This study explores the effect of silver nanoparticles on heat transfer and flow behavior within the context of the Ellis fluid model. It specifically considers electroosmotic forces in a nonuniform divergent channel with compliant walls. The analysis involves studying thermal transport in silver-blood nanofluid flow, using MATHEMATICA 13.2 software to obtain exact solutions for velocity and temperature distribution. Findings reveal that certain parameters, such as wall damping and wall elastic properties, increase skin friction, while compliant wall parameters generally reduce flow velocity. Additionally, wall rigidity and tension parameters lead to larger trapped boluses. Notably, a 1% concentration of nanoparticles enhances heat transfer by up to 13.75%, offering control over heat transfer rates. This research introduces a novel perspective by examining compliant wall impacts on heat transfer analysis in the context of electroosmotic flow within the Ellis fluid model, incorporating silver nanoparticles with potential therapeutic applications due to their antibacterial properties.

Problem statement: The study offers theoretical formulations for high-viscosity particulate flows in inclined reservoirs, taking into account the presence of homogeneous spheroidal particles of various types to produce discrete two-phase suspensions. Purpose: The primary objective of this analytical and comparative study is to identify the most dependable nanoparticles among hafnium and crystal metals that are suspended in an Eyring–Powell fluid through an inclined channel while being subjected to external magnetic and gravitational forces. Solution methodology: The flow dynamics of multiphase flows are formulated utilizing the stress tensor of the base fluid. The regular perturbation method (RPM) is employed to attain a more closed-form solution. The perturbation method is frequently employed in engineering problems to obtain an approximated solution, even when demonstrating the convergence of the solution is challenging. The rough solution is also validated through a thorough parametric analysis that shows the role of relevant parameters that contribute to the multiphase flow. Results: A concise parametric study is carried out against some of the most pertinent parameters and reveals that additional particles have promising effects on the momentum of each multiphase flow, whereas Eyring–Powell multiphase suspensions lessen in momentum due to strong internal viscous forces. The velocity of fluid and particle phases diminish with Hartmann number M and Froude number Fr. The second-order material constant B and concentration of nanoparticles C boost the motion of the fluid. The velocities of the particulate phase are quicker than the fluid phase. The hafnium particle is more reliable than crystal particles. Solution benchmark: Numerical and graphical findings have also been compared with the existing literature for the limiting case and found to be fully in agreement. Applications: This study’s findings provide a wider understanding of subterranean flows, specifically within the petroleum sector, with a focus on multiphase flows. Originality: The current study represents the authors’ original work and has not been previously submitted or published elsewhere.