Rotating Disk Study Tracks Heat and Entropy in Hybrid Nanofluid Flow

A new numerical study has mapped how a hybrid nanofluid behaves when it flows over a spinning, stretching disk, tracking heat transfer, microstructural rotation and entropy generation in three dimensions. The work, published in the journal Boundary Value Problems, models a MoS2-SiO2/KO hybrid nanofluid under an inclined magnetic field, with the fluid and its embedded nanoparticles allowed to sit at different temperatures rather than being forced into a single shared thermal state.

The researchers, Humaira Yasmin, Iskander Tlili, Saima Noor and Anwar Saeed, framed the problem as a coupled, highly non-linear boundary-value system describing three-dimensional non-equilibrium boundary layer flow over the rotating disk. To solve it they used a shooting optimization method with a spatial step size of 0.01 and a far-field edge set at 6.0.

Numerical rigor was a central concern of the paper. The authors report that maximum residual errors reach the order of 10 to the power of minus 7, described as a 99.92 percent achievement, and that grid independence was validated up to a mesh of 300 by 300 nodes. The computed maximum time step equals 2.45 times 10 to the power of minus 6, with convergence tracking held below a global tolerance of 1.0 times 10 to the power of minus 7. The team states that this guarantees the numerical convergence of the solution.

At the heart of the thermal analysis is a Non-Equilibrium Two-Temperature Framework, which captures the thermal slip gap between the fluid matrix and the solid nanoparticle clusters.

One of the clearest quantitative findings concerns thermal radiation. Increasing the thermal radiation parameter from 0.0 to 1.2 thickens the thermal boundary layer, and the study reports a 36.98 percent increase in the Nusselt number of the hybrid suspension.

The inter-phase heat transfer coefficient, which governs how readily energy passes between the fluid and the nanoparticles, produced the opposite trend. Setting it to 1.0 reduces local convective currents, producing a decay of 11.45 percent and pushing the system toward total temperature equilibrium. In other words, stronger coupling between the phases flattens the very temperature differences that drive the non-equilibrium behavior the model is designed to capture.

The entropy analysis connects the flow dynamics to thermodynamic cost. Raising the applied magnetic parameter from 0.0 to 4.0 induces a strong Lorentz drag, and the study reports a 64.19 percent increase in Ohmic dissipation entropy along with a significant rise in skin friction.

The Brinkman number, which compares viscous heat generation to heat conduction, shaped the balance between the two main sources of irreversibility. As it rises, fluid friction exergy destruction grows faster than thermal irreversibility.

The paper is published as open access, and the version currently available is an accepted-manuscript release shared early to provide faster access to peer-reviewed research. The publishers note that it is citable and carries a permanent DOI, but that it remains subject to further edits and will be replaced automatically by the final Version of Record.

For readers following hybrid nanofluid research, the study’s contribution lies in combining a three-dimensional rotating-disk geometry, micropolar microstructural rotation, two-temperature thermal behavior and entropy accounting in a single converged numerical framework, with the reported grid and tolerance checks offered as evidence that the quantitative percentages rest on a stable solution rather than a mesh artifact.

Subject of Research: Numerical analysis of three-dimensional micropolar hybrid nanofluid flow, heat transfer and entropy generation over a rotating stretching disk

Article Title: Three-dimensional thermodynamic analysis of micropolar hybrid nanofluid stagnation point flow with thermal non-equilibrium phase disparities and grid convergence uncertainty over a rotating stretching disk

Article References: Yasmin, H., Tlili, I., Noor, S., & Saeed, A. (2026). Three-dimensional thermodynamic analysis of micropolar hybrid nanofluid stagnation point flow with thermal non-equilibrium phase disparities and grid convergence uncertainty over a rotating stretching disk. Boundary Value Problems. https://doi.org/10.1186/s13661-026-02376-9

Image Credits: AI Generated

DOI: 10.1186/s13661-026-02376-9

Keywords: hybrid nanofluid, rotating disk, entropy generation, magnetic field, thermal radiation, Nusselt number, Bejan number, boundary layer, numerical simulation, grid convergence, micropolar fluid, two-temperature model