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Understanding and managing the complex rheological behavior of fluid models is crucial for many real-world applications, such as industrial fluid dynamics, biomedical engineering, and environmental management. This study aims to predict the unsteady magnetohydrodynamic (MHD) flow of a second-grade tetra hybrid nanofluid in a porous medium containing uniformly dispersed dust particles. To address this challenge, we develop a mathematical model utilizing a non-fractional approach with ramping conditions. Our methodology incorporates Laplace and Sumudu transforms to analyze the velocity fields of both the fluid and dust particles. Additionally, we examine the heat transfer characteristics and the underlying dynamics of the magnetized second-grade tetra hybrid nanofluid flow. The momentum transfer of the dust particles is modeled using a separate equation. Key outcomes of this research include visual representations of novel findings, facilitating comparison with existing literature. Numerical simulations based on Sumudu and Laplace transformations produce velocity profiles for both fluid and dust particles, as well as temperature distributions, aligning with theoretical expectations. These results demonstrate the effectiveness of Laplace and Sumudu transforms in analyzing and simulating the turbulent MHD flow of nanofluids through porous media with dispersed dust particles.
Dolat Khan (Tue,) studied this question.