Effects of Variable Viscosity and Thermal conductivity on Natural-Convection of Nanofluids Past a Vertical Plate in Porous Media

2013 ◽  
Vol 30 (3) ◽  
pp. 265-275 ◽  
Author(s):  
A. Noghrehabadi ◽  
M. Ghalambaz ◽  
A. Ghanbarzadeh
Keyword(s):  
Thermal Conductivity ◽  
Brownian Motion ◽  
Natural Convection ◽  
Differential Equations ◽  
Vertical Plate ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Increase With Increase ◽  
Dimensional Parameters ◽  
Brownian Motion And Thermophoresis

ABSTRACTThe effects of variable viscosity and thermal conductivity on the natural convection heat transfer over a vertical plate embedded in a porous medium saturated by a nanofluid are investigated. In the nanofluid model, a gradient of nanoparticles concentration because of Brownian motion and thermophoresis forces is taken into account. The nanofluid viscosity and the thermal conductivity are assumed as a function of local nanoparticles volume fraction. The appropriate similarity variables are used to convert the governing partial differential equations into a set of highly coupled nonlinear ordinary differential equations, and then, they numerically solved using the Runge-Kutta-Fehlberg method. The practical range of non- dimensional parameters is discussed. The results show that the range of Lewis number as well as Brownian motion and thermophoresis parameters which were used in previous studies should be reconsidered. The effect of non-dimensional parameters on the boundary layer is examined. The results show that the reduced Nusselt number would increase with increase of viscosity parameter and would decrease with increase of thermal conductivity parameter.

Transient two-dimensional natural convection flow of a nanofluid past an isothermal vertical plate using Buongiorno’s model

2017 ◽  
Vol 27 (1) ◽  
pp. 23-47 ◽  
Author(s):  
Marneni Narahari ◽  
Suresh Kumar Raju Soorapuraju ◽  
Rajashekhar Pendyala ◽  
Ioan Pop
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Brownian Motion ◽  
Natural Convection ◽  
Vertical Plate ◽  
Volume Fraction ◽  
Convection Flow ◽  
Nanoparticle Volume Fraction ◽  
Natural Convection Flow ◽  
Content Type

Purpose The purpose of this paper is to present a numerical investigation of the transient two-dimensional natural convective boundary-layer flow of a nanofluid past an isothermal vertical plate by incorporating the effects of Brownian motion and thermophoresis in the mathematical model. Design/methodology/approach The problem is formulated using the Oberbeck–Boussinesq and the standard boundary-layer approximations. The governing coupled non-linear partial differential equations for conservation of mass, momentum, thermal energy and nanoparticle volume fraction have been solved by using an efficient implicit finite-difference scheme of the Crank–Nicolson type, which is stable and convergent. Numerical computations are performed and the results for velocity, temperature and nanoparticle volume fraction are presented in graphs at different values of system parameters such as Brownian motion parameter, thermophoresis parameter, buoyancy ratio parameter, Prandtl number, Lewis number and dimensionless time. The results for local and average skin-friction and Nusselt number are also presented graphically and discussed thoroughly. Findings It is found that the velocity, temperature and nanoparticle volume fraction profiles enhance with respect to time and attain steady-state values as time progresses. The local Nusselt number is found to decrease with increasing thermophoresis parameter, while it increases slightly with increasing Brownian motion parameter. To validate the present numerical results, the steady-state local Nusselt number results for the limiting case of a regular fluid have been compared with the existing well-known results at different Prandtl numbers, and the results are found to be in an excellent agreement. Research limitations/implications The present analysis is limited to the transient laminar natural convection flow of a nanofluid past an isothermal semi-infinite vertical plate in the absence of viscous dissipation and thermal radiation. The unsteady natural convection flow of a nanofluid will be investigated for various physical conditions in a future work. Practical implications Unsteady flow devices offer potential performance improvements as compared with their steady-state counterparts, and the flow fields in the unsteady flow devices are typically transient in nature. The present study provides very useful information for heat transfer engineers to understand the heat transfer enhancement with the nanofluid flows. The present results have immediate relevance in cooling technologies. Originality/value The present research work is relatively original and illustrates the transient nature of the natural convective nanofluid boundary-layer flow in the presence of Brownian motion and thermophoresis.

Second Law Analysis of Heat and Mass Transfer of Nanofluids Along a Plate With Prescribed Surface Heat Flux

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Waqar A. Khan ◽  
Richard Culham ◽  
A. Aziz
Keyword(s):  
Mass Transfer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Entropy Generation Rate ◽  
Second Law ◽  
Second Law Analysis ◽  
Brownian Motion And Thermophoresis

A model based on the works of Buongiorno, which includes the effects of Brownian motion and thermophoresis, is used to develop the governing equations for convection in nanofluids. The analysis includes examples with water and ethylene glycol as the base fluids and nanoparticles of Cu and Al2O3. An assumption of zero nanoparticle flux is used at the surface of the plate to make the model more physically realistic. The model accounts for the effects of both Brownian motion and thermophoresis in the mass boundary condition. Using suitable transformations, the governing partial differential equations are converted into ordinary differential equations which are solved numerically. The dimensionless velocity, temperature, and concentration gradients are used in the second law analysis to determine heat and mass transfer rates. It is shown that the dimensionless entropy generation rate strongly depends upon the solid volume fraction of the nanoparticles, local Reynolds number, and group parameters.

Magnetohydrodynamic, Thermal Radiation and Convective Boundary Effects of Free Convection Flow Past a Vertical Plate Embedded in a Porous Medium Saturated with a Nanofluid

2015 ◽  
Vol 31 (5) ◽  
pp. 607-616 ◽  
Author(s):  
H. Ali Agha ◽  
M. N. Bouaziz ◽  
S. Hanini
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Brownian Motion ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Heat And Mass Transfer ◽  
Vertical Plate ◽  
Volume Fraction ◽  
Convection Flow ◽  
Convective Boundary

AbstractA numerical analysis was performed to study the effects of combined magnetohydrodynamic and thermal radiation under convective boundary condition over a semi infinite vertical plate embedded in a non-Darcy porous medium. Coupled heat and mass transfer of free convective boundary layer with viscous nanofluid are considered. The model used for the nanofluid includes the effects of Brownian motion and thermophoresis mechanisms, while the Darcy-Forchheimer model is used for the porous medium. The governing partial differential equations are transformed into the ordinary differential equations using the similarity transformations. The accuracy of the method is observed by a comparison with other works reduced to a common case. Many results are tabulated and representative set is displayed graphically to illustrate the influence of the various parameters of interest on different profiles. Extensive numerical investigations show that the flow field, temperature, concentration and nanoparticle volume fraction shapes are significantly influenced by magnetic parameter, regular Lewis number, Brownian motion parameter, thermophoresis parameter, regular buoyancy ratio parameter and Biot number. Heat and mass transfer rates are significantly affected by the level of the applied magnetic field and the convective heat coefficient.

Heat Transfer Phenomena in a Moving Nanofluid Over a Horizontal Surface

2012 ◽  
Vol 28 (3) ◽  
pp. 579-588 ◽  
Author(s):  
K. Vajravelu ◽  
K. V. Prasad
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Brownian Motion ◽  
Differential Equations ◽  
Volume Fraction ◽  
Numerical Study ◽  
Fluid Viscosity ◽  
Variable Fluid Properties ◽  
Non Linear ◽  
Fluid Properties

AbstractA numerical study is carried out to study the effects of variable fluid properties on the boundary layer flow and heat transfer of a nanofluid at a flat sheet. The effects of Brownian motion, thermophoresis and viscous dissipation due to frictional heating are also considered. The temperature-dependent variable fluid properties, namely, the fluid viscosity and the thermal conductivity are assumed to vary, respectively, as an inverse function and a linear function of temperature. Using a similarity transformation, the governing non-linear partial differential equations of the model problem are transformed into coupled non-linear ordinary differential equations and these equations are solved numerically by Keller-Box method. Velocity, temperature, and nanoparticles volume fraction profiles are presented and analyzed for several sets of values of the governing parameters; namely, variable fluid viscosity, variable thermal conductivity, Brownaian motion, thermophoresis and plate-velocity parameters with changes in the Prandtl and Schmidt numbers. It is observed that there is an increase in the skin friction in the upstream movement of the plate: But quite the opposite is true in the downstream movement of the plate. Also, the effect of the Schmidt number and the Brownian motion parameter is to reduce the Sherwood number, where as the effect of thermophoresis parameter is to enhance it.

Brownian motion and thermophoresis effects on natural convection of alumina–water nanofluid

2012 ◽  
Vol 227 (1) ◽  
pp. 100-110 ◽  
Author(s):  
Habib Aminfar ◽  
Mohammad Reza Haghgoo
Keyword(s):  
Heat Transfer ◽  
Brownian Motion ◽  
Natural Convection ◽  
Volume Fraction ◽  
Effective Properties ◽  
Solid Volume Fraction ◽  
Convection Heat Transfer ◽  
Conservation Equation ◽  
Nanoparticles Volume Fraction ◽  
Brownian Motion And Thermophoresis

In this article a ‘two-component four-equation non-homogeneous equilibrium’ model has been adopted to accurately simulate the process of natural convection of Al2O3–water nanofluid inside a vertical square cavity. The aforementioned model considers conservation equation of nanoparticles which is highly coupled to other equations (mass, momentum, and energy equations for nanofluid) and includes the effects of Brownian motion and thermophoresis as the two most important mechanisms of slip velocity in laminar flow. The distribution of nanoparticles volume fraction is obtained by solving these four equations simultaneously. Renewing the effective properties of nanofluid from the nanoparticles, volume fraction distribution is another advantage of this model. Numerical results are in good agreement with published experimental data and emphasize that the use of the nanofluid for natural convection heat transfer enhancement in enclosure is impracticable for the studied range of solid volume fraction [Formula: see text]. Also, heat transfer rate decreases with an increase in nanoparticle volume fraction.

Free Convection Flow of a Nanofluid Past an Isothermal Inclined Plate

2013 ◽  
Vol 390 ◽  
pp. 129-133 ◽  
Author(s):  
Marneni Narahari ◽  
S. Akilu ◽  
A. Jaafar
Keyword(s):  
Nusselt Number ◽  
Brownian Motion ◽  
Volume Fraction ◽  
Convection Flow ◽  
Inclined Plate ◽  
Convective Boundary ◽  
Linear Ordinary Differential Equations ◽  
Keller Box Method ◽  
Brownian Motion And Thermophoresis ◽  
Layer Flow

In this paper, the natural convective boundary-layer flow of a nanofluid over an isothermal inclined plate is investigated numerically with the effects of Brownian motion and thermophoresis in the nanofluid model. The equations governing the flow are expressed in the form of coupled non-linear ordinary differential equations using the similarity analysis. These equations are then solved numerically by an implicit finite-difference method known as the Keller-box method. The effect of inclination angle on the dimensionless velocity, temperature, nanofluid volume fraction and Nusselt number has been analyzed through graphs. Brownian motion and thermophoresis effects on the Nusselt number at an inclined plate are also discussed.

Effects of Variable Viscosity and Thermal Conductivity of CuO-Water Nanofluid on Heat Transfer Enhancement in Natural Convection: Mathematical Model and Simulation

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Eiyad Abu-Nada
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Cylinder Surface ◽  
Transfer Enhancement

Heat transfer enhancement in horizontal annuli using variable thermal conductivity and variable viscosity of CuO-water nanofluid is investigated numerically. The base case of simulation used thermal conductivity and viscosity data that consider temperature property dependence and nanoparticle size. It was observed that for Ra≥104, the average Nusselt number was deteriorated by increasing the volume fraction of nanoparticles. However, for Ra=103, the average Nusselt number enhancement depends on aspect ratio of the annulus as well as volume fraction of nanoparticles. Also, for Ra=103, the average Nusselt number was less sensitive to volume fraction of nanoparticles at high aspect ratio and the average Nusselt number increased by increasing the volume fraction of nanoaprticles for aspect ratios ≤0.4. For Ra≥104, the Nusselt number was deteriorated everywhere around the cylinder surface especially at high aspect ratio. However, this reduction is only restricted to certain regions around the cylinder surface for Ra=103. For Ra≥104, the Maxwell–Garnett and the Chon et al. conductivity models demonstrated similar results. But, there was a deviation in the prediction at Ra=103 and this deviation becomes more significant at high volume fraction of nanoparticles. The Nguyen et al. data and the Brinkman model give completely different predictions for Ra≥104, where the difference in prediction of the Nusselt number reached 50%. However, this difference was less than 10% at Ra=103.

Numerical Solution of Transient Heat Conduction Equation for Heat-Treatable Alloys Whose Thermal Properties Change With Time and Temperature

1977 ◽  
Vol 99 (3) ◽  
pp. 471-478 ◽  
Author(s):  
K. Farnia ◽  
J. V. Beck
Keyword(s):  
Thermal Conductivity ◽  
Thermal Properties ◽  
Differential Equations ◽  
Numerical Solution ◽  
Precipitation Hardening ◽  
Elevated Temperatures ◽  
Volume Fraction ◽  
Transient Heat Conduction ◽  
Computer Assisted ◽  
Al 2024

Changes in microstructure occur in as-received aluminum alloy (Al-2024-T351) when it is subjected to elevated temperatures (150–260°C). These changes, which are called precipitation hardening, in turn influence the thermal properties, making them time as well as temperature dependent. A computer-assisted transient experimental procedure has been developed to determine the values of thermal conductivity of as-received Al-2024-T351 under the influence of precipitation-hardening. Based on isothermal experimental data and related algebraic modeling of the thermal conductivity, a mathematical model in the form of two differential equations is proposed. Instantaneous values of volume fraction of precipitate and thermal conductivity can be predicted using this model. A method for the simultaneous numerical solution of the partial differential equation of conduction and the proposed differential equations of precipitation are also given. The influence of precipitation—hardening on temperature distribution and on values of thermal conductivity is shown graphically for several cases involving the Al-2024-T351 material.

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