An Analytical Study Of Convection In A Mushy Layer Under Gravity Inclination
Keywords: Mushy layer; Weakly nonlinear; Analytical approach; Chimney convection; Gravity inclination.
Abstract: The problem of weekly nonlinear convection in a horizontal mushy layer under suitable assumptions and approximations in a gravity inclined environment is studied analytically by applying a modified perturbation technique. The finite amplitude solution for the weakly nonlinear problem is obtained under a near eutectic approximation, large far field temperature and for large Stefan number in a gravity inclined environment. Specific information with regard to the convective solutions are obtained with regard to the behaviour of the system. From the results it appears that the chimney formation gets promoted as the system gets destabilised when the concentration ratio is increased while, the formation of chimneys occurs at a larger Darcy Rayleigh number when the concentration ratio is decreased. Also, it is found that the gravity inclination reduces the tendency for chimney formation under the given physical conditions. It is concluded that by a proper choice of the inclination parameter and the governing parameters, it is possible to have a good control over the formation of chimneys convection so that the appearance of freckles in the resulting solid during the solidification process could be avoided. The results are in excellent agreement with the available results in the limiting cases.
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