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The transient start‐up flow solution with slip is a useful tool to verify computational fluid dynamics (CFD) simulations. However, a highly accurate, open‐source black box solution does not seem to be available. Our method provides a fast, automated, and rigorously verified open‐source implementation that can compute the hydrodynamic eigenmodes of a two‐dimensional channel flow beyond the standard floating‐point precision. This allows for a very accurate computation of the corresponding Fourier series solution. We prove that all roots are found in all special cases for the general flow problem with different slip lengths on the channel walls. The numerical results confirm analytically derived asymptotic power laws for the leading hydrodynamic eigenmode and the characteristic timescale in the limiting cases of small and large slip. The code repository including test cases is publicly available (DOI: https://doi.org/10.5281/zenodo.6806351). The Navier slip boundary condition for numerical simulations in OpenFOAM is also publicly available (DOI: https://doi.org/10.5281/zenodo.7037712).

Compared with methanol (pure) and blood, methanol‐ and blood‐based nanofluids are significant with numerous characteristics, including thermophysical effects and immersion rate of CO2 in tray column absorber. Blood‐based liquids show importance in biological treatments like digestion as well as breathing systems. Mixed convective conditions and suction or injection are helpful in controlling the heating or the cooling in industrial applications. Keeping this in view, we examined the physical perception of entropy generation (EG) in a mixed convective hybrid nanofluid (HBN) flow with chemical reaction, cross‐diffusion, and transpiration in a curved surface with activation energy and thermal radiation. Transformed principal equations are determined with the assistance of a fourth‐order Runge–Kutta method with a shooting technique. We obtained solutions for two different cases, that is, for hybrid (mixture of cases) (magnetite + hematite + blood) and (magnetite + hematite + methanol). Obtained results are discussed via graphs and tables. Also, we discussed the effects of the Bejan number and the EG. We found that the EG appears more conspicuously in the case of magnetite + hematite + methanol compare to magnetite + hematite + blood case. We also found that in the magnetite + hematite + methanol case the flow and heat transfer characteristics are more pronounced compared with that in the case of magnetite + hematite + blood. This helps us to choose magnetite + hematite + blood or magnetite + hematite + methanol compositions in the manufacturing industry. Furthermore, the rate of heat transfer can be enhanced up to 16.42% in the case of methanol‐based HBN while the rate of heat transfer can be enhanced up to 19.16% in the case of blood‐based HBN.

<abstract> <p>For entire heat transfer practitioners from the last ten years, heat transmission performance in cooling and heating applications has become foremost concern. Hence, research towards innovative heat transference fluids is enormously powerful and stimulating. This study examines flow and thermal management in axisymmetric magneto hydrodynamic Polyethylene glycol (PEG) based hybrid nanofluid flow induced by a swirling cylinder. Flow and heat transfer is analyzed and compared for PEG+ <italic>Cu</italic>₂<italic>O</italic> + <italic>MgO</italic> and PEG+Graphene+ <italic>Cu</italic> + <italic>Ag</italic> hybrid nanofluid flow. Shooting technique (R-K 4^th order) is applied to work out the flow equations numerically. Simulated results are demonstrated via graphs. The computational results are validated with the published research work and found a modest concurrence. The foremost outcome of this investigation is found to be the axial, swirl and radial velocities in hybrid nanofluid are observed to decay with improvement in Reynolds number, nanofluid volume fraction and magnetic parameter. Platelet shaped nanoparticle colloidal suspension exhibit more decaying axial, swirl and radial velocity compared to spherical shaped nanoparticle colloidal suspension. It is detected that heat transmission rate is higher in <italic>PEG</italic> + <italic>Cu</italic>₂<italic>O</italic> + <italic>MgO</italic> Hybrid nanofluid compared with <italic>PEG</italic> + <italic>Graphene</italic> + <italic>Cu</italic> + <italic>Ag</italic> Hybrid nanofluid. For cooling purpose one can adopt PEG+<italic>Cu</italic>₂<italic>O</italic> + <italic>MgO</italic> hybrid nanofluid.</p> </abstract>

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