zbMATH — the first resource for mathematics

Natural convection in an annular fluid layer rotating at weak angular velocity. (English) Zbl 0793.76084
The authors have presented a study of natural convection in an annular fluid layer confined between two horizontal circular cylinders rotating at the same angular velocity. The following assumptions were made: (i) both the cylinders are isothermal, the other cylinder being warmer; (ii) the geometry is two-dimensional; (iii) the weak rotation regime was considered, for which centrifugal acceleration is neglected; (iv) a non- inertial coordinate system rotating with the cylinders was considered, in order to remove uniform, solid-body rotation effects from the pure natural convection flow. The governing equations are solved using perturbation and numerical methods.
Two flow regimes were distinguished by the authors consisting of shear flow and solid-body rotation. The former is characterized by the existence of a large fluid core tied up to gravity, which does not take part in the rotation of the cylinders. It is also shown that bifurcation is possible if the Rayleigh number is high enough. At higher Rayleigh numbers hysteresis effects are evidenced, with both regimes overlapping within a given range of Reynolds numbers.
The information contained in this valuable and interesting paper should be useful for both researchers and practical engineers handling problems of this nature.

76R10 Free convection
76U05 General theory of rotating fluids
80A20 Heat and mass transfer, heat flow (MSC2010)
Full Text: DOI