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The paper focuses on an investigation into instability of Dean flows of nanofluids in curved channels restricted by two concentric cylinders. The flow is caused by a constant azimuthal pressure gradient. Critical values of the Dean number, which serves as the instability criterion, were found numerically by the collocation method. Functional dependencies of the critical Dean number on the ratio between the radii of the concave and convex walls (0.1…0.99), as well as dimensionless parameters describing the temperature gradient (−3…6), the relative density of the nanoparticles (0…4), the ratio of the Brownian and thermophoretic diffusion (0.1…0.9), Prandtl (0.1…10) and Schmidt (10…100) number were revealed. It was shown that an increase in the relative density of the nanoparticles, the ratio of the Brownian and thermophoretic diffusion, and Schmidt number causes instability under conditions of either positive or negative temperature gradients. An increase in the Prandtl number enforces flow stability for the negative temperature gradient and deteriorates stability for the positive temperature gradient. In light of the complexity of the physical problem in the present paper, only axisymmetric perturbations are considered as the first step to be further developed in future investigations.

Purpose The paper aims to consider heat transfer in incompressible flow in a rotating flat microchannel with allowance for boundary slip conditions of the first and second order. The novelty of the paper encompasses analytical and numerical solutions of the problem, with the latter based on the lattice Boltzmann method (LBM). The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). An increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes a similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which takes into account the second-order boundary conditions. Design/methodology/approach The paper is based on the comparisons of an analytical solution and a numerical solution, which employs the lattice Boltzmann method. Both mathematical approaches used the first-order and second-order slip boundary conditions. The results obtained using both methods agree well with each other. Findings The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). The increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes the similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which considers the second-order boundary conditions. Originality/value The novelty of the paper encompasses analytical and numerical solutions of the problem, whereas the latter are based on the LBM.

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