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This paper addresses a significant research gap in the study of Rayleigh surface wave propagation within a piezoelectric medium characterized by piezoelectric properties, thermal effects and voids. Previous research has often overlooked the crucial aspects related to voids. This study aims to provide analytical solutions for Rayleigh waves propagating through a medium consisting of a nonlocal piezo-thermo-elastic material with voids under the Moore–Gibson–Thompson thermo-elasticity theory with memory dependencies.

The analytical solutions are derived using a wave-mode method, and roots are computed from the characteristic equation using the Durand–Kerner method. These roots are then filtered based on the decay condition of surface waves. The analysis pertains to a medium subjected to stress-free and isothermal boundary conditions.

Computational simulations are performed to determine the attenuation coefficient and phase velocity of Rayleigh waves. This investigation goes beyond mere calculations and examines particle motion to gain deeper insights into Rayleigh wave propagation. Furthermore, this investigates how kernel function and nonlocal parameters influence these wave phenomena.

The results of this study reveal several unique cases that significantly contribute to the understanding of Rayleigh wave propagation within this intricate material system, particularly in the presence of voids.

This investigation provides valuable insights into the synergistic dynamics among piezoelectric constituents, void structures and Rayleigh wave propagation, enabling advancements in sensor technology, augmented energy harvesting methodologies and pioneering seismic monitoring approaches.

This study formulates a novel governing equation for a nonlocal piezo-thermo-elastic medium with voids, highlighting the significance of Rayleigh waves and investigating the impact of memory.

The particle distribution in a fluid is mostly not homogeneous. The inhomogeneous dispersion of solid particles affects the velocity profile as well as the heat transfer of fluid. This study aims to highlight the effects of varying density of particles in a fluid. The fluid flows through a wavy curved passage under an applied magnetic field. Heat transfer is discussed with variable thermal conductivity.

The mathematical model of the problem consists of coupled differential equations, simplified using stream functions. The results of the time flow rate for fluid and solid granules have been derived numerically.

The fluid and dust particle velocity profiles are being presented graphically to analyze the effects of density of solid particles, magnetohydrodynamics, curvature and slip parameters. Heat transfer analysis is also performed for magnetic parameter, density of dust particles, variable thermal conductivity, slip parameter and curvature. As the number of particles in the fluid increases, heat conduction becomes slow through the fluid. Increase in temperature distribution is noticed as variable thermal conductivity parameter grows. The discussion of variable thermal conductivity is of great concern as many biological treatments and optimization of thermal energy storage system’s performance require precise measurement of a heat transfer fluid’s thermal conductivity.

This study of heat transfer with inhomogeneous distribution of the particles in a fluid has not yet been reported.