Numerical study of the flow in a square cavity filled with Carbopol-TiO₂ nanofluid

Numerical investigation on natural convection heat transfer of Tiwari - Das model nanofluid inside a square cavity with thermal radiation and magnetic field is carried out in this analysis. Ethylene Glycol$\left(\mathrm{E}\mathrm{G}\right)$is considered as base fluid and $\mathrm{T}\mathrm{i}{\mathrm{O}}_2$ (Titanium Oxide) considered as nanoparticles for the present investigation. The side horizontal walls of cavity are assumed to be adiabatic and isothermal conditions on both sides walls are considered in this analysis. The finite difference method is implemented to solve the governing non-linear partial differential equations representing momentum and temperature equations. The sway of volume fraction parameter$(0.01\le \varphi \le 0.09)$, magnetic field parameter$(1.0\le \mathrm{M}\le 3.0)$, Rayleigh number $(100\le \mathrm{R}\mathrm{a}\le 1000)$, radiation parameter $(0.1\le \mathrm{R}\le 0.9)$, Reynolds number $(0.1\le \mathrm{R}\mathrm{e}\le 0.5)$ and Prandtl number $(5.2\le \mathrm{P}\mathrm{r}\le 7.2)$ on $\mathrm{T}\mathrm{i}{\mathrm{O}}_2-\mathrm{E}\mathrm{G}$ nanofluid flow and heat transfer is illustrated through graphs. Furthermore, the codes of average Nusselt number with dissimilar values of pertinent parameters are also calculated and results are depicted through graphs. The result shows that, temperature of $\mathrm{T}\mathrm{i}{\mathrm{O}}_2-\mathrm{E}\mathrm{G}$ nanofluid escalates inside the cavity with higher values of (M). Higher heat can be transferred from hot wall to cold wall when radiation parameter (R) intensifies.

Natural convection in a cavity with non-uniformly heated bottom wall, partly filled with a non-Newtonian nanofluid (Cu-water) layer and partly with air layer is studied numerically in this work. The mixture of water and copper nanoparticles shows a shear-thinning rheological behavior. The nanofluid's rheological parameters, i.e. consistency and flow index, are obtained according to the solid volume fraction, based on experimental data given in the literature. The general equations governing the physical problem are solved using the finite volume method over a wide range of Rayleigh number (10³ ≤ Ra₁ ≤ 10⁶), volume fraction of nanoparticles (0% ≤ ϕ ≤ 5%), filling level of the lower phase (0.25 H ≤ H_nf ≤ H) and the aspect ratio of the cavity (0.5 ≤ A ≤ 4.0). The results show that both flow intensity and heat transfer are enhanced when increasing these parameters. Predictive correlations relating the average Nusselt number to the quoted parameters have been proposed.

In this study, double diffusive free convection of nanofluid within a confined rectangular duct is investigated numerically. The momentum and energy equations are placed in the form of difference equations and solved numerically. The left wall conditions for the concentration and temperature are lesser than those of the right wall and the upper and lower walls are insulated. Different nanofluids are considered such as mixtures with copper, diamond, silicon oxide and titanium oxide, suspended in water. Brinkman and Maxwell models are used to characterize the nanofluid. Tiwari and Das model is opted to define the nanofluid behavior. The simulations are conducted using different nanoparticles, thermal Grashof number 1 ≤ GrT ≤ 20, solute Grashof number 1 ≤ GrC ≤ 15, solid volume fraction 0 ≤ Φ ≤ 0.05, Dufour number 0 ≤ Df ≤ 1, Brinkman number 0 ≤ Br ≤ 2, and Soret number 0 ≤ Sr ≤ 5. Additionally, behavior of volumetric flow strength, skin friction, heat transport intensity and Sherwood number is also examined. The thermal Grashof number, Brinkman number, Dufour, Soret and Schmidt parameters accelerate the velocity and temperature and dwindle the concentration whereas the reversal effect was obtained for the solid volume fraction. The concentration Grashof number diminishes the velocity and temperature and intensifies the concentration. The silver nanoparticles produce the highest velocity whereas diamond nanoparticles cause the lowest velocity and temperature. The maximum temperature is attained with silicon oxide.

This paper investigates numerically the flow of a temperature-dependent viscoplastic fluid containing hybrid Ag and MgO nanoparticles through a ventilated heated cavity. A new approach for modeling the hybrid nanoparticle migration is proposed. The proposed model, which is based on Buongiorno’s non-homogeneous model, takes into account the nanoparticles mass flux due to both Brownian and thermophoretic diffusion, for each solid constituent. This is done by adding a mass conservation equation for each nanoparticle type, considering no mass flux at the walls. The results reveal that the nanoparticle distribution is the same for both constituents due to the dominance of inertia and buoyancy forces over slip mechanisms.

In this achievement, the physical perspectives on 3D natural convection MHD flow of GO- MoS₂ / Water (H₂O)-Ethylene glycol (C₂H₆O₂) (50:50 Vol%) hybrid nanofluid under the effect of thermal ray, shape and slip factors has been presented using Runge- Kutta Fehlberg 5th order (RKF-5) numerical procedure. The infiltration of diverse parameters for instance: suction/ injection parameters, thermal radiation, and nanoparticle shapes (Cylinders, Platelets, and Bricks), on velocity and temperature profiles are exemplified qualitatively through graphs. Outputs indicate that: Lorentz force created by augmenting magnetic square parameter (M) causes diminution in the velocity profile. The radiation parameter has used to breakdown hydrogen bonds of fluid molecules. Additionally, strong hydrogen bonding of hybrid nanofluid (GO- MoS₂) causes a sharp increase in thermal conductivity and, consequently, increment in temperature profile (H₂ bond_{Hybrid‐phase} > H₂ bond_Nano‐phase). Increasing the shape factor has always increased temperature profile and heat transfer rate, so the number of hydrogen bonds also decreases.

The present paper examines the viscous laminar mixed convection flow of a Bingham viscoplastic fluid in order to enhance the thermal performance and thus reduce the pressure drop. To achieve this, three-dimensional numerical simulations for vertical, inclined, and round backward facing step inside a horizontal rectangular duct are established.

The effects of variation in buoyancy, viscous and inertia forces variations as well as the step shape, on thermal and hydrodynamic behaviours of the fluid are investigated. The structure of the flow is significantly influenced by the variation of Bingham and Richardson numbers and the backward facing steps shape. It is found that the recirculation zones, which are the main source of thermal and hydrodynamic losses, are intensified with the increase in buoyancy forces represented by the Richardson number. Moreover, the recirculation zones are attenuated as the viscous forces predominate. It is also noticed that the recirculation zones decrease or disappear as the geometry is modified by reducing the angle or the shape of the step. The change of the step shape reduces significantly the pressure drops of about 11.77% and 58.83% for the inclined and rounded backward facing steps; respectively, compared to the vertical backward facing step. However, the pressure coefficient decreases along the duct and increases in presence of a recirculation zone. Also, the highest value of the total Nusselt number is obtained for a round backward facing step in mixed convection. Otherwise, an increase in the Bingham number extends the plug structure in the three geometries.