Influence of hall current and acoustic pressure on a thermoelastic plate in a two-temperature model undergoing ramp-type heating

• This study proposes a comprehensive thermoelastic model incorporating acoustic pressure effects to investigate thermoacoustic-mechanical behaviors in elastic medium. • This novel model aims to advance the overarching theory of thermoelasticity within the framework of two-temperature (2T) linear theory. • Utilizing normal mode (harmonic wave) approximation, specific boundary value problems within the applied theory of magneto-thermal acoustic systems were solved. This study proposes a novel thermoelastic model that incorporates Hall current effects, acoustic pressure, and ramp-type heating within the framework of the two-temperature (2T) linear theory. Essentially, this model aims to advance the overarching theory of thermoelasticity enabling both thermal-acoustic and mechanical analyses of elastic plate material under a strong external magnetic field to produce a Hall current. Normal mode (harmonic wave) approximation solved specific boundary value problems within the applied theory of magneto-thermal acoustic systems. Constitutive equations were formulated, yielding two distinct temperatures: conductive and thermodynamics, acoustic pressure displacements, and mechanical stress distribution. The study examines the thermoacoustic interactions and resulting stresses within the material under both external mechanical loads and magnetic fields subjected to ramp-type heating. Notably, the study delves into the effects of Hall current, relaxation times, and ramp-type heating parameters, elucidating their significance within the given context. The wave propagation of physical quantities is represented graphically and discussed and analyzed theoretically.