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Asymptotic expansion of the solution of the steady Stokes equation with variable viscosity in a two-dimensional tube structure
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13.The simplest coupled diffusion-convection equation iswhere Cɛ is the concentration, uɛ is the fluid velocity, and pɛ is the pressure. If uɛ is small with respect to Cɛ, we can write an expansion for Cɛ with respect to the small parameter that is the ratio of magnitudes of uɛ and Cɛ. Then for the terms of this expansion, the third equation may be solved before the fluid motion equations. Another possible approach is the successive approximations (fixed point iterations)where n is the number of the iteration. In both approaches, we get a problem with the variable viscosity.
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