Quantum magneto–photo–thermo–hydroelastic waves in a damaged porous semiconductor with Hall current under sinusoidal heating

Purpose This study aims to investigate the coupled quantum magneto–photo–thermo–hydroelastic response of a damaged, fluid-saturated porous semiconductor under sinusoidal heating. It examines how prescribed skeleton damage; Hall current and quantum carrier gradients influence longitudinal and transverse wave amplitudes and phases. Particular attention is given to distinguishing the mechanical, thermal, electronic and hydraulic contributions to the coupled response. Design/methodology/approach A linear depth-dependent model retains longitudinal and transverse displacement, temperature, fourth-order carrier transport, pore pressure and microtemperature. Integer-order Lord–Shulman conduction and sinusoidal surface heat and carrier fluxes yield a 14-state system. Seven decaying modes satisfy seven surface conditions. All numerical coefficients are dimensionless mechanism-comparison values, not calibrated material data. Findings Hall coupling produces transverse motion that reverses sign with the signed Hall parameter and vanishes in the zero-Hall limit. Increasing the quantum parameter from 0.01 to 0.10 reduces the baseline surface carrier amplitude from 0.252191 to 0.222488. Damage changes dynamic compliance without implying a universal increase in displacement. An independent collocation calculation agrees with the baseline modal fields to a maximum field-scaled discrepancy of 4.24 × 10−10 on 0 ≤ x ≤ 10. The uncoupled thermal limit reproduces Fourier and Lord–Shulman analytical solutions. Originality/value The contribution is the combined damaged porous skeleton, transverse Hall force and fourth-order carrier closure, rather than a new eigensolver. The results provide testable amplitude–phase signatures; experimental calibration remains necessary.