6533b854fe1ef96bd12aead7

RESEARCH PRODUCT

Thermally unstable throughflow of a power–law fluid in a vertical porous cylinder with arbitrary cross–section

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Abstract The present paper investigates how the cross–sectional shape of a vertical porous cylinder affects the onset of thermoconvective instability of the Rayleigh–Benard type. The fluid saturating the porous medium is assumed to be a non–Newtonian power–law fluid. A linear stability analysis of the vertical thorughflow is carried out. Three special shapes of the cylinder cross–section are analysed: square, circular and elliptical. The effect of changing the power–law index is investigated. The stability of a steady base state with vertical throughflow is analysed. The resulting stability problem is a differential eigenvalue problem that is solved numerically through the shooting method. The dimensionless numbers here considered are the non–Newtonian version of the Darcy–Rayleigh number, R a , the Peclet number, P e , and the power–law index, n. Results are presented in the form of marginal stability curves with R a plotted as a function of the cylinder aspect ratio, by assuming different values of P e and n. The critical values of R a are also computed. Results show that the critical Rayleigh number R a c for instability depends only on P e and n, and is independent of the shape of the cylinder cross–section. The geometry of the sidewall just contributes the selection of the allowed wavenumbers.