Nanofluids rheology for viscoelastic Oldroyd-B fluid: a revised model

Abstract

A revised model is used to study Rayleigh-Bénard convection of a viscoelastic Oldroyd-B nanofluid layer with physically realistic boundary condition i.e. the flux of nanoparticle volume fraction is zero on the boundaries. Combined behaviours of thermophoretic effects and Brownian motions due to the presence of nanoparticles is emphasized. It is found that for the case of Oldroyd-B nanofluids oscillatory convection sets in before stationary convection. For stationary convection viscoelastic nanofluid acts just as a Newtonian nanofluid due to the absence of viscoelastic parameters in the expression of thermal Rayleigh number. Interestingly, oscillatory motions come into existence due to viscoelasticity of the Oldroyd-B fluid. Further, the stress relaxation parameter hastens the onset of oscillatory convection while strain retardation parameter has the effect of postponing it. Behaviour of parameters under consideration is numerically seen using the software Mathematica. The critical frequency of oscillation as a function of strain retardation parameter for various values of physical parameters is computed and its effect on the stability of the system is depicted graphically.