## THERMAL SCIENCE

International Scientific Journal

### THERMOSOLUTAL INSTABILITY IN A HORIZONTAL FLUID LAYER AFFECTED BY ROTATION

**ABSTRACT**

Thermosolutal convective instability in a horizontal layer affected by rotation is studied. Stationary convection and over-stability cases are considered for different boundary conditions. Analytical solutions were obtained when both boundaries are free and numerical results were obtained for the cases of free and rigid boundaries. The numerical computations of this problem were performed using the method of expansion of Chebyshev polynomials. This method is better suited to the solution of hydrodynamic stability problems than expansions in other sets of orthogonal polynomials. This method not only has high accuracy but also allows stationary and over-stable modes to be treated simultaneously, which is important if perchance the critical eigenvalue flits between the different modes in response to changing parameter values. The results obtained show that the effect of both solute concentration and rotation is to stabilize the system for stationary convection case and for the over-stability case when both boundaries are free. However when both boundaries are rigid some unexpected behavior are obtained in the case of over-stability.

**KEYWORDS**

PAPER SUBMITTED: 2017-12-03

PAPER REVISED: 2018-02-20

PAPER ACCEPTED: 2018-02-21

PUBLISHED ONLINE: 2018-03-04

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**Issue 2**, PAGES [1139 - 1149]

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