Two-Dimensional Generalized Magneto-Thermo-Viscoelasticity Problem for a Spherical Cavity with One Relaxation Time Using Fractional Derivative

Abstract

The present paper is aimed to studying the two-dimensional generalised magneto-thermo-viscoelasticity problem for a spherical cavity with one relaxation time using fractional derivative. The formulation is applied to generalised thermoelasticity based on the theory of generalised thermoelastic diffusion with one relaxation time. The spherical cavity of the solid surface is assumed to be traction free and subjected to both heating and an external magnetic field. The Laplace transform technique is used to obtain the general solution. The inverse Laplace transform is carried out using a numerical inversion method based. The temperature, displacement, and stresses are obtained and represented graphically with the help of Mathcad software.

Keywords

• Fractional order
• spherical cavity
• electromagnetic field
• magneto-thermo-viscoelasticity

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