Fundamental theorems and variational criterion in modified couple stress under multi-phase-lags and rotation

Present study involves a new mathematical formulation of modified couple stress thermoelastic diffusion under multi-phase-lags model in rotating frame of reference. The governing equations for multi-phase-lags model in rotating frame of reference are obtained with the aid of modified Fourier’s and Fick’s laws and used to explore the energy, uniqueness, reciprocity theorems and variational criterion. Instantaneous concentrated body forces, heat and chemical potential sources along with moving heat and chemical potential sources are taken to illustrate the applications of the reciprocity theorem for a specific case. It has been observed that results obtained are dominated by the physical field. Some well-known results are also explored as special cases. The multi-phase-lags and rotation in modified couple stress material makes it more realistic as all the field quantities depend upon information from surrounding at a particular point. Physical views presented in this article may be useful for the design (composition, arrangement, device, etc.) new material, geophysics and other scientific domains. Also, the study has tremendous applications in material science, geomechanics, soil dynamics and electronic industry.