Rayleigh-Bénard convection in an elastico-viscous Walters’ (model B’) nanofluid layer

Abstract

Abstract. In this study, the onset of convection in an elastico-viscous Walters' (model B') nanofluid horizontal layer heated from below is considered. The Walters' (model B') fluid model is employed to describe the rheological behavior of the nanofluid. By applying the linear stability theory and a normal mode analysis method, the dispersion relation has been derived. For the case of stationary convection, it is observed that the Walters' (model B') elastico-viscous nanofluid behaves like an ordinary Newtonian nanofluid. The effects of the various physical parameters of the system, namely, the concentration Rayleigh number, Prandtl number, capacity ratio, Lewis number and kinematics visco-elasticity coefficient on the stability of the system has been numerically investigated. In addition, sufficient conditions for the non-existence of oscillatory convection are also derived.

Linear stability analysis of electro‐convection in dielectric Oldroydian nanofluid

“…The values of these thermal Rayleigh numbers versus wave numbers are computed numerically using the Software MATHEMATICA (version‐12). The fixed permissible values of dimensionless parameters taken by various researchers (Chand and Rana, 12,13 Rana and Chand, 14 Tzou, 18 Yadav et al, 21 Sharma et al, 34 and Rana et al 39 ) during investigations are $${\lambda }_{1}=0.6,$$ $${\lambda }_{2}=0.4,$$ $${P}_{r}=5,$$ $${R}_{n}=-0.1,\unicode{x02007}{N}_{A}=-1,$$ $$${L}_{n}=200,{R}_{e}=100.$$$…”

“…where v′ ρ′, p′, T′ ∈ E′, ′, ϕ′ and φ′ denote the perturbations of the equilibrium state. Substituting perturbations from Equation (15) in Equations ( 2), ( 7), ( 11) and ( 12), using basic solutions (14), we get linear nondimensional perturbed equations as (omitting astrisks for convenience) is the non-dimensional strain retardation time parameter. The identity ≡ ∇ curlcurl graddiv − 2 has been utilized to derive Equation ( 16).…”

“…Many researchers used both experimental and numerical methods to investigate the properties of nanofluids, as well as their applications and possibilities. [7][8][9][10][11][12][13][14] Various researchers have found that the thermal conductivity of nanofluids is influenced by many factors namely, particle size, volume fraction, pH, and zeta potential. They also observed that a low volume fraction of metal oxides in nanofluids shows no significant improvement in the thermal conductivity while adding 4%-5% metal oxides by volume result in 10%-20% rise in thermal conductivity.…”

“…Nanofluids have a lot of potential in today's world because of their unique thermophysical properties, which makes them useful for a wide range of applications such as nano‐composites, oil drilling, electrical cooling, biomedicine, and nanostructure creation transportation. Many researchers used both experimental and numerical methods to investigate the properties of nanofluids, as well as their applications and possibilities 7–14 . Various researchers have found that the thermal conductivity of nanofluids is influenced by many factors namely, particle size, volume fraction, pH, and zeta potential.…”

Study of Brinkman–Bènard nanofluid convection with idealistic and realistic boundary conditions and by considering the effects of shape of nanoparticles

“…[18][19][20][21][22] Reported works thus far considered Newtonian nanoliquids without dusty particles (of size bigger than that of nanoparticles). Rana et al, 23 Rana and Chand, 24 and Chand et al 25 considered Newtonian/non-Newtonian nanoliquids with/without dusty particles and obtained the condition for the existence of stationary and oscillatory convections in such nanoliquids in the presence/absence of a porous medium.…”