Entropy Generation and Statistical Analysis of MHD Hybrid Nanofluid Unsteady Squeezing Flow between Two Parallel Rotating Plates with Activation Energy.

Squeezing flow is a flow where the material is squeezed out or disfigured within two parallel plates. Such flow is beneficial in various fields, for instance, in welding engineering and rheometry. The current study investigates the squeezing flow of a hybrid nanofluid (propylene glycol-water mixture combined with paraffin wax-sand) between two parallel plates with activation energy and entropy generation. The governing equations are converted into ordinary differential equations using appropriate similarity transformations. The shooting strategy (combined with Runge-Kutta fourth order method) is applied to solve these transformed equations. The results of the conducted parametric study are explained and revealed in graphs. This study uses a statistical tool (correlation coefficient) to illustrate the impact of the relevant parameters on the engineering parameters of interest, such as the surface friction factor at both plates. This study concludes that the squeezing number intensifies the velocity profiles, and the rotating parameter decreases the fluid velocity. In addition, the magnetic field, rotation parameter, and nanoparticle volumetric parameter have a strong negative relationship with the friction factor at the lower plate. Furthermore, heat source has a strong negative relationship with heat transfer rate near the lower plate, and a strong positive correlation with the same phenomena near the upper plate. In conclusion, the current study reveals that the entropy generation is increased with the Brinkman number and reduced with the squeezing parameter. Moreover, the results of the current study verify and show a decent agreement with the data from earlier published research outcomes.

Three-dimensional numerical analysis of flow and heat transfer of bi-directional stretched nanofluid film exposed to an exponential heat generation using modified Buongiorno model.

The heat transfer characteristics of copper/water nanofluid flow over a bi-directional stretched film are theoretically studied. The used mathematical model accounts for nanofluid effective dynamic viscosity and thermal conductivity. The model of the current study utilizes the modified Buongiorno model to scrutinize the effect of haphazard motion, nanoparticles' thermo-migration, and effective nanofluid properties. 3D flow is driven by having the nanofluid film elongation in two directions. The thermal analysis of the problem considers the nonlinear internal heat source and Newton heating conditions. In modeling the problem, the Prandtl boundary layer approximations are employed. Moreover, the nonlinear problem set of governing equations for investigating the transport of water conveying copper nanoparticles was non-dimensionalized before being treated numerically. The current parametric study investigates the impact of governing parameters on nanoparticles velocities, temperature, and concentration distributions. The presence of copper nanoparticles leads to a higher nanofluid temperature upon heating. The temperature enhances with the nanoparticles Brownian movement and thermo-migration aspects. Furthermore, involving a heat source phenomenon augments the magnitude of the heat transfer rate. Moreover, the velocity ratio factor exhibits decreasing behavior for x-component velocity and increasing behavior for y-component velocity. In conclusion, the study results proved that for larger values of Nb and Nt the temperature is higher. In addition, it is clear from the investigations that the Lewis number and Brownian motion factor decline the nanoparticle concentration field.

Numerical analysis of Casson nanofluid three-dimensional flow over a rotating frame exposed to a prescribed heat flux with viscous heating.

This study investigates heat transfer characteristics and three-dimensional flow of non-Newtonian Casson nanofluid over a linearly stretching flat surface in the rotating frame of a reference. The current model includes the Buongiorno nanofluid model comprises nanoparticles' haphazard motion and thermo-migration. It also considered mechanisms for viscous heating and constant heat flux at the boundary. The nonlinear partial differential system modeling includes the non-Newtonian Casson fluid model and the boundary layer approximation. The system governing equations were nondimensionalized and numerically solved. A parametric study was conducted to analyze the significance of dimensionless parameters on velocities, the concentration, temperatures, Nusselt number, friction factors, and Sherwood number. The study reveals that the Casson nanoliquid temperature enhanced significantly due to the mechanisms of haphazard motion and thermo-migration. The momentum layer thickness of nano Casson fluid reduced due to the rotation phenomenon while the thermal layer structure amended notably. In the absence of rotation, there is no transverse velocity. The thermal layer structure is enhanced owing to the viscous heating process. The intense haphazard motion and thermo-migration mechanisms lead to maximum heat transfer rate at the plate. In addition, results show that the Coriolis force strength elevation shows similar axial and transverse velocities behavior. In addition, the nanoparticle concentration is observed higher due to the rotation aspect and Casson fluid parameter. Furthermore, the Casson fluid factor decreases with velocities, but the trend is the opposite for the high Casson fluid factor. The thermal and solute layer thickness growth is due to the nanoparticles' thermo-diffusion. In conclusion, the larger rotation factor increases the friction factors. The maximum plate heat transfer rate is when higher Nb and Nt are higher.

Radiation effects on 3D rotating flow of Cu-water nanoliquid with viscous heating and prescribed heat flux using modified Buongiorno model.

In this article, the three-dimensional (3D) flow and heat transport of viscous dissipating Cu-H2O nanoliquid over an elongated plate in a rotating frame of reference is studied by considering the modified Buongiorno model. The mechanisms of haphazard motion and thermo-migration of nanoparticles along with effective nanoliquid properties are comprised in the modified Buongiorno model (MBM). The Rosseland radiative heat flux and prescribed heat flux at the boundary are accounted. The governing nonlinear problem subjected to Prandtl's boundary layer approximation is solved numerically. The consequence of dimensionless parameters on the velocities, temperature, and nanoparticles volume fraction profiles is analyzed via graphical representations. The temperature of the base liquid is improved significantly owing to the existence of copper nanoparticles in it. The phenomenon of rotation improves the structure of the thermal boundary layer, while, the momentum layer thickness gets reduced. The thermal layer structure gets enhanced due to the Brownian movement and thermo-migration of nanoparticles. Moreover, it is shown that temperature enhances owing to the presence of thermal radiation. In addition, it is revealed that the haphazard motion of nanoparticles decays the nanoparticle volume fraction layer thickness. Also, the skin friction coefficients found to have a similar trend for larger values of rotation parameter. Furthermore, the results of the single-phase nanoliquid model are limiting the case of this study.

Entropy Generation Optimization for Rarified Nanofluid Flows in a Square Cavity with Two Fins at the Hot Wall.

Computational Fluid Dynamics (CFD) is utilized to study entropy generation for the rarefied steady state laminar 2-D flow of air-Al2O3 nanofluid in a square cavity equipped with two solid fins at the hot wall. Such flows are of great importance in industrial applications, such as the cooling of electronic equipment and nuclear reactors. In this current study, effects of the Knudsen number (Kn), Rayleigh number (Ra) and the nano solid particle's volume fraction ( ϕ ) on entropy generation were investigated. The values of the parameters considered in this work were as follows: 0 ≤ K n ≤ 0.1 , 10 3 ≤ R a ≤ 10 6 ,   0 ≤ ϕ ≤ 0.2 . The length of the fins (LF) was considered to be fixed and equal to 0.5 m, whereas the location of the fins with respect to the lower wall (HF) was set to 0.25 and 0.75 m. Simulations demonstrated that there was an inverse direct effect of Kn on the entropy generation. Moreover, it was found that when Ra was less than 104, the entropy generation, due to the flow, increased as ϕ increases. In addition, the entropy generation due to the flow will decrease at Ra greater than 104 as ϕ increases. Moreover, the entropy generation due to heat will increase as both the ϕ and Ra increase. In addition, a correlation model of the total entropy generation as a function of all of the investigated parameters in this study was proposed. Finally, an optimization technique was adapted to find out the conditions at which the total entropy generation was minimized.