 

  18. Abd-Alla AM, Salama AA, Abd-El-Salam MR, Hosham HA (2007) An implicit finite-difference method for solving the transient coupled thermoelastic of an annular fin. Appl Math Inf Sci 1:62–73

    MathSciNet  Google Scholar 

  19. Sadd MH (2005) Elasticity: theory, application, and numerics. Elsevier, Amsterdam

    Google Scholar 

  20. Jain MK (1987) Numerical solution of differential equations, 2nd edn. Wiley, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Taif University, Ta’if, Saudi Arabia

    A. M. Abd-Alla

  2. Mathematics Department, J.T.C., King Abdul Aziz University, Jeddah, Saudi Arabia

    S. R. Mahmoud

Authors
  1. A. M. Abd-Alla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. R. Mahmoud
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. M. Abd-Alla.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abd-Alla, A.M., Mahmoud, S.R. Magneto-thermoelastic problem in rotating non-homogeneous orthotropic hollow cylinder under the hyperbolic heat conduction model. Meccanica 45, 451–462 (2010). https://doi.org/10.1007/s11012-009-9261-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-009-9261-8

Search

Navigation