https://doi.org/10.1140/epjs/s11734-025-01743-4
Regular Article
Comparative analysis di-hybrid, tri-hybrid, tetra-hybrid on bioconvective Sisko nanofluid over porous vertical cone/plate with thermal radiation, heat generation, viscous dissipation and chemical reaction
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, 600127, Chennai, Tamil Nadu, India
Received:
17
July
2024
Accepted:
6
June
2025
Published online:
24
June
2025
The principal aim is to explore and quantitatively analyze how thermal radiation and heat source impact on magnetohydrodynamics flow of a tetra-hybrid Sisko nano-fluid comprising nanoparticles like 
and water as base fluid. Gyrotactic micro-organisms are suspended in and around a porous vertical cone and plate. As tetra-nanoparticles in Sisko fluids are relevant to heat management and nanotechnology applications, there has been an increasing interest in studying their effect on cone geometry especially by considering the influence of heat generation, thermal radiation, and chemical reaction. This model also compares the heat and mass transfer efficiency of tetra-hybrid nanofluid with that of di- and tri- hybrid nanofluids over two different geometries, such as vertical cone and plate. The governing partial differential equations (PDEs) are transformed into highly nonlinear ordinary differential equations (ODEs) solved numerically by means of 5th-order Runge–Kutta–Fehlberg method with shooting technique. The shooting technique is utilized to convert the boundary value problem into an initial value problem. This method ensures that the numerical solutions obtained are highly precise and effective which makes a substantial significance to the current problem. The obtained results are analyzed both numerically and graphically for dimensionless variables, such as velocity, temperature, concentration, and micro-organism density. Comparative analysis for heat and mass transfer effects between hybrid, tri-hybrid, and tetra-hybrid Sisko nanofluids is performed over different geometries. The results of the present study proved that increasing thermal radiation parameter, heat source, and magnetic parameter magnifies the heat transfer in tetra-hybrid nanofluids. The efficiency of heat and mass transfer of tetra-hybrid Sisko nanofluid flow over a vertical cone has been found to be notably higher than that over a vertical plate. This study also reveals that the heat transfer enhancement for tetra-hybrid Sisko nanofluids is 66.99%, significantly surpassing the 42.11% observed for tri-hybrid Sisko nanofluids. Compared to water alone, nanofluids with 4% volume fraction of each of tetra-hybrid nanoparticles boost heat transfer by 24.88%. The most significant improvements are observed for the impact of magnetic field, thermal radiation, and heat source parameters which exhibit energy enhancement as 70.1%, 60.6%, and 60.8%, respectively. Additionally, an overview of the current findings with previous investigations confirming the validity and a strong degree of agreement of the results. These numerical assessments also indicate that the tetra-hybrid Sisko nanofluid reveals more efficient heat transmission over cone geometry compared to plate configuration. The cone geometry promotes a more streamlined and convergent flow which increases the heat transfer due to increased surface area contact with the fluid and reduced boundary layer thickness as the shape of the cone allows for the better distribution of nanoparticles within the fluid. Tetra-hybrid nanoparticles play a vital role in enhancing thermal properties and this model presents a superior choice for industrial purposes demanding substantial heat transfer capabilities.
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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.
