https://hal.archives-ouvertes.fr/hal-02285050/document

Rayleigh-Bénard convection of Casson fluids

In this paper, we propose to explore experimentally the origin of the onset of motion in a well-known Carbopol gel, a concentrated suspension of microgels, when submitted to a vertical temperature gradient, namely, the Rayleigh-Benard Convection (RBC). We consider three possible scenarios: (i) the gel behaves as an elasto-viscoplastic material, (ii) the gel presents a low-stress viscosity μ+ below the yield stress τy, and (iii) the gel can be considered as a two phase system, say the microgels and the solvent, i.e., a porous medium. We propose a complete rheological characterization of Carbopol 940. Creep measurements lead to obtain an instantaneous viscosity plateau μ+∼tm with m≈1. For the first time, we measure and provide permeability values k in the Carbopol gels. We show that k = O(10−14) m2 and k∝τy0.2. Our study focuses on the reference case of the RBC with no-slip conditions at walls, and new results are provided. The results lead to the conclusion that the control parameter is the (inverse) of th...

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Origin of the onset of Rayleigh-Bénard convection in a concentrated suspension of microgels with a yield stress behavior

Laminar natural convection of yield stress fluids in annular spaces between concentric cylinders

In this work, the buoyancy-induced convection from an isothermal spheroid is studied in a Bingham plastic fluid. Extensive results on the morphology of approximate yield surfaces, temperature profiles, and the local and average Nusselt numbers are reported to elucidate the effects of the pertinent dimensionless parameters: Rayleigh number, 102 ≤ Ra ≤ 106; Prandtl number, 20 ≤ Pr ≤ 100; Bingham number, 0 ≤ Bn ≤ 103, and aspect ratio, 0.2 ≤ e ≤ 5. Due to the fluid yield stress, fluid-like (yielded) and solid-like (unyielded) regions coexist in the flow domain depending upon the prevailing stress levels vis-a-vis the value of the fluid yield stress. The yielded parts progressively grow in size with the rising Rayleigh number while this tendency is countered by the increasing Bingham and Prandtl numbers. Due to these two competing effects, a limiting value of the Bingham number (Bn
 max) is observed beyond which heat transfer occurs solely by conduction due to the solid-like behaviour of the fluid everywhere in the domain. Such limiting values bear a positive dependence on the Rayleigh number (Ra) and aspect ratio (e). In addition to this, oblate shapes (e 1) impede it. Finally, simple predictive expressions for the maximum Bingham number and the average Nusselt number are developed which can be used to predict a priori the overall heat transfer coefficient in a new application. Also, a criterion is developed in terms of the composite parameter Bn∙Gr-1/2 which predicts the onset of convection in such fluids. Similarly, another criterion is developed which delineates the conditions for the onset of settling due to buoyancy effects. The paper is concluded by presenting limited results to delineate the effects of viscous dissipation and the temperature-dependent viscosity on the Nusselt number. Both these effects are seen to be rather small in Bingham plastic fluids.

Natural convection in Bingham plastic fluids from an isothermal spheroid: Effects of fluid yield stress, viscous dissipation and temperature-dependent viscosity

Rayleigh–Bénard convection of a viscoplastic liquid in a trapezoidal enclosure

The influence of viscoplastic rheological features on the Rayleigh-Benard convection is investigated by numerical means in order to compare with first experimental results given by Darbouli et al. The fluid is modeled by a regularized Herschel-Bulkley law which is often used to fit numerous pasty fluids. Natural convection in a two-dimensional square cavity heated from below is considered. Critical values of Oldroyd number Od and yield number Y are provided. Numerical results highlight a stabilizing effect of the yield stress as well as a destabilizing effect of increasing shear-thinning coefficient n as the increase in n enhances the heat transfer in the range of our calculations. Unyielded regions are located in the square corners of the cavity and in the cavity where convection occurs. The unyielded zones size increases with the increase in Od and can invade all the cavity for sufficiently large values of Od.

Chong Li

Papers

Natural convection in shear‐thinning yield stress fluids in a square enclosure