Effects of variable thermal conductivity and fractional order of heat transfer on a perfect conducting infinitely long hollow cylinder

• The theory of generalized magneto-thermoelasticity with variable thermal conductivity and fractional order of heat transfer is introduced.
• The problem of an infinite long hollow cylinder in the presence of an axial uniform magnetic field is solved.
• Both the fractional order of heat transfer and the variable thermal conductivity has the same effect on all fields.

A fractional model of the equations of generalized magneto-thermoelasticity for a perfect conducting isotropic thermoelastic media which is assumed to have variable thermal conductivity depending on the temperature is given. This model is applied to solve a problem of an infinite long hollow cylinder in the presence of an axial uniform magnetic field. The solution is obtained by a direct approach. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions. Numerical computations for the temperature, the displacement and the stress distributions as well as the induced magnetic and electric fields are carried out and represented graphically. The results indicate that the thermal conductivity and time-fractional order play a major role in all considered distributions.

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