Thesis (M.Sc.) - Cairo University - Faculty Of Science - Department Of Physics

The present thesis is concerned with the onset of thermal convection of a viscous fluid occupying the annular region between two rotating rigid concentric spherical surfacesThe fluid is assumed to be self - gravitating and uniformly heated from insideA general solution , which satisfies the relevant boundary conditions , is constructedThis solution yields an eigenvalue equation for the determination of the critical Rayleigh number , Rc , characterizing the onset of convection for the general asymmetric case and , of course , for the special axisymmetric caseThe effect of the shell thickness , expressed in terms of the ratio of the inner to the outer radius a = Ri / Ro , and the rotation , expressed in terms of the Taylor number T , on Rc is investigated for both the axisymmetric and non - axisymmetric casesThe effect of variation of the Prandtl number ? on Rc is also investigated and discussedThe critical Rayleigh numbers Rc for the rotating and non - rotating sphere , reported previously in the literature , arise as a natural outcome by extrapolating our results to the case where the interior sphere vanishesThis limit is performed by letting the radius ratio a tends to zeroFurthermore , the limit for high rotation , T? ? , is found to approach an asymptotic value for the function Rc / T2 / 3 which proves to be valid for all values of the parameter aThe isotherms and streamlines of the axisymmetric solution have been computed for typical values of T and aThe obtained maps agree with the expected cellular structure for these fields

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