Thermal-Diffusion Dynamics of Unsteady MHD Viscoelastic Flow in Porous Medium using the Laplace Transform Approach

Abstract

This research focuses on the thermal diffusion phenomenon—commonly known as the Soret effect—within the context of an unsteady magneto-hydrodynamic (MHD) viscoelastic fluid flowing through a vertical porous domain. The model incorporates the effects of chemical reactions, thermal radiation, and diffusive transport. Governing partial differential equations are non-dimensionalised and analytically solved using the Laplace transform method, with suitable boundary constraints. The influence of parameters such as Grashof number, magnetic field strength, and Schmidt number is quantitatively visualized via MATLAB to interpret the velocity, temperature, and concentration characteristics of the system.