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A more focused scientific approach in the context of a mixture of thermoelastic solids would entail investigating the basic ideas guiding the behavior of the complex materials, including constitutive model development, multi-scale modeling at various length scales, and design optimization for thermoelastic solids with their precise properties. The present work is set up to study the effect of the magnetic field as an external effect on the mixture of two interacting thermoelastic solids. The fundamental mathematical equations were shown and solved by the analytical harmonic wave solution to give the solution of the descriptive functions of the discussed problem. The displacements and stresses for the mixture of the two interreacted thermoelastic solids with the mutual temperature were clarified in the 2-D and 3-D. The results are analyzed and discussed. The obtained solution for the functions is finite everywhere. The solutions for the quantities of practical interest are represented graphically with different choices of the wave number of the harmonic wave as the magnetic field with time. In addition to the numerous physical factors in the governing field equations as depicted in the figures, boundary conditions also play a role in the current damping phenomenon.
Mohamed I. M. Hilal (2024) studied this question.