Solar Energy Utilization of Radiative Implication of Trihybrid Xue‐Modeled Nanofluid Flow for Oblique Stagnation Point Flows

The unsteady viscous nanofluid flow near a three-dimensional stagnation point was studied numerically under microgravity environment. g-Jitter is one of the effects occurs under microgravity environment that producing a fluctuating gravitational field. Three different types of nanoparticles were induced in the study that is copper (Cu), alumina (Al2O3), and titania (TiO2) which then produce a water-based typed of nanofluid. In addition, different shape of nanoparticle was applied on the study in analyzing the performance of each types of nanoparticle. The fluid system was then mathematically formulated into a system of partial differential equation based on physical law and principle such as conservation of mass, Newton’s second law and conservation of energy. The system of equation then undergoes semi-similar transformation technique in reducing the complexity of the problem into non dimensionless form. Keller box method was applied into the dimensionless system of equations in solving the problem numerically. The problem was analyzed in term of velocity and temperature profiles together with skin friction coefficient and Nusselt number. The results shown that temperature profile, skin friction coefficient and Nusselt number were increase while velocity profile decreased as nanoparticle volume fraction decreased. The results indicated that, the needle-shaped nanoparticles give the highest enhancement on the heat transfer of the nanofluid compared to sphere and disk-shaped nanoparticles with more than 14% significant different. In addition, alumina hold the highest velocity profile while copper hold the lowest velocity profile.

This article reports an unsteady two-dimensional Magneto-hydrodynamic (MHD) boundary layer flow of an incompressible electrically conducting fluid over a slippery stretching sheet surrounded in a porous medium. The Roseland boundary layer approximation with the radiative heat flux is employed within the current analysis. The influence of the velocity slip, thermal radiation, heat source, and buoyancy force is also considered within the current analysis, which makes significant effects on the flow field passages. The unsteady system of non-dimensional partial differential equations (PDEs) with corresponding boundary conditions are solved by implementing the explicit finite difference scheme. In the presence of pertinent parameters such as viscous dissipation, heat source or sink, Prandtl number, Grashof number, thermal radiation, magnetic field, and Darcy number, the accurate movement of the electrically conducting fluid over a slippery sheet is shown graphically in the form of velocity, temperature, skin friction coefficient, and Nusselt number. Unlike the other studies, wherein the system of PDEs is commonly transformed into a system of ordinary differential equations via the similarity transformations, the current study provides an efficient numerical procedure to solve a given system of PDEs without using the similarity transformations which exemplify the precise movement of an electrically conducting fluid over a slippery surface. It has been anticipated that the current boundary layer analysis would provide a platform for solving the system of the nonlinear PDEs of the other unsolved boundary layer models that are associated with the two-dimensional unsteady MHD flow over a slippery stretching surface embedded in a porous medium.

Dynamic viscosity of colloidal silica suspensions at low and high volume fractions

The purpose of this research is to study the effect of heat generation on mixed convection flow on Nano fluids over a horizontal circular cylinder of a heated in two dimension form. A stream of fluids are steady and incompressible, a stream flowing vertically upwards for circular cylinder and the boundary layer at the stagnation point. Three different types of nanoparticles considered are Cu, Al2O3, and TiO2. Mixed convection flow in Nano fluids on the surface of a circular cylinder will cause the boundary layer. The governing boundary layer equations are transformed into a non-dimensional form, and then the non-dimensional forms are transformed into a similar boundary equations by using stream function. Furthermore, an implicit finite-difference scheme known as the Keller-box method is applied to solve numerically the resulting similar boundary layer equations. The result of the research by varying the non-dimensional parameters are mixed convection, Prandtl number, nanoparticle volume fraction, heat generation, and radius of a cylinder are as follows. First, the velocity profile increase and temperature profile decrease when mixed convection parameter increase. Second, the velocity and temperature profiles decrease when Prandtl number parameter increase. Third, the velocity profile with the variation of nanoparticle volume fraction (χ) is increased when the value of χ is 0,1 ≤ χ ≤ 0,15 and the velocity profile decreases when the value of χ is 0,19 ≤ χ ≤ 0,5 while the temperature profile is increasing when the value of χ is 0,1 ≤ χ ≤ 0,5. Fourth, the velocity and temperature profiles increase when heat generation and the radius of the cylinder increase. The last, Cu, Al2O3, and TiO2 nanoparticles produce the same velocity and temperature profiles, but the three types of nanoparticles are different at the velocity and temperature values.

In this study, the steady stagnation point flow and heat transfer of three different types of nanofluid over a linearly shrinking/stretching sheet is investigated numerically. A similarity transformation is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using the fourth-order Runge-Kutta method with shooting technique. The effects of the governing parameters on the nanofluid flow and heat transfer characteristics are analyzed and discussed. Numerical results for the local Nusselt number, skin friction coefficient, velocity profiles and temperature profiles are presented for different values of the solid volume fraction (&phi) and for three different types of nanoparticles (Cu, Al₂O₃ and TiO₂) in stretching or shrinking cases. It is found that the skin friction coefficient and the heat transfer rate at the surface are highest for Cu-water nanofluid compared to the Al₂O₃-water and TiO₂-water nanofluids. Furthermore, it was seen that the effect of the solid volume fraction of nanoparticles on the heat transfer and fluid flow characteristics is more important compared to the type of the nanoparticles.

This paper demonstrates the applicability of the large parameter spectral perturbation method (LSPM) to a coupled system of partial differential equations that cannot be solved exactly. The LSPM is a numerical method that employs the Chebyshev spectral collocation method in the solution of a sequence of ordinary differential equations (ODEs) that are derived from decomposing coupled systems of nonlinear partial differential equations (PDEs) using series expansion about a large parameter. The validity of the LSPM is applied to the problem of boundary layer flow and heat transfer in a micropolar fluid past a permeable flat plate in the presence of heat generation and thermal radiation. The coupled nature of the PDEs that define the problem under investigation precludes the option of using series-based methods that seek to generate analytical solutions even in the presence of small or large parameters. The present study demonstrates that the LSPM can easily overcome this limitation while giving very accurate results in a computationally efficient manner. For qualitative validation of the results and the numerical method used, calculations were carried out to graphically obtain the velocity, microrotation, and temperature profiles for selected physical parameter values. The results obtained were found to correlate with the results from a published literature. For quantitative confirmation of our findings, the LSPM numerical solutions were again validated against known results from the literature and against results obtained using the multidomain bivariate spectral quasilinearisation method (MD-BSQLM), and the results were observed to be in perfect agreement. Further accuracy validation is displayed by using residual error and solution error analysis on the governing PDEs and their underlying solutions. This study’s findings indicate that the heat generation and thermal radiation parameters have related effects on the temperature profile, enhancing both the fluid temperature and the thermal boundary layer thickness.

In this article, the magnetohydrodynamic stagnation point flow and heat transfer of an incompressible viscous nanofluid over a shrinking/stretching permeable sheet is investigated theoretically and analytically. The ambient fluid velocity, stretching/shrinking velocity of sheet and the wall temperature are assumed to vary linearly with the distance from the stagnation point. The similarity solution is used to reduce the governing system of partial differential equations to a set of highly non-linear ordinary differential equations which are then solved analytically using a very efficient technique, namely homotopy analysis method. Expressions for velocity and temperature fields are developed in series form and graphical results are presented to investigate the influence of various pertinent parameters. Here, three different types of nanoparticles, namely copper [Formula: see text], alumina [Formula: see text] and titania [Formula: see text] with water as the base fluid are considered. It is observed that, for all three nanoparticles, the magnitude of the skin friction coefficient and local Nusselt number increases with the nanoparticle volume fraction Φ. The highest values of the skin friction coefficient and the local Nusselt number were obtained for the [Formula: see text] nanoparticles compared to [Formula: see text] and [Formula: see text].

This article investigates the unsteady mixed convention two-dimensional flow of magnetohydrodynamic Casson hybrid nanofluids (alumina oxide and titanium oxide nanoparticles with base fluid water) flow through porous media over a linearly stretched sheet. We analyzed the heat and mass transfer in mixed convection, thermal radiation, variable thermal conductivity, variable mass diffusivity, and chemical reaction in the presence of thermophoresis and Brownian motion. A system of partial differential equations is reduced to a solvable system of ordinary differential equations by applying a suitable similarity transformation. We used the Runga–Kutta method along with the shooting procedure to solve the flow, heat, and mass transfer equations along with boundary conditions. The results obtained from MATLAB codes are compared with previously published results of the same type in a limiting case. The results of the velocity, temperature, and concentration profile of the hybrid nanofluid for varying different flow parameters are obtained in the form of graphs, while the rate of shear stress, rate of heat, and mass transfer are expressed in tables. We noticed that velocity and temperature diminish as an unsteady parameter increases; however, the reverse trend was observed in the nanoparticle concentration profile. With an increase in the thermal radiation parameter, the resultant velocity and temperature profile improves, while the concentration of nanoparticle profiles decreases. The velocity and temperature increase with higher Brownian motion, while the velocity increases and temperature decreases with higher thermophoresis.

The water in oil microemulsion or reverse micelle has been used in the past two decades for the synthesis of many different types of nanoparticles. The nano meter sized aqueous cores of the reverse micelle provide an appropriate stabilized environment for the production of nanoparticles of fairly uniform size, through chemical reactions occurring in the core and it also acts as steric stabilizers to inhibit the aggregation of nanoparticles formed. The water in oil microemulsion has been used to synthesize different types of core nano particles (metals, and semiconductors) as well as core-shell/ composite nanoparticles. This article describes the preparation techniques, and the various techniques used to characterize these core and core-shell nanoparticles as well as insights in to the effects of various process parameters on the terminal particle size. A brief review of our modeling work based on stochastic population balance is also presented, which can be used to describe the formation of both core and coreshell nanoparticles. In addition, we have also presented a brief review of the work on the synthesis of anisotropic nanostructures like nanorods and nanowires by templating against surfactant micelles and reverse micelles. Some findings of our work, addressing the engineering issues, such as possibility of reusing surfactant and organic phases are also included in this article.

Radiative property model for non-gray particle based on dependent scattering

This paper explores the impact of chemical reaction and thermal radiation on time-dependent hydromagnetic thin-film flow of a second-grade fluid across an inclined flat plate embedded in a porous medium. The thermal radiation based on the Rosseland approximation is incorporated in the energy equation. Uniform applied magnetic field and first-order homogenous chemical reaction are included in the momentum and concentration equations, respectively. The novel mathematical flow model is constructed by using a set of partial differential equations (PDEs). The PDEs are then transformed into an equivalent set of ordinary differential equations (ODEs) and solved by applying the Laplace transform method. However, the time domain solutions are obtained by using the INVLAP subroutine of MATLAB. Physical parameters influencing thin-film velocity, temperature, and concentration are illustrated graphically, while those affecting skin friction, heat, and mass transfer rates are presented in a tabular form. It is found that thin-film velocity and temperature boost with increasing values of thermal radiation, but thin-film velocity decreases with increasing values of chemical reaction and magnetic field. The current investigation is to enhance heat and mass transfer in the design of mechanical systems involving the thin film flow of second-grade fluids over an inclined flat plate after applying thermal radiation and chemical reaction.

Adding nanoparticles (NPs) to metalworking fluids (MWFs) has been shown to improve performance in metal cutting. Zinc oxide nanoparticles (ZnO NPs) and titanium dioxide nanoparticles (TiO2 NPs), for example, have exhibited the ability to improve lubricant performance, decrease the heat created by machining operations, reduce friction and wear, and enhance thermal conductivity. ZnO and TiO2 NPs are also relatively inexpensive compared to many other NPs. Precautionary concerns of human health risks and environmental impacts, however, are especially important when adding NPs to MWFs. The goal of this research is to investigate the potential environmental and human health effects of these nanoenabled products during early design and development. This research builds on a prior investigation of the stability and toxicity characteristics of NPs used in metalworking nanofluids (MWnF™). The previous study only investigated one type of NP at one level of concentration. This research expands on the previous investigations through the valuation of three different types of NPs that vary in morphology (size and shape) and was conducted over a wide range of concentrations in the base fluid. In the presented work, mixtures of a microemulsion (TRIM® MicroSol® 585XT), two different types of TiO2 NPs (referred to as TiO2A and TiO2B) and one type of ZnO NP were used to evaluate MWnF™ stability and toxicity. Dynamic light scattering was used to assess stability over time and an embryonic zebrafish assay was used to assess toxicological impacts. The results reveal that, in general, the addition of these NPs increased toxicity relative to the NP-free formulation. The lowest rate of zebrafish malformations occurred at 5 g/L TiO2A NP, which was even lower than for the base fluid. This result is particularly promising for future MWnF™ development, given that the mortality rate for 5 g/L TiO2A was not significantly different than for the base fluid.

Metal-based nanoparticles have been extensively investigated for a set of biomedical applications. According to the World Health Organization, in addition to their reduced size and selectivity for bacteria, metal-based nanoparticles have also proved to be effective against pathogens listed as a priority. Metal-based nanoparticles are known to have non-specific bacterial toxicity mechanisms (they do not bind to a specific receptor in the bacterial cell) which not only makes the development of resistance by bacteria difficult, but also broadens the spectrum of antibacterial activity. As a result, a large majority of metal-based nanoparticles efficacy studies performed so far have shown promising results in both Gram-positive and Gram-negative bacteria. The aim of this review has been a comprehensive discussion of the state of the art on the use of the most relevant types of metal nanoparticles employed as antimicrobial agents. A special emphasis to silver nanoparticles is given, while others (e.g., gold, zinc oxide, copper, and copper oxide nanoparticles) commonly used in antibiotherapy are also reviewed. The novelty of this review relies on the comparative discussion of the different types of metal nanoparticles, their production methods, physicochemical characterization, and pharmacokinetics together with the toxicological risk encountered with the use of different types of nanoparticles as antimicrobial agents. Their added-value in the development of alternative, more effective antibiotics against multi-resistant Gram-negative bacteria has been highlighted.

The theory of analytic systems of partial differential equations was first systematically investigated by Riquier and Elie Cartan around 1900. The existence of local solutions involves an algebraic problem, finding formal power series solutions, and an analytic problem, proving the convergence of formal power series solutions. Cartan defined the notion of an involutive system of partial differential equations and, using his theory of exterior differential systems, was able to show the existence of formal power series solutions for involutive partial differential equations of first order and to prove the convergence by the Cauchy-Kowalewski theorem. His result was extended by Kihler to systems of partial differential equations of higher order and is known today as the Cartan-Kihler theorem. Adjoining to a system of partial differential equations of order k the equations obtained by differentiating the original equations gives rise to a system of partial differential equations of order k +1, the prolongation of the system, which has the same solutions as the original equations. Cartan conjectured that, by prolonging a system a sufficient number of times, one would obtain an involutive system; this result was proved by Kuranishi in 1957 within the framework of Cartan's theory of exterior differential systems, and is now referred to as the Cartan-Kuranishi prolongation theorem. In 1961, Spencer introduced, in his fundamental paper [6] on the deformation of pseudogroup structures, certain cohomology groups Hkj associated to a partial differential equation (see ? 3), which are dual to homology groups of a Koszul complex; and so the cohomology groups Hki vanish for all sufficiently large k (see Lemma 3.1). The vanishing of these cohomology groups was shown by Serre to be equivalent to Cartan's notion of involutiveness (see V. W. Guillemin and S. Sternberg [3]). It then became possible to analyse the role played by involutiveness in Cartan's theory of partial differential equations. In this paper, we prove the Cartan-Kahler theorem for systems of linear partial differential equations formulated in terms of Ehresmann's theory of

In this study, the steady laminar mixed convection boundary layer flow of a nanofluid near the stagnation-point on a vertical plate with prescribed surface temperature is investigated. Here, both assisting and opposing flows are considered and studied. Using appropriate transformations, the system of partial differential equations is transformed into an ordinary differential system of two equations, which is solved numerically by shooting method, coupled with Runge-Kutta scheme. Three different types of nanoparticles, namely copper Cu, alumina Al R 2 R O R 3 R and titania TiO R 2 R with water as the base fluid are considered. Numerical results are obtained for the skin-friction coefficient and Nusselt number as well as for the velocity and temperature profiles for some values of the governing parameters, namely, the nanoparticle volume fraction parameter ���� and mixed convection parameter λ It is found that the highest rate of heat transfer occurs in the mixed convection with assisting flow while the lowest one occurs in the mixed convection with opposing flow. Moreover, the skin friction coefficient and the heat transfer rate at the surface are highest for copper-water nanofluid compared to the alumina-water and titania-water nanofluids.