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Linear stability of convective motion in a tall vertical annulus was analysed in the paper. The base flow was generated by a non-uniform distribution of heat sources in the radial direction. The base flow velocity and temperature were obtained analytically solving the system of Navier-Stokes equations under the Boussinesq approximation. The linear stability problem was solved for axi-symmetric and asymmetric perturbations by a collocation method based on the Chebyshev polynomials. Numerical results showed that there were three destabilising factors: (1) increase of the gap between the cylinders, (2) increase of the density of internal heat sources towards to the outer boundary of the annulus and (3) increase of the Prandtl number.

− Semi-analytical solutions of eddy current testing problems require several computational steps. One of the steps where numerical methods are needed is calculation of complex eigenvalues without good initial approximation for the roots. In the presented paper we describe three eddy current testing problems with cylindrical symmetry where a cylindrical inclusion in a conducting medium is of finite size. In all three cases eigenvalue problem reduces to transcendental equations containing Bessel functions in a complex plane. The algorithm of the solution of such problems is described in the paper. Results of numerical computation are presented.

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