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The axisymmetric problem in two-dimensional transversely isotropic magneto-thermoelastic (TIMT) solid due to inclined load with Green–Naghdi (GN)-III theory and two temperature (2T) has been studied. The Laplace and Hankel transform has been used to get the expressions of temperature distribution, displacement, and stress components with the horizontal distance in the physical domain. The effect of Green–Naghdi theories of type I, II, and III theories of thermoelasticity has been studied graphically on the resulting quantities. A special case for the magneto-thermoelastic isotropic medium has also been studied.

Axisymmetric deformation in transversely isotropic magneto-thermoelastic solid with Green–Naghdi III due to inclined load