Convection in Oldroyd-B fluid: Amplitude equation

The near-threshold behavior of thermal convection in viscoelastic polymeric Oldroyd-B type fluids in an infinite horizontal layer heated from below is determined for free and conductive boundary conditions, at the upper and lower limiting surfaces. Linear and nonlinear coefficients corresponding to the different bifurcations are evaluated up to third order of the amplitude equation. A rigorous analytical and numerical calculation of the coefficients of the Ginzburg-Landau equation in the Oldroyd-B model convection is presented.