DataSheet1_Influence of dual stratification on the magnetohydrodynamic flow of Jeffrey nanofluid over an exponentially stretching permeable sheet with viscous dissipation and Joule heating.docx

Nanoparticles show superior potential for enhancing thermal properties compared to conventional particle–liquid suspensions. This investigation delves into magnetohydrodynamics (MHD) drift, heat, and mass transfer effects within a Jeffery nanoparticle liquid. The study includes transference equations that consider the influences of thermophoresis and Brownian motion on particle deposition. The analysis examines the impact of a nanofluid through a porous, exponentially elongating sheet, focusing on the double-stratification effects on heat and mass transference. The primary emphasis is on the formulated thermal energy equation, which incorporates Joule heating, heat generation, and ohmic dissipation terms. The initial step involves transforming the non-linear primary equations and their related boundary conditions into non-dimensional forms using similarity variables. The homotopy analysis method is then applied to obtain analytical results for the equations. Graphical representations of the impacts of various parameters on velocity and temperature values are presented, along with a detailed discussion of these impacts. A comprehensive analysis of specific parameters on the drag force factor-reduced Nusselt number and Sherwood number is provided and illustrated. Additionally, this research is applicable in environmental engineering, particularly in managing thermal pollution in water bodies, by aiding in predicting temperature distribution and the mixing behavior of effluents.