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.

Double Diffusive Convection in Flow Couple Stress Nanofluid in a Permeable Wall Vertical Channel in the Presence of a Magnetic Field

2019 ◽  
Vol 26 ◽  
pp. 30-44
Author(s):  
Noureddine Messaoudi ◽  
Mohamed Nadjib Bouaziz ◽  
Hamza Ali Agha
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Couple Stress ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Strong Impact

In this work, the flow of a couple stress nanofluid in a vertical channel with heat and mass transfer in the presence of a magnetic field and taking account the Brownian motion, the thermophoresis as well as the effect of Soret and Dufour was simulated numerically using Matlab following the code bvp4c. The nonlinear partial differential equations governing this particular flow are transformed into a system of ordinary differential equations via the similarity technique. The influence of the parameters describing the behavior of the problem studied on the velocity, temperature, concentration and volume fraction fields of the nanoparticles, as well as on the coefficient of friction, Nusselt and Sherwood numbers, were highlighted for the end of the study. understand their effect on heat and mass transfer. The rheology of the nanofluid and the magnetic field have a strong impact on the velocity and temperature profiles, while the parameters of Brownian motion and thermophoresis promote heat transfer.

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.

Numerical investigation of three-dimensional nanofluid flow with heat and mass transfer on a nonlinearly stretching sheet using the barycentric functions

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Soraya Torkaman ◽  
Ghasem Barid Loghmani ◽  
Mohammad Heydari ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Operational Matrices ◽  
Nanofluid Flow ◽  
Content Type ◽  
Nonlinearly Stretching Sheet

Purpose The purpose of this paper is to investigate a three-dimensional boundary layer flow with considering heat and mass transfer on a nonlinearly stretching sheet by using a novel operational-matrix-based method. Design/methodology/approach The partial differential equations that governing the problem are converted into the system of nonlinear ordinary differential equations (ODEs) with considering suitable similarity transformations. A direct numerical method based on the operational matrices of integration and product for the linear barycentric rational basic functions is used to solve the nonlinear system of ODEs. Findings Graphical and tabular results are provided to illustrate the effect of various parameters involved in the problem on the velocity profiles, temperature distribution, nanoparticle volume fraction, Nusselt and Sherwood number and skin friction coefficient. Comparison between the obtained results, numerical results based on the Maple's dsolve (type = numeric) command and previous existing results affirms the efficiency and accuracy of the proposed method. Originality/value The motivation of the present study is to provide an effective computational method based on the operational matrices of the barycentric cardinal functions for solving the problem of three-dimensional nanofluid flow with heat and mass transfer. The convergence analysis of the presented scheme is discussed. The benefit of the proposed method (PM) is that, without using any collocation points, the governing equations are converted to the system of algebraic equations.

Unsteady convective heat and mass transfer of a nanofluid in Howarth’s stagnation point by Buongiorno’s model

2015 ◽  
Vol 25 (5) ◽  
pp. 1176-1197 ◽  
Author(s):  
Saeed Dinarvand ◽  
Reza Hosseini ◽  
Ioan Pop
Keyword(s):  
Mass Transfer ◽  
Nusselt Number ◽  
Brownian Motion ◽  
Heat And Mass Transfer ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Buongiorno’S Model ◽  
Brownian Motion And Thermophoresis

Purpose – The purpose of this paper is to do a comprehensive study on the unsteady general three-dimensional stagnation-point flow and heat transfer of a nanofluid by Buongiorno’s model. Design/methodology/approach – In this study, the convective transport equations include the effects of Brownian motion and thermophoresis. By introducing new similarity transformations for velocity, temperature and nanoparticle volume fraction, the basic equations governing the flow, heat and mass transfer are reduced into highly non-linear ordinary differential equations. The resulting non-linear system has been solved both analytically and numerically. Findings – The analysis shows that velocity, temperature and nanoparticle concentration profiles in the respective boundary layers depend on five parameters, namely unsteadiness parameter A, Brownian motion parameter Nb, thermophoresis parameter Nt, Prandtl number Pr and Lewis number Le. It is found that the thermal boundary layer thickens with a rise in both of the Brownian motion and the thermophoresis effects. Therefore, similar to the earlier reported results, the Nusselt number decreases as the Brownian motion and thermophoresis effects become stronger. A correlation for the Nusselt number has been developed based on a regression analysis of the data. This correlation predicts the numerical results with a maximum error of 9 percent for a usual domain of the physical parameters. Originality/value – The stagnation point flow toward a wavy cylinder (with nodal and saddle stagnation points) that a little attention has been given to it up to now. The examination of unsteadiness effect on the general three-dimensional stagnation-point flow. The application of an interesting and global model (Boungiorno’s model) for the nanofluid that incorporates the effects of Brownian motion and thermophoresis. The study of the effects of Brownian motion and thermophoresis on the nanofluid flow, heat and mass transfer characteristics. The prediction of correlation for the Nusselt number based on a regression analysis of the data. General speaking, we can tell the problem with this geometry, characteristics, the applied model, and comprehensive results, was Not studied and analyzed in literature up to now.

A Note on Double Dispersion Effects in a Nanofluid Flow in a Non-Darcy Porous Medium

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
F. G. Awad ◽  
P. Sibanda ◽  
P. V. S. N. Murthy
Keyword(s):  
Mass Transfer ◽  
Brownian Motion ◽  
Heat And Mass Transfer ◽  
Linearization Method ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Transfer Characteristics ◽  
Dispersion Effects ◽  
Brownian Motion And Thermophoresis ◽  
Double Dispersion

A non-Darcian model has been employed to investigate a nanofluid flow in a porous layer with double dispersion effects. The model incorporates Brownian motion and thermophoresis to study heat and mass transfer characteristics within the nanofluid. A similarity transformation is used to obtain a system of ordinary differential equations that are solved numerically using a linearization method. The effects of fluid and physical parameters such as thermal and solutal dispersions, the Brownian motion, and thermophoresis on the heat and mass transfer characteristics of the nanofluid are determined, and for some limiting cases, compared to results in the literature.

scholarly journals Stagnation Point Flow of Nanofluid over a Moving Plate with Convective Boundary Condition and Magnetohydrodynamics

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Fazle Mabood ◽  
Nopparat Pochai ◽  
Stanford Shateyi
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Friction Factor ◽  
Heat And Mass Transfer ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Convective Boundary Condition ◽  
Stagnation Point Flow ◽  
Moving Plate ◽  
Convective Boundary

A theoretical investigation is carried out to examine the effects of volume fraction of nanoparticles, suction/injection, and convective heat and mass transfer parameters on MHD stagnation point flow of water-based nanofluids (Cu and Ag). The governing partial differential equations for the fluid flow, temperature, and concentration are reduced to a system of nonlinear ordinary differential equations. The derived similarity equations and corresponding boundary conditions are solved numerically using Runge-Kutta Fehlberg fourth-fifth order method. To exhibit the effect of the controlling parameters on the dimensionless velocity, temperature, nanoparticle volume fraction, skin friction factor, and local Nusselt and local Sherwood numbers, numerical results are presented in graphical and tabular forms. It is found that the friction factor and heat and mass transfer rates increase with magnetic field and suction/injection parameters.

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.

Sign in / Sign up

Export Citation Format

Share Document