Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 7

Brownian motion Related Publications

7 Numerical Approach to a Mathematical Modeling of Bioconvection Due to Gyrotactic Micro-Organisms over a Nonlinear Inclined Stretching Sheet

Authors: Madhu Aneja, Sapna Sharma

Abstract:

The water-based bioconvection of a nanofluid containing motile gyrotactic micro-organisms over nonlinear inclined stretching sheet has been investigated. The governing nonlinear boundary layer equations of the model are reduced to a system of ordinary differential equations via Oberbeck-Boussinesq approximation and similarity transformations. Further, the modified set of equations with associated boundary conditions are solved using Finite Element Method. The impact of various pertinent parameters on the velocity, temperature, nanoparticles concentration, density of motile micro-organisms profiles are obtained and analyzed in details. The results show that with the increase in angle of inclination δ, velocity decreases while temperature, nanoparticles concentration, a density of motile micro-organisms increases. Additionally, the skin friction coefficient, Nusselt number, Sherwood number, density number are computed for various thermophysical parameters. It is noticed that increasing Brownian motion and thermophoresis parameter leads to an increase in temperature of fluid which results in a reduction in Nusselt number. On the contrary, Sherwood number rises with an increase in Brownian motion and thermophoresis parameter. The findings have been validated by comparing the results of special cases with existing studies.

Keywords: thermophoresis, Brownian motion, bioconvection, inclined stretching sheet, finite element method, Gyrotactic micro-organisms

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6 FEM Simulation of Triple Diffusive Magnetohydrodynamics Effect of Nanofluid Flow over a Nonlinear Stretching Sheet

Authors: Rama Bhargava, Rangoli Goyal

Abstract:

The triple diffusive boundary layer flow of nanofluid under the action of constant magnetic field over a non-linear stretching sheet has been investigated numerically. The model includes the effect of Brownian motion, thermophoresis, and cross-diffusion; slip mechanisms which are primarily responsible for the enhancement of the convective features of nanofluid. The governing partial differential equations are transformed into a system of ordinary differential equations (by using group theory transformations) and solved numerically by using variational finite element method. The effects of various controlling parameters, such as the magnetic influence number, thermophoresis parameter, Brownian motion parameter, modified Dufour parameter, and Dufour solutal Lewis number, on the fluid flow as well as on heat and mass transfer coefficients (both of solute and nanofluid) are presented graphically and discussed quantitatively. The present study has industrial applications in aerodynamic extrusion of plastic sheets, coating and suspensions, melt spinning, hot rolling, wire drawing, glass-fibre production, and manufacture of polymer and rubber sheets, where the quality of the desired product depends on the stretching rate as well as external field including magnetic effects.

Keywords: FEM, thermophoresis, Brownian motion, diffusiophoresis

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5 Boundary Layer Flow of a Casson Nanofluid past a Vertical Exponentially Stretching Cylinder in the Presence of a Transverse Magnetic Field with Internal Heat Generation/Absorption

Authors: G. Sarojamma, K. Vendabai

Abstract:

An analysis is carried out to investigate the effect of magnetic field and heat source on the steady boundary layer flow and heat transfer of a Casson nanofluid over a vertical cylinder stretching exponentially along its radial direction. Using a similarity transformation, the governing mathematical equations, with the boundary conditions are reduced to a system of coupled, non –linear ordinary differential equations. The resulting system is solved numerically by the fourth order Runge – Kutta scheme with shooting technique. The influence of various physical parameters such as Reynolds number, Prandtl number, magnetic field, Brownian motion parameter, thermophoresis parameter, Lewis number and the natural convection parameter are presented graphically and discussed for non – dimensional velocity, temperature and nanoparticle volume fraction. Numerical data for the skin – friction coefficient, local Nusselt number and the local Sherwood number have been tabulated for various parametric conditions. It is found that the local Nusselt number is a decreasing function of Brownian motion parameter Nb and the thermophoresis parameter Nt.

Keywords: thermophoresis, boundary layer flow, Brownian motion, casson nanofluid, exponentially stretching cylinder, Heat Transfer, Internal heat generation/absorption

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4 Flow and Heat Transfer of a Nanofluid over a Shrinking Sheet

Authors: N. Bachok, N. L. Aleng, N. M. Arifin, A. Ishak, N. Senu

Abstract:

The problem of laminar fluid flow which results from the shrinking of a permeable surface in a nanofluid has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented which depends on the mass suction parameter S, Prandtl number Pr, Lewis number Le, Brownian motion number Nb and thermophoresis number Nt. It was found that the reduced Nusselt number is decreasing function of each dimensionless number.

Keywords: Nanofluid, boundary layer, shrinking sheet, thermophoresis, similarity solution, Brownian motion

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3 Experimental Investigation of Heat Transfer and Flow of Nano Fluids in Horizontal Circular Tube

Authors: Sattar Al-Jabair, Abdulhassan Abd. K, Khalid Sultan

Abstract:

We have measured the pressure drop and convective heat transfer coefficient of water – based AL(25nm),AL2O3(30nm) and CuO(50nm) Nanofluids flowing through a uniform heated circular tube in the fully developed laminar flow regime. The experimental results show that the data for Nanofluids friction factor show a good agreement with analytical prediction from the Darcy's equation for single-phase flow. After reducing the experimental results to the form of Reynolds, Rayleigh and Nusselt numbers. The results show the local Nusselt number and temperature have distribution with the non-dimensional axial distance from the tube entry. Study decided that thenNanofluid as Newtonian fluids through the design of the linear relationship between shear stress and the rate of stress has been the study of three chains of the Nanofluid with different concentrations and where the AL, AL2O3 and CuO – water ranging from (0.25 - 2.5 vol %). In addition to measuring the four properties of the Nanofluid in practice so as to ensure the validity of equations of properties developed by the researchers in this area and these properties is viscosity, specific heat, and density and found that the difference does not exceed 3.5% for the experimental equations between them and the practical. The study also demonstrated that the amount of the increase in heat transfer coefficient for three types of Nano fluid is AL, AL2O3, and CuO – Water and these ratios are respectively (45%, 32%, 25%) with insulation and without insulation (36%, 23%, 19%), and the statement of any of the cases the best increase in heat transfer has been proven that using insulation is better than not using it. I have been using three types of Nano particles and one metallic Nanoparticle and two oxide Nanoparticle and a statement, whichever gives the best increase in heat transfer.

Keywords: Newtonian, Brownian motion, NUR factor

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2 Delay-range-Dependent Exponential Synchronization of Lur-e Systems with Markovian Switching

Authors: Shouming Zhong, Xia Zhou

Abstract:

The problem of delay-range-dependent exponential synchronization is investigated for Lur-e master-slave systems with delay feedback control and Markovian switching. Using Lyapunov- Krasovskii functional and nonsingular M-matrix method, novel delayrange- dependent exponential synchronization in mean square criterions are established. The systems discussed in this paper is advanced system, and takes all the features of interval systems, Itˆo equations, Markovian switching, time-varying delay, as well as the environmental noise, into account. Finally, an example is given to show the validity of the main result.

Keywords: Synchronization, Markov Chain, Brownian motion, M-matrix, delay-range-dependent, generalized Itō's formula

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1 Effects of Nanolayer Structure and Brownian Motion of Particles in Thermal Conductivity Enhancement of Nanofluids

Authors: S. Hossainpour, M. Izadi, D. Jalali-Vahid

Abstract:

Nanofluids are novel fluids that are going to have an important role in future industrial thermal device designs. Studies are being predominantly conducted on the mechanism of these heat transfers. The key to this attraction is in the increase in thermal conductivity brought about by the Nanofluids compared with the base fluid. Different models have been proposed for calculation of effective thermal conduction that has been gradually modified. In this investigation effect of nanolayer structure and Brownian motion of particles are studied and a new modified thermal conductivity model is proposed. Temperature, concentration, nanolayer thickness and particle size are taken as variables and their effect are studied simultaneously on the thermal conductivity of the fluids, showing the concentration of the nanoparticles to affect the nanolayer thickness which also affects the Brownian motion.

Keywords: Brownian motion, Relative thermal conductivity, Nanolayer structure

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