In this master's thesis, we analyze the stability of the Taylor-Couette flow of a viscoelastic fluid during a phase transition that is time and place-dependent. The derivation of the stability equations, which we solved numerically using Wolfram Mathematica, is based on the equilibrium Orr-Sommerfeld equation and the continuum equation for mass conservation. Considering the linear theory of small perturbations of the harmonic form, approximated by Bessel functions, the time stability of the Taylor-Couette flow was determined using the Singular value decomposition method. We found that the flow of the viscoelastic fluid is most stable when the phase transition depends only on time. The elasticity in the viscoelastic fluid increases the rigidity of the fluid, and consequently, the flow becomes more stable.
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