Heat transfer and entropy analysis of shaped nanoparticles in stratified binary nanofluid flow over an exponentially curved Riga surface

Abstract

The problem of controlling heat transmission and flow efficiency in advanced engineering systems, such as aerospace thermal management and next-generation cooling devices, is critically hampered by energy losses due to friction and thermal irreversibility. This study addresses that gap by investigating how nanoparticle shape influences the flow and entropy production of a magnetohydrodynamic tantalum‑water/ethylene glycol nanoliquid over an exponentially extending curved permeable surface, a geometry that better portrays real industrial curvatures than conventional flat plates. The novelty lies in three simultaneous advances: (i) using non‑spherical nanoparticle shapes (tetrahedron, column, and lamina) on an exponentially curved Riga plate, (ii) incorporating both thermal stratification and porous-medium effects, and (iii) quantifying entropy generation and the Bejan number, factors rarely combined in curved-surface nanofluid research. The governing partial differential equations (PDEs) are reduced to ordinary differential equations (ODEs) via similarity transformations and solved numerically using the MATLAB bvp4c solver. Key quantitative results show that lamina‑shaped nanoparticles produce the highest temperature enhancement and entropy generation, with the Nusselt number increasing by up to 18% relative to tetrahedral particles at the same modified Hartmann number. Conversely, columnar shapes yield the lowest thermal performance. The heat transmission rate is most sensitive to the modified Hartmann number for lamina particles, increasing by 12% over the tested Hartmann range. The main conclusion is that particle shape is a first‑order control parameter: lamina geometries maximize thermal output and entropy, making them ideal for high‑heat‑flux applications, while columnar shapes minimize irreversibility for energy‑efficient designs. These findings offer a predictive tool for tailoring nanoparticle morphology in curved-surface systems, and the model’s predictions are validated against limiting cases from prior flat‑plate studies, confirming its reliability for practical deployment.