Optimization of response function on hydromagnetic buoyancy-driven rotating flow considering particle diameter and interfacial layer effects: Homotopy and sensitivity analysis

In this study, the preparation of nanofluid (NF) is performed by the two-stage method by dispersing nanoparticles (NP) into the base fluid (BF). Hybrid nanofluids (HNFs) were prepared in the solid volume fractions (SVFs) of SVF = 0.1, 0.2, 0.3, 0.4 and 0.5% and mono nanofluids (MNFs) were made in SVF = 0.1 and 0.3%. After ensuring stability, the thermal conductivity (TC) of HNFs and MNFs is measured by the hot wire method at a temperature range of T = 20–60 °C. The results indicate that the TC (For HNFs and MNFs) increases as the temperature increases. Increasing the SVF also increases TC, which is more evident in the higher SVFs. According to the obtained results, the highest increase in the TC is related to the MWCNT-CuO-cerium oxide/water HNF in SVF = 0.5% and T = 60 °C, which is a 26.7% increase compared to BF. In SVF = 0.3%, the MNFs containing MWCNTs NPs have a better performance than the HNFs. Compared to the results with the relationship of Lu-Lin, it was found that the temperature is critical in increasing the TC. There are no temperature parameters in the Lu-Lin model, therefore there is a difference between the laboratory results and the Lu-Lin model results. Finally, based on experimental data, a mathematical relationship between temperature and SVF was proposed to predict the TC for HNF water/cerium oxide-CuO-MWCNT. Comparing the experimental data to the outputs of the proposed relationship shows that this relationship is accurate.

A numerical study on heat transfer and entropy generation in natural convection of non-Newtonian nanofluid flow has been explored within a differentially heated two-dimensional wavy porous cavity. In the present study, copper (Cu)–water nanofluid is considered for the investigation where the specific behavior of Cu nanoparticles in water is considered to behave as non-Newtonian based on previously established experimental results. The power-law model and the Brinkman-extended Darcy model has been used to characterize the non-Newtonian porous medium. The governing equations of the flow are solved using the finite volume method with the collocated grid arrangement. Numerical results are presented through streamlines, isotherms, local Nusselt number and entropy generation rate to study the effects of a range of Darcy number (Da), volume fractions (ϕ) of nanofluids, Rayleigh numbers (Ra), and the power-law index (n). Results show that the rate of heat transfer from the wavy wall to the medium becomes enhanced by decreasing the power-law index but increasing the volume fraction of nanoparticles. Increase of porosity level and buoyancy forces of the medium augments flow strength and results in a thinner boundary layer within the cavity. At negligible porosity level of the enclosure, effect of volume fraction of nanoparticles over thermal conductivity of the nanofluids is imperceptible. Interestingly, when the Darcy–Rayleigh number Ra^*gg 10, the power-law effect becomes more significant than the volume fraction effect in the augmentation of the convective heat transfer process. The local entropy generation is highly dominated by heat transfer irreversibility within the porous enclosure for all conditions of the flow medium. The particular wavy shape of the cavity strongly influences the heat transfer flow pattern and local entropy generation. Interestingly, contour graphs of local entropy generation and local Bejan number show a rotationally symmetric pattern of order two about the center of the wavy cavity.

Mixed convective flow and heat transfer characteristics of nanofluid inside a double lid driven cavity with a square heat generating block is analyzed numerically based on heat line approach. The water- alumina nanofluid is chosen as the operational fluid through the enclosure. The governing partial differential equations with proper boundary conditions are solved by Finite Element Method using Galerkin’s weighted residual scheme. Calculations are performed for different solid volume fraction (χ) of nanoparticles 0 ≤ χ ≤ 0.15. Results are shown in terms of stream lines, isothermal lines, heat lines, average Nusselt number, average velocity and average temperature. An enhancement in heat transfer rate is observed with the increase of nanoparticles volume fraction.

This report presents the three-dimensional electromagnetohydrodynamic flow of a zinc-oxide–water nanofluid past a bidirectional Riga plate with velocity slips and thermal and mass convection conditions. The Cattaneo–Christov heat and mas flux model, thermal radiation, chemical reaction and activation energy are considered to analyze the flow problem. The volume fraction of the ZnO nanoparticles is taken 6% in this analysis. An appropriate set of similarity variables is used to transform the partial differential equations into ordinary differential equations. During this process, some parameters are found and influences of these factors on the flow profiles are shown and discussed in detail. A numerical technique called NDSolve is considered for the solution of the nanofluid flow problem. The results showed that higher solid volume fraction and slip parameter have reduced velocities profiles and the increasing solid volume fraction and thermal Biot number have increased the temperature profile. Additionally, the concentration Biot number has increased the concentration profile. The modified Hartmann number has significantly increased the velocity profile. Dual impacts in velocity profiles along primary and secondary direction has been observed due to stretching ratio parameter. A comparison of current results has been carried with a fine agreement amongst current and established results.

Investigating the thermal properties of single-grade engine oil (SAE 50) with the simultaneous addition of MWCNT and CuO nanoparticles

The aim of this paper is to present a comparative analysis of spherically and cylindrically shaped nanoparticles immersed separately in a graphene oxide/water nanofluid mixture over a rotating disk influenced by Hall current. The disk’s surface is permeable with suction/injection impact. In order to reveal the thermal integrity of the flow, the effect of nanoparticle diameter and the liquid–solid interfacial layer at the molecular level is also introduced. Estimates of thermal conductivity, interfacial layer thickness and the radius of both spherical and cylindrical particles are taken from experimental studies and utilized to investigate the thermal behavior of the flows. The Tiwari–Das model for nanofluid flow is considered that incorporates the thermal radiative impact in the energy equation. The equations obeying boundary layer theory are resolved to ordinary differential equations using a transformation, and further numerically computed with the bvp4c scheme. The velocities and the temperature profiles are graphically demonstrated versus the dimensionless parameters. Quantities of physical interest such as surface heat flux and surface drag coefficient are tabulated numerically. The results show that the surface drag is larger for nanofluids having cylindrical particles than for nanofluids containing spherical particles. Is also found that the heat transfer rate is greater for nanofluids containing cylindrical particles than spherical particles at higher interfacial layer thicknesses.

A number of processes for fabricating dense, solid materials begin with a solid powder that is to be fashioned--without melting--into an article with a particular geometric shape. Moreover, it is often the case that the small, discrete particles are dispersed in a continuous liquid phase, such as in ceramic slips, filled molten polymers, as well as suspensions used in some powder metallurgy and composite fabrication processes. Further, in these cases it is often the flow behavior or deformability of the solid-liquid suspension that is of central importance in a particular materials fabrication process, since such operations as mold-filling, pressing, extrusion, transport through pipes and channels, and even some mixing and separation processes, must take advantage of certain of the rheological characteristics of the suspension. In particular, it is the fact that such suspensions possess distinctly fluid-like properties (that is, even though they may contain a significant amount of a non-fluid-like solid phase) which allows them to be deformed. Difficulties arise, of course, as the volume fraction of the dispersed solid phase is increased, since in this case the suspension behaves like a fluid with a viscosity that is significantly higher than that of the liquid alone. For a variety of reasons, of course, it is desirable to use a suspension with a high volume fraction of solids (φs)--such as in shape-forming operations where the goal is to prepare a shaped article with a high solids volume fraction--even though the suspension’s high “viscosity” makes that shape-forming operation more difficult. What is needed, of course, is a detailed, quantitative knowledge of the relationship between φs and the “viscosity” of a given suspension, for a variety of flow conditions, in order to design a shape-forming process, or perhaps to improve an existing one.

The present study focuses on the problem of mixed convection fl uid fl ow and heat transfer of nanofl uid in a ventilated square cavity. The cavity contains two heated blocks subjected to external Al2O3–water (with particle diameter of 47 nm)nanofl uid, while temperature and nanoparticle concentration are dependent on thermal conductivity and eff ective viscosity insidea square cavity. The governing equations have been solved utilizing the fi nite volume method,while the SIMPLER algorithm is used to couple velocity and pressure fi elds. The natural convection eff ect is obtained by heating from the blocks on the bott om wall and cooling from the inlet fl ow. Using the developed code, the eff ect of Richardson number, the aspect ratio of hot blocks, solid volume fraction, and cavity inclination angles on the thermal behavior and fl uid fl ow inside the cavity are studied. The study has been executed for the Richardson number in the range of 0.1 ≤ Ri ≤ 10, solid volume fraction 0 ≤ φ ≤ 0.06, aspect ratio 0.5 ≤ AR ≤ 1, and cavity inclination angles between 0° and 90°.The obtained results are presented in the form of streamline and isotherm counter and Nusselt diagrams. It was observed from the results that for both obstacles and in all ranges of the parameters in this study, adding nanoparticles to the base fl uid or increasing the volume fraction of the nanoparticles causes the Nusselt number increases. Also, the rate of heat transfer increases when the Reynolds number increases.

A two-dimensional single-phase natural convective heat transfer in a cavity with centrally located thin partition utilizing nanofluids has been numerically analyzed. The nanofluid used, which is composed of aluminum nanoparticles in suspension of Benzene, was provided at various solid volume fractions. The study is carried out numerically for a range of Rayleigh numbers, solid volume fractions, partition heights, and aspect ratios. Regions with the same velocity and temperature distributions are identified as a symmetry of sections. One-half of such a rectangular region is chosen as the computational domain, taking into account the symmetry about the thin partition. The governing equations are modeled by a stream function-vorticity formulation and are solved numerically by finite-difference schemes. Comparison with previously published numerical and experimental results showed excellent agreement. It is demonstrated that the partition height has a strong effect on both the heat transfer rate and the flow pattern. Results are presented in the form of streamlines and isotherm plots. The variation in the local Nusselt number along the thin partition provides valuable insight into the physical processes. A new correlation is proposed for the heat transfer studies in a wide range of thermal and geometric parameters.

Disengagement of dispersed cerium oxalate from nitric-oxalic acid medium in a batch settler: Measurements and CFD simulations

Visualization of heat transport due to natural convection for hot materials confined within two entrapped porous triangular cavities via heatline concept

Nanofluids receive recognition from researchers and scientists because of their high thermal transfer rates. They have impactful industrial and technological modules in daily activities. In recent times, the heat transfer rate has been strengthened even more by a certain type of nanofluid known as "carbon nanotubes". The water-based magnetohydrodynamic flow with the nanoparticles MWCNT and SWCNT over an axially rotating stretching disk is highlighted in this article. In addition, the perspectives of viscous dissipation and MHD were taken into consideration. In order to formulate the physical problem, Xue's model is considered with the thermophysical properties and characteristics of carbon nanofluid. The current modeled system of partial differential equations is transformed into an ordinary differential equation system by the suggesting of the best similarity technique. Later, the transformed system of ordinary differential equations is solved numerically by using the Keller box method and the shooting method. Figures and charts are used to study and elaborate the physical behavior of the key subjective flow field parameters. The saturation in the base fluid is considered in both kinds of carbon nanotubes, the single-wall (SWCNTs) and the multiwall (MWCNTs). It is noted that the heat transfer mechanism shows some delaying behavior due to the increase in the Eckert number and the volume fraction elevation values. For the larger volume fraction values and the magnetic parameter, the skin friction increases. In addition, while the temperature profile increases with the Biot numbers, it falls for the increasing values of the Prandtl number. Furthermore, it is noted that the irreversibility of the thermal energy is influenced by the Biot number, temperature difference, Brinkmann number, and magnetic field, which all have dynamic effects on the entropy and the Bejan number.

Mixed convection in a lid-driven cavity filled with single and multiple-walled carbon nanotubes nanofluid having an inner elliptic obstacle

An analysis of the steady freeand mixed-convection boundary-layer flow past a horizontal impermeable surface embedded in a porousmedium filledwith a nanofluid is performed in this paper. Similarity solutions are obtained for the convective flow above a heated surface or below a cooled surface, where wall temperature is a power function of the distance from the origin. The similarity equations are solved numerically for three types of metallic or nonmetallic nanoparticles such as copper (Cu), alumina (Al2O3), and titania (TiO2) in a water-based fluid to investigate the effect of the solid volume fraction or nanoparticle volume fraction parameter# of the nanofluid on the flow and heat transfer characteristics. The case of conventional or regular fluid (# 0) is also considered for comparison with known results from the open literature. The comparison shows excellent agreement. The surface velocity, the local Nusselt number, and the velocity and temperature profiles are presented and discussed. It is found that the solid volume fraction affects the fluid flow and heat transfer characteristics in some way.

Numerical investigation for heat transfer enhancement using nanofluids over ribbed confined one-end closed flat-plate