The Bénard problem for an Oldroyd–Oskolkov fluid of second order
Abstract
Abstract A model is analysed which generalizes an Oldroyd fluid in line with Oskolkov’s general classification of Oldroyd fluids of order N. We analyse the thermal convection problem where a horizontal layer of fluid is heated from below when that fluid is an Oldroyd fluid of order 2 according to the definition of Oskolkov. The thresholds for linear instability are calculated in detail, and the critical Rayleigh and wave numbers are determined. The key is to employ a very important classification of Anatoly P. Oskolkov to show that the constitutive equation for a generalized Burgers fluid is a natural extension of the constitutive equation for a Oldroyd fluid.
Fields of Study & Subjects
Rheology and Fluid Dynamics Studies
Nanofluid Flow and Heat Transfer
Elasticity and Material Modeling
Publication details
- Journal / source
- The European Physical Journal Plus
- Publisher
- Springer Science and Business Media LLC
- Volume
- 141
- Issue
- 2
- Publication date
- 14 February 2026
- Language
- EN