https://doi.org/10.1140/epjs/s11734-026-02244-8
Regular Article
Innovative Python-based numerical and semi-analytical study of 
/
nanofluid performance in a parabolic trough solar collector
1
Department of Mechanical Engineering, NT.C., Islamic Azad University, Tehran, Iran
2
Department of Mechanical Engineering, Babol Noshirvani University of Technology, P.O. Box 484, Babol, Iran
a
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b
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Received:
15
November
2024
Accepted:
3
March
2026
Published online:
4
April
2026
Abstract
The effects of a two-dimensional Williamson nanofluid flow over a stretching sheet within a parabolic trough solar collector (PTSC) are examined in this study. A solar thermal collector carries out the process of absorbing sunlight and converting this radiant energy into useful thermal energy. The use of nanofluids, owing to their potential for enhanced thermal conductivity and heat transfer properties, can improve the energy conversion efficiency of PTSCs under optimized conditions. The boundary-layer equations of the Williamson nanofluid model produce partial differential equations. Through a similarity transformation, the partial differential equations are converted into nonlinear ordinary differential equations. Using Python, the nonlinear ordinary differential equations are solved using the Akbari–Ganji method (AGM) for approximate analytical solutions and the finite element method (FEM) for numerical solutions. This study conducts a performance analysis of PTSC using two nanofluids, ferro-engine oil 
and alumina–engine oil 
. The influence of porous media parameters indicates a reduction in heat transfer rate due to increased thermal resistance, while altering the velocity distribution based on the permeability of the medium. The concentration of nanoparticles is also adjusted to understand its influence on different performance aspects of the device. An increase in Reynolds number influences momentum transport, while a rise in Brinkman number enhances entropy generation due to viscous dissipation effects. The 
nanofluid outperforms the 
nanofluid in terms of thermodynamic efficiency when tested under the same parameters. The models proposed in this study provide insights into optimizing the efficiency of solar thermal energy systems. This study introduces novel modeling approaches for optimizing the efficiency of solar thermal energy systems, leveraging Williamson nanofluids in PTSC.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
