Thermocapillary Flow of a Thin Nanoliquid Film Over an Unsteady Stretching Sheet

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
S. Maity ◽  
Y. Ghatani ◽  
B. S. Dandapat
Keyword(s):  
Stretching Sheet ◽  
Volume Fraction ◽  
The Other ◽  
Two Dimensional ◽  
Nanoparticle Volume Fraction ◽  
Governing Equations ◽  
Unsteady Stretching Sheet ◽  
Planar Film ◽  
Two Dimensional Flow ◽  
Film Thinning

The two-dimensional flow of a thin nanoliquid film over an unsteady stretching sheet is studied under the assumption of planar film thickness when the sheet is heated/cooled along the stretching direction. The governing equations of momentum, energy are solved numerically by using finite difference method. The rate of film thinning decreases with the increase in the nanoparticle volume fraction. On the other hand, thermocapillary parameter influences the film thinning. A boundary within the film is delineated such that the sign of Tz changes depending on the stretching distance from the origin. Further the boundary for Tz > 0 enlarges when the volume fraction of the nanoparticle increases.

Influence of chemically radiative nanoparticles on flow of Maxwell electrically conducting fluid over a convectively heated exponential stretching sheet

2019 ◽  
Vol 16 (6) ◽  
pp. 791-805
Author(s):  
Atul Kumar Ray ◽  
Vasu B.
Keyword(s):  
Stretching Sheet ◽  
Volume Fraction ◽  
Maxwell Fluid ◽  
Nanoparticle Volume Fraction ◽  
Analysis Method ◽  
Content Type ◽  
Electrically Conducting ◽  
Exponential Stretching ◽  
Homotopy Analysis ◽  
Exponential Stretching Sheet

Purpose This paper aims to examine the influence of radiative nanoparticles on incompressible electrically conducting upper convected Maxwell fluid (rate type fluid) flow over a convectively heated exponential stretching sheet with suction/injection in the presence of heat source taking chemical reaction into account. Also, a comparison of the flow behavior of Newtonian and Maxwell fluid containing nanoparticles under the effect of different thermophysical parameters is elaborated. Velocity, temperature and nanoparticle volume fractions are assumed to have exponential distribution at boundary. Buongiorno model is considered for nanofluid transport. Design/methodology/approach The equations, which govern the flow, are reduced to ordinary differential equations using suitable transformation. The transformed equations are solved using a robust homotopy analysis method. The convergence of the homotopy series solution is explicitly discussed. The present results are compared with the results reported in the literature and are found to be in good agreement. Findings It is observed from the present study that larger relaxation time leads to slower recovery, which results in a decrease in velocity, whereas temperature and nanoparticle volume fraction is increased. Maxwell nanofluid has lower velocity with higher temperature and nanoparticle volume fraction when compared with Newtonian counterpart. Also, the presence of magnetic field leads to decrease the velocity of the nanofluid and enhances the skin coefficient friction. The existence of thermal radiation and heat source enhance the temperature. Further, the presence of chemical reaction leads to decrease in nanoparticle volume fraction. Higher value of Deborah number results in lower the rate of heat and mass transfer. Originality/value The novelty of present work lies in understanding the impact of fluid elasticity and radiative nanoparticles on the flow over convectively heated exponentially boundary surface in the presence of a magnetic field using homotopy analysis method. The current results may help in designing electronic and industrial applicants. The present outputs have not been considered elsewhere.

The Effect of Vertical Throughflow on Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: A Revised Model

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
D. A. Nield ◽  
A. V. Kuznetsov
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Porous Media ◽  
Thermal Instability ◽  
Volume Fraction ◽  
Critical Rayleigh Number ◽  
Nanoparticle Volume Fraction ◽  
Governing Equations ◽  
Medium Layer ◽  
Vertical Throughflow

The model developed in our previous paper (Nield and Kuznetsov, 2011, “The Effect of Vertical Throughflow on Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid,” Transp. Porous Media, 87(3), pp. 765–775) is now revised to accommodate a more realistic boundary condition on the nanoparticle volume fraction. The new boundary condition postulates zero nanoparticle flux through the boundaries. We established that in the new model, oscillatory instability is impossible. We also established that the critical Rayleigh number depends on three dimensionless parameters, and we derived these three parameters from the governing equations. We also briefly investigated the major trends.

Thermoelastic Dynamic Behaviors of a FGM Hollow Cylinder Under Non-Axisymmetric Thermo-Mechanical Loads

2012 ◽  
Vol 29 (1) ◽  
pp. 109-120 ◽  
Author(s):  
H. Xie ◽  
H.-L. Dai ◽  
Y.-N. Rao
Keyword(s):  
Hollow Cylinder ◽  
Material Properties ◽  
Radial Direction ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Two Dimensional ◽  
Governing Equations ◽  
Mechanical Loads ◽  
Temperature Boundary

AbstractThis paper is concerned with two-dimensional (r, θ) thermoelastic dynamic responses of a long functionally graded hollow cylinder subjected to asysmmetrical thermal and mechanical loads. The material properties, except the Poisson's ratio, are assumed to be temperature independent and vary exponentially and continuously in the radial direction. By means of finite difference method and Newmark method, the motion governing equations of the long FGM hollow cylinder are solved. Comparisons between this paper's results and the corresponding analytical results validate the proposed solution. In addition, the effects of the volume fraction, temperature boundary conditions on the hollow cylinder's deformations and stresses distributions are examined, and many other valuable thermoelastic dynamic characteristics are revealed.

Further contributions on the two-dimensional flow in a sudden expansion

1997 ◽  
Vol 330 ◽  
pp. 169-188 ◽  
Author(s):  
N. ALLEBORN ◽  
K. NANDAKUMAR ◽  
H. RASZILLIER ◽  
F. DURST
Keyword(s):  
Laminar Flow ◽  
Continuation Method ◽  
Sudden Expansion ◽  
Two Dimensional ◽  
Governing Equations ◽  
Bifurcation Structure ◽  
Bifurcation Points ◽  
Flow Parameters ◽  
Two Dimensional Flow ◽  
The Stability

Two-dimensional laminar flow of an incompressible viscous fluid through a channel with a sudden expansion is investigated. A continuation method is applied to study the bifurcation structure of the discretized governing equations. The stability of the different solution branches is determined by an Arnoldi-based iterative method for calculating the most unstable eigenmodes of the linearized equations for the perturbation quantities. The bifurcation picture is extended by computing additional solution branches and bifurcation points. The behaviour of the critical eigenvalues in the neighbourhood of these bifurcation points is studied. Limiting cases for the geometrical and flow parameters are considered and numerical results are compared with analytical solutions for these cases.

scholarly journals Flow and Heat Transfer of Cu-Water Nanofluid between a Stretching Sheet and a Porous Surface in a Rotating System

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
M. Sheikholeslami ◽  
H. R. Ashorynejad ◽  
G. Domairry ◽  
I. Hashim
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Base Fluid ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Rotation Parameter ◽  
Nanoparticle Volume Fraction ◽  
Heat Transfer Characteristics ◽  
Rotating System ◽  
Flow And Heat Transfer

The aim of the present paper is to study the flow of nanofluid and heat transfer characteristics between two horizontal plates in a rotating system. The lower plate is a stretching sheet and the upper one is a solid porous plate. Copper (Cu) as nanoparticle and water as its base fluid have been considered. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions using similarity transformation, which is then solved analytically using the homotopy analysis method (HAM). Comparison between HAM and numerical solutions results showed an excellent agreement. The results for the flow and heat transfer characteristics are obtained for various values of the nanoparticle volume fraction, suction/injection parameter, rotation parameter, and Reynolds number. It is shown that the inclusion of a nanoparticle into the base fluid of this problem is capable of causing change in the flow pattern. It is found that for both suction and injection, the heat transfer rate at the surface increases with increasing the nanoparticle volume fraction, Reynolds number, and injection/suction parameter and it decreases with power of rotation parameter.

scholarly journals Statistical Modeling for Nanofluid Flow: A Stretching Sheet with Thermophysical Property Data

2020 ◽  
Vol 4 (1) ◽  
pp. 3 ◽  
Author(s):  
Alias Jedi ◽  
Azhari Shamsudeen ◽  
Noorhelyna Razali ◽  
Haliza Othman ◽  
Nuryazmin Ahmat Zainuri ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Nonlinear Ordinary Differential Equation ◽  
Numerical Results ◽  
Nanoparticle Volume Fraction ◽  
Nanofluid Flow ◽  
Property Data ◽  
Layer Flow

This paper reports the use of a numerical solution of nanofluid flow. The boundary layer flow over a stretching sheet in combination of two nanofluids models is studied. The partial differential equation that governs this model was transformed into a nonlinear ordinary differential equation by using similarity variables, and the numerical results were obtained by applying the shooting technique. Copper (Cu) nanoparticles (water-based fluid) were used in this study. This paper presents and discusses all numerical results, including those for the local Sherwood number and the local Nusselt number. Additionally, the effects of the nanoparticle volume fraction, Brownian motion Nb, and thermophoresis Nt on the performance of heat transfer are discussed. The results show that the stretching sheet has a unique solution: as the nanoparticle volume fraction φ (φ = 0), Nt (Nt = 0.1), and Nb decrease, the rate of heat transfer increases. Furthermore, as φ (φ = 0) and Nb decrease, the rate of mass transfer increases. The data of the Nusselt and Sherwood numbers were tested using different statistical distributions, and it is found that both datasets fit the Weibull distribution for different values of Nt and rotating φ.

Numerical Study of Non-Newtonian Maxwell Fluid in the Region of Oblique Stagnation Point Flow over a Stretching Sheet

2015 ◽  
Vol 32 (2) ◽  
pp. 175-184 ◽  
Author(s):  
T. Javed ◽  
A. Ghaffari
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Shooting Method ◽  
Stretching Sheet ◽  
Numerical Study ◽  
Maxwell Fluid ◽  
Governing Equations ◽  
Boundary Layer Equations ◽  
Parameter Ratio ◽  
Two Dimensional Flow

AbstractIn this article, a numerical study is carried out for the steady two-dimensional flow of an incompressible Maxwell fluid in the region of oblique stagnation point over a stretching sheet. The governing equations are transformed to dimensionless boundary layer equations. After some manipulation a system of ordinary differential equations is obtained, which is solved by using parallel shooting method. A comparison with the previous studies is made to show the accuracy of our results. The effects of involving parameters are discussed in detail and the streamlines are drawn to predict the flow pattern of the fluid. It is observed that increasing velocities ratio parameter (ratio of straining to stretching velocity) helps to decrease the boundary layer thickness. Furthermore, the velocity of fluid increases by increasing the obliqueness parameter.

A Study on Hydromagnetic Pulsating Flow of a Nanofluid in a Porous Channel With Thermal Radiation

2016 ◽  
Vol 33 (2) ◽  
pp. 213-224 ◽  
Author(s):  
A. Vijayalakshmi ◽  
S. Srinivas
Keyword(s):  
Heat Transfer ◽  
Titanium Dioxide ◽  
Thermal Radiation ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Porous Channel ◽  
Nanoparticle Volume Fraction ◽  
Governing Equations ◽  
Nanofluid Flow

AbstractThe present study investigates the hydromagnetic pulsating nanofluid flow in a porous channel with thermal radiation. In this work, we considered water as the base fluid and silver (Ag), copper (Cu), alumina (Al2O3) and titanium dioxide (TiO2) as nanoparticles. The Maxwell-Garnetts and Brinkman models are used to evaluate the effective thermal conductivity and viscosity of the nanofluid. The governing equations are solved analytically and the influence of various parameters on velocity, temperature and heat transfer rate has been discussed through graphical results. From the results, it is found that the rate of heat transfer enhances with an increase of nanoparticle volume fraction. Further, the heat transfer rate is higher for silver nanoparticles as compared with copper, alumina and titanium dioxide.

scholarly journals Cu-Al2O3 Water Hybrid Nanofluid Transport in a Periodic Structure

Processes ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 285
Author(s):  
Aiman Alshare ◽  
Wael Al-Kouz ◽  
Waqar Khan
Keyword(s):  
Periodic Structure ◽  
Volume Fraction ◽  
Reynolds Numbers ◽  
Hybrid Nanofluid ◽  
Nanoparticle Volume Fraction ◽  
Pumping Power ◽  
Computational Investigation ◽  
Governing Equations ◽  
The Cost ◽  
Volume Method

The present work is a computational investigation of nanofluid and hybrid nanofluid transport in a periodic structure. The governing equations for this work along with the appropriate boundary conditions are solved using the finite-volume method. The simulations are carried out using five wavy amplitudes of the channel shape for a range of Reynolds numbers from 102 to103. It is found that increasing the amplitude and increasing the nanoparticle volume fraction achieve enhancement of the heat transfer at the cost of increased pumping power. Correlations for the friction factor and the Nusselt number for both fluid types are provided.

Lubrication Theory for Micropolar Fluids

1971 ◽  
Vol 38 (3) ◽  
pp. 646-650 ◽  
Author(s):  
S. J. Allen ◽  
K. A. Kline
Keyword(s):  
Flow Field ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Two Dimensional ◽  
Slider Bearing ◽  
Governing Equations ◽  
Micropolar Fluids ◽  
Linear Ordinary Differential Equations ◽  
Two Dimensional Flow ◽  
Order Of Magnitude

The equations governing the flow of a fluid with rigid, spherical substructure are summarized. A two-dimensional flow field is considered and applied to the geometry of a slider bearing. Order-of-magnitude arguments are used which reduce the governing equations to a system of coupled, linear, ordinary differential equations. The equations are solved subject to appropriate boundary conditions and the effects of substructure discussed with the help of a specific numerical example.

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