The Stability Analysis And Numerical Calculation Of The Shear Flow Of The Oldroyd-B Fluid

The O-B shear fluid fixed on the wall was described asRe and We are the Reynolds and Weissenberg numbers, respectively R_e =(?)The boundary conditions are as followsChapterâ…¢discussed the boundary conditions on the model, that is, slip equation,we know that when the parameters satisfy a₂ > 8, cquation(3) exhibits a maximum and a minimum ofσ_ω. If we require that the velocity V₁ = v_ω+ F(v_ω) be a monotonic function of v_ωi.e., we demand that the steady-state solutions be unique for a given value of V₁. This requirement is met in the general case when and in the case whenIn this article we use the following slip equationwhereσ_ωis the shear stress exerted by the fluid on the wall, v_ωis the relative velocity of the fluid with respect to the wall, andα₁,a₂,a₃ are material parameters.The steady-state solution of O-B fluid as followsWhere v_ω, and V₁, are the relative velocity of the fluid with respect to the wall.On the boundary the Jacobi matrix in the steady-state solution as followsThen, the eigenvalue of Jacobi matrix Df(l, v_ω) as follows The steady-state solution(7) of equations(1)is stable when it meet followingTheorem: The steady-state solution(7) of O-B fluid(1)is stable when it meet(13). The last part of the paper we do some numerical experiments, verify the reasonablenessof the stability conditions.