This paper analyzes the effects of yield stress AND nanoparticles transport on the natural convection of viscoplastic Casson nanofluids. The non-linear coupled partial differential equations are solved numerically using Buongiorno’s mathematical model. The governing parameters for the problem are the Rayleigh number (Ra), yield number (Y), AND THERMOPHORESIS AND BROWNIANMOTION parameters (N t&Nb). The effects of these parameters on the fluid flow, heat AND mass transfer, AND the shape of yielded AND unyielded regions are examined AND discussed in detail. The results demonstrate that the heat AND mass transfer rates increase as the Rayleigh number increases, while the opposite behaviors are observed with increasing the yield number. The fluid is difficultly yielded at low Rayleigh number. The heat AND mass transfer are primarily due to conduction at the high values of the yield number. The main effect of THERMOPHORESIS AND BROWNIAN MOTION parameters is on temperature AND concentration distribution in the cavity. These parameters also show significant impacts on critical heat AND mass transfer.

A study based on the theoretical investigation of THERMOPHORESIS AND BROWNIAN MOTION effects on radiative heat transfer in the neighborhood of stagnation point. THERMOPHORESIS AND BROWNIAN MOTION play an important role in thermal AND mass concentration analyses. These analyses help to comprehend the core ideas to carry out in the discipline of science AND technology. An electrically conducting nanofluid is considered which is described by the Buongiorno transport model. The power-law form of the stretching wall velocity allows the similarity solution, the transformed system of the ordinary differential equations is computed numerically with the efficient rapid convergent spectral scheme. The obtained results for velocity, temperature, concentration, shear strain, mass AND heat transfer rates are presented graphically for various values of the pertinent parameters. The outcomes divulge that with the increase of power-law exponent, mass AND heat transfer rates enhance. The information for the volume AND high-temperature transfer rate is provided in the form of Tables. The obtained results are matched with the existing results AND are shown to be a good agreement.

This innovative study investigates the flow of ternary hybrid nanofluid containing gyrotactic microorganisms in microchannel. The magnetic field, THERMOPHORESIS, AND BROWNIAN MOTION effects are analyzed. The transformation of the PDEs system into ODEs is carried out by using the group transformation method. The innovative findings examine the Newtonian AND non-Newtonian models derived from the system of ODEs. Several graphs illustrate how different parameters affect the velocity profile, temperature, concentration, AND microorganisms. The power-law index value increases the fluid flow velocity by about 9% at n = 3, 36% at n = 4 relative to the case of n = 2.5 at the center of the boundary layer. Moreover, the ternary hybrid nanofluid exhibits a greater temperature compared to the nanofluid. The current results are compared to the researchers' findings to confirm the validity of the obtained results. When the PrANDtl number is between 6 AND 10, the Nusselt number reaches 45.49%.

Efficiency volatility modeling in stock markets, as seen by academic people AND operators in Finance science, in terms of its application in predicting stock efficiency, is of considerable importance. Financial AND capital markets in the country has taken effective stepsto develop.This paper aims to develop a model for estimating AND forecasting volatility of stock returns is done in the Tehran Stock Exchange. All three models use data on prices, daily top 50 shooters in a 5-year period from 2008 to 2013, is employed BROWNIAN MOTION, Fractional BROWNIAN MOTION AND GARCH models. using Excel AND Eviews AND MATLAB software was designed with the fractional BROWNIAN model. Tests AND comparisons using MSE, RMSE, AND MAE were performed. Comparing the results of the model of BROWNIAN MOTION, fractional BROWNIAN fashion model AND GARCH, the GARCH model has identified as a top model.

Statistical analysis of fractional BROWNIAN MOTION process is one of the most important issues in the field of stochastic processes. The most important issue in the study of this process is statistical inference about the Hurst parameters of the fractional BROWNIAN MOTION. One of the methods for estimation of aforementioned parameter is maximum likelihood approach. Due to the computational complexity of this approach to give a closed estimate, it is attempting to derive the parameter estimated through the numerical method approach. Also, the theoretical result of the paper is evaluated in a simulation study for different scenarios.

The onset of convection in a porous medium saturated by a dielectric nanofluid with vertical AC electric field is investigated. The flux of volume fraction of a nanoparticle with the effect of THERMOPHORESIS is taken to be zero on the boundaries AND the eigenvalue problem is solved using the Galerkin method. The model used for nanofluid incorporates the combined effect of BROWNIAN diffusion, THERMOPHORESIS AND electrophoresis, while for porous medium Darcy model is employed. The results show that increase in the AC electric Rayleigh-Darcy number, the Lewis number, the modified diffusivity ratio AND the concentration Rayleigh-Darcy number are to hasten the onset of convection. The size of convection cells does not depend on nanofluid parameters, but decreases with increasing the AC electric Rayleigh-Darcy number. The non-existence of oscillatory convection is also obtained.

In this paper, the nanofluid forced convection heat transfer in the case of single AND two phase approachs is studied. The fully-developed flow AND steady Darcy-Brinkman-Forchheimer equation is employed in porous channel AND is solved with homotopy perturbation method. The thermal equilibrium model is assumed between nanofluid AND solid phases. It is assumed that the nanoparticles are distributed non-uniformly inside the channel. As a result, the volume fraction distribution equation is also coupled with governing equations. It is observed that as the Schmidt number is increased, the wall temperature gradient is decreased AND as a consequence the local Nusselt number is decreased. The effects of Lewis number, Schmidt number AND modified diffusivity ratio on the volume fraction distribution are also studied AND discussed. Heat transfer of single AND two phase approaches are also compared.

In this research, effect of nanoparticles diameter on free convection of aluminum oxide-water was investigated in a cavity by single phase AND two phase models. The range of Rayleigh number is considered 105-107 in volume fractions of 0.01 to 0.03 for nanoparticles with various diameters (25, 33, 50 AND 100 nm). Given that the two phase nature of nanofluids, necessity of modeling by this method is increasing. Single phase approach (in contrary of two-phase modeling) for nanofluids is based on that the behaviors of each two solid phase (nanoparticles) AND liquid phase (base fluid) are completely similar. In this study, Eulerian-Eulerian approach AND mixture model was used given that BROWNIAN MOTION AND THERMOPHORESIS effects. BROWNIAN MOTION AND THERMOPHORESIS creates under influences of volume fraction gradient AND temperature gradient, respectively that cause to creating slip between nanoparticles AND base fluid; thus, kind of non-uniformity creates on behavior between nanoparticles AND base fluid. This non-uniformity leads to significant effects on results of two phase modeling that creates better agreement to single phase modeling with experimental results. Results indicate that heat transfer decreases with increasing diameter AND volume fraction of nanoparticles. Also, effect of nanoparticle diameter on flow AND heat transfer is tangible.

In this study, the onset of nanofluid convection confined within a Hele-Shaw cell is investigated by performing a classical linear stability analysis. The model used for nanofluid combines the effects of BROWNIAN MOTION AND THERMOPHORESIS, while for Hele-Shaw cell Brinkman model are employed. The new stability equations are formulated by introducing new characteristic dimensionless parameters such as the Hele-Shaw number, the Hele-Shaw Rayleigh number AND the nanoparticle concentration Hele-Shaw Rayleigh number. The resulting stability equations are solved numerically by using higher order Galerkin method. It is found that the nanoparticle concentration Hele-Shaw Rayleigh number, the Lewis number AND the modified diffusivity ratio hasten the onset of convection, while the Hele-Shaw number delays the onset of convection.A comparison is also made between the existing boundary conditions for nanoparticle AND obtained that the zero nanoparticle flux boundary conditions under the thermophoretic effects has more destabilizing effect than the fixed nanoparticle boundary conditions.