Thermoelastic Response of Micropolar Solids Influenced by Locality and Hall Current under Green–Lindsay Theory with Memory Dependence

In the present study, we examined the effects of Hall current and nonlocality on a micropolar thermoelastic solid. The problem was analyzed within the framework of the Green–Lindsay (G–L) theory, and analytical expressions for the physical fields were derived using the normal mode method. Graphical results were presented to evaluate the influence of the magnetic field, nonlocal parameter, and Hall current on the behavior of various physical quantities. MATLAB software was employed to carry out the numerical computations. The results reveal that both the nonlocal parameter and Hall current significantly affect the distribution of the physical fields. A comparative analysis was conducted to highlight the differences between the cases with and without the inclusion of nonlocality and Hall current. The findings underscore the strong influence of these external parameters and demonstrate the model’s relevance to a range of applied fields, including astronomy, acoustics, engineering, and physics.