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.
Abstract: This paper focuses on the study of two dimensional magnetohydrodynamic (MHD) steady incompressible viscous Williamson nanofluid with exponential internal heat generation containing gyrotactic microorganism over a stretching sheet. The governing equations and auxiliary conditions are reduced to a set of non-linear coupled differential equations with the appropriate boundary conditions using similarity transformation. The transformed equations are solved numerically through spectral relaxation method. The influences of various parameters such as Williamson parameter γ, power constant λ, Prandtl number Pr, magnetic field parameter M, Peclet number Pe, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.
Abstract: In this paper, the problem proposed by Von Karman is treated in the attendance of additional flow field effects when the liquid is spaced above the rotating rigid disk. To be more specific, a purely viscous fluid flow yield by rotating rigid disk with Navier’s condition is considered in both magnetohydrodynamic and hydrodynamic frames. The rotating flow regime is manifested with heat source/sink and chemically reactive species. Moreover, the features of thermophoresis and Brownian motion are reported by considering nanofluid model. The flow field formulation is obtained mathematically in terms of high order differential equations. The reduced system of equations is solved numerically through self-coded computational algorithm. The pertinent outcomes are discussed systematically and provided through graphical and tabular practices. A simultaneous way of study makes this attempt attractive in this sense that the article contains dual framework and validation of results with existing work confirms the execution of self-coded algorithm for fluid flow regime over a rotating rigid disk.
Abstract: The use of CO2 in oil recovery and in CO2 capture and storage is gaining traction in recent years. These applications involve heat transfer between CO2 and the base fluid, and hence, there arises a need to improve the thermal conductivity of CO2 to increase the process efficiency and reduce cost. One way to improve the thermal conductivity is through nanoparticle addition in the base fluid. The nanofluid model in this study consisted of copper (Cu) nanoparticles in varying concentrations with CO2 as a base fluid. No experimental data are available on thermal conductivity of CO2 based nanofluid. Molecular dynamics (MD) simulations are an increasingly adopted tool to perform preliminary assessments of nanoparticle (NP) fluid interactions. In this study, the effect of the formation of a nanolayer (or molecular layering) at the gas-solid interface on thermal conductivity is investigated using equilibrium MD simulations by varying NP diameter and keeping the volume fraction (1.413%) of nanofluid constant to check the diameter effect of NP on the nanolayer and thermal conductivity. A dense semi-solid fluid layer was seen to be formed at the NP-gas interface, and the thickness increases with increase in particle diameter, which also moves with the NP Brownian motion. Density distribution has been done to see the effect of nanolayer, and its thickness around the NP. These findings are extremely beneficial, especially to industries employed in oil recovery as increased thermal conductivity of CO2 will lead to enhanced oil recovery and thermal energy storage.
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.
Abstract: This paper analyses the heat transfer performance and
fluid flow using different nanofluids in a square enclosure. The
energy equation and Navier-Stokes equation are solved numerically
using finite volume scheme. The effect of volume fraction
concentration on the enhancement of heat transfer has been studied
icorporating the Brownian motion; the influence of effective thermal
conductivity on the enhancement was also investigated for a range of
volume fraction concentration. The velocity profile for different
Rayleigh number. Water-Cu, water AL2O3 and water-TiO2 were
tested.
Abstract: This paper deals with the theoretical and numerical
investigation of magneto hydrodynamic boundary layer flow of a
nanofluid past a wedge shaped wick in heat pipe used for the cooling
of electronic components and different type of machines. To
incorporate the effect of nanoparticle diameter, concentration of
nanoparticles in the pure fluid, nanothermal layer formed around the
nanoparticle and Brownian motion of nanoparticles etc., appropriate
models are used for the effective thermal and physical properties of
nanofluids. To model the rotation of nanoparticles inside the base
fluid, microfluidics theory is used. In this investigation ethylene
glycol (EG) based nanofluids, are taken into account. The non-linear
equations governing the flow and heat transfer are solved by using a
very effective particle swarm optimization technique along with
Runge-Kutta method. The values of heat transfer coefficient are
found for different parameters involved in the formulation viz.
nanoparticle concentration, nanoparticle size, magnetic field and
wedge angle etc. It is found that, the wedge angle, presence of
magnetic field, nanoparticle size and nanoparticle concentration etc.
have prominent effects on fluid flow and heat transfer characteristics
for the considered configuration.
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.
Abstract: The thermal conductivity of a fluid can be
significantly enhanced by dispersing nano-sized particles in it, and
the resultant fluid is termed as "nanofluid". A theoretical model for
estimating the thermal conductivity of a nanofluid has been proposed
here. It is based on the mechanism that evenly dispersed
nanoparticles within a nanofluid undergo Brownian motion in course
of which the nanoparticles repeatedly collide with the heat source.
During each collision a rapid heat transfer occurs owing to the solidsolid
contact. Molecular dynamics (MD) simulation of the collision
of nanoparticles with the heat source has shown that there is a pulselike
pick up of heat by the nanoparticles within 20-100 ps, the extent
of which depends not only on thermal conductivity of the
nanoparticles, but also on the elastic and other physical properties of
the nanoparticle. After the collision the nanoparticles undergo
Brownian motion in the base fluid and release the excess heat to the
surrounding base fluid within 2-10 ms. The Brownian motion and
associated temperature variation of the nanoparticles have been
modeled by stochastic analysis. Repeated occurrence of these events
by the suspended nanoparticles significantly contributes to the
characteristic thermal conductivity of the nanofluids, which has been
estimated by the present model for a ethylene glycol based nanofluid
containing Cu-nanoparticles of size ranging from 8 to 20 nm, with
Gaussian size distribution. The prediction of the present model has
shown a reasonable agreement with the experimental data available
in literature.
Abstract: The problem of magnetohydrodynamics boundary layer flow and heat transfer on a permeable stretching surface in a second grade nanofluid under the effect of heat generation and partial slip is studied theoretically. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the PDE’s are transformed into a set of ODE’s with the help of local similarity transformations. The differential equations are solved by variational finite element method. The effects of different controlling parameters on the flow field and heat transfer characteristics are examined. The numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically. The comparison confirmed excellent agreement. The present study is of great interest in coating and suspensions, cooling of metallic plate, oils and grease, paper production, coal water or coal-oil slurries, heat exchangers technology, materials processing exploiting.
Abstract: The linear stability of nanofluid convection in a horizontal porous layer is examined theoretically when the walls of the porous layer are subjected to time-periodic temperature modulation. The model used for the nanofluid incorporates the effects of Brownian motion and thermopherosis, while the Darcy model is used for the porous medium. The analysis revels that for a typical nanofluid (with large Lewis number) the prime effect of the nanofluids is via a buoyancy effect coupled with the conservation of nanoparticles. The contribution of nanoparticles to the thermal energy equation being a second-order effect. It is found that the critical thermal Rayleigh number can be found reduced or decreased by a substantial amount, depending on whether the basic nanoparticle distribution is top-heavy or bottom-heavy. Oscillatory instability is possible in the case of a bottom-heavy nanoparticle distribution, phase angle and frequency of modulation.
Abstract: Numerical investigation on the generality of nanoparticle velocity equation had been done on the previous published work. The three dimensional governing equations (continuity, momentum and energy) were solved using finite volume method (FVM). Parametric study of thermal performance between pure water-cooled and nanofluid-cooled are evaluated for volume fraction in the range of 1% to 4%, and nanofluid type of gamma-Al2O3 at Reynolds number range of 67.41 to 286.77. The nanofluid is modeled using single and two phase approach. Three different existing Brownian motion velocities are applied in comparing the generality of the equation for a wide parametric condition. Deviation in between the Brownian motion velocity is identified to be due to the different means of mean free path and constant value used in diffusion equation.
Abstract: Thermal conductivity is an important characteristic of
a nanofluid in laminar flow heat transfer. This paper presents an
improved model for the prediction of the effective thermal
conductivity of nanofluids based on dimensionless groups. The
model expresses the thermal conductivity of a nanofluid as a function
of the thermal conductivity of the solid and liquid, their volume
fractions and particle size. The proposed model includes a parameter
which accounts for the interfacial shell, brownian motion, and
aggregation of particle. The validation of the model is verified by
applying the results obtained by the experiments of Tio2-water and
Al2o3-water nanofluids.
Abstract: This paper examines long-range dependence or longmemory
of financial time series on the exchange rate data by the
fractional Brownian motion (fBm). The principle of spectral density
function in Section 2 is used to find the range of Hurst parameter (H)
of the fBm. If 0< H
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.
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.
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.
Abstract: This paper argues that increased uncertainty, in certain
situations, may actually encourage investment. Since earlier studies
mostly base their arguments on the assumption of geometric Brownian
motion, the study extends the assumption to alternative stochastic
processes, such as mixed diffusion-jump, mean-reverting process, and
jump amplitude process. A general approach of Monte Carlo
simulation is developed to derive optimal investment trigger for the
situation that the closed-form solution could not be readily obtained
under the assumption of alternative process. The main finding is that
the overall effect of uncertainty on investment is interpreted by the
probability of investing, and the relationship appears to be an invested
U-shaped curve between uncertainty and investment. The implication
is that uncertainty does not always discourage investment even under
several sources of uncertainty. Furthermore, high-risk projects are not
always dominated by low-risk projects because the high-risk projects
may have a positive realization effect on encouraging investment.
Abstract: Real options theory suggests that managerial flexibility embedded within irreversible investments can account for a significant value in project valuation. Although the argument has become the dominant focus of capital investment theory over decades, yet recent survey literature in capital budgeting indicates that corporate practitioners still do not explicitly apply real options in investment decisions. In this paper, we explore how real options decision criteria can be transformed into equivalent capital budgeting criteria under the consideration of uncertainty, assuming that underlying stochastic process follows a geometric Brownian motion (GBM), a mixed diffusion-jump (MX), or a mean-reverting process (MR). These equivalent valuation techniques can be readily decomposed into conventional investment rules and “option impacts", the latter of which describe the impacts on optimal investment rules with the option value considered. Based on numerical analysis and Monte Carlo simulation, three major findings are derived. First, it is shown that real options could be successfully integrated into the mindset of conventional capital budgeting. Second, the inclusion of option impacts tends to delay investment. It is indicated that the delay effect is the most significant under a GBM process and the least significant under a MR process. Third, it is optimal to adopt the new capital budgeting criteria in investment decision-making and adopting a suboptimal investment rule without considering real options could lead to a substantial loss in value.
Abstract: For decades financial economists have been attempted to determine the optimal investment policy by recognizing the option value embedded in irreversible investment whose project value evolves as a geometric Brownian motion (GBM). This paper aims to examine the effects of the optimal investment trigger and of the misspecification of stochastic processes on investment in real options applications. Specifically, the former explores the consequence of adopting optimal investment rules on the distributions of corporate value under the correct assumption of stochastic process while the latter analyzes the influence on the distributions of corporate value as a result of the misspecification of stochastic processes, i.e., mistaking an alternative process as a GBM. It is found that adopting the correct optimal investment policy may increase corporate value by shifting the value distribution rightward, and the misspecification effect may decrease corporate value by shifting the value distribution leftward. The adoption of the optimal investment trigger has a major impact on investment to such an extent that the downside risk of investment is truncated at the project value of zero, thereby moving the value distributions rightward. The analytical framework is also extended to situations where collection lags are in place, and the result indicates that collection lags reduce the effects of investment trigger and misspecification on investment in an opposite way.