Instability thresholds for thermal convection in a Kelvin–Voigt fluid of variable order

Abstract We present numerical techniques for calculating instability thresholds in a model thermal convection complex viscoelastic fluid of Kelvin–Voigt type. The theory presented is valid various orders an exponential fading memory term, and the strategy obtaining neutral curves discussed general case. Specific results are order zero, also known as Navier–Stokes–Voigt fluid, fluids 1 2. For latter cases it shown that oscillatory may occur, nature stationary branches investigated detail, including where transition from one to other takes place.