Dual solutions of an unsteady magnetohydrodynamic stagnation-point flow of a nanofluid with heat and mass transfer in the presence of thermophoresis

2017 ◽  
Vol 232 (2) ◽  
pp. 155-164 ◽  
Author(s):  
Aurang Zaib ◽  
Krishnendu Bhattacharyya ◽  
SA Urooj ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Stagnation Point ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Mass Transfer Rate ◽  
Skin Friction Coefficient ◽  
Dual Solutions ◽  
The Self ◽  
Stagnation Point Flow ◽  
Self Similar

The unsteady two-dimensional magnetohydrodynamic stagnation point flow of a nanofluid with thermophoresis effect is investigated numerically. The technique of similarity transformation is implemented to obtain the self-similar ordinary differential equations and then the self-similar equations are solved numerically using shooting method. This analysis explores the conditions of the existence, non-existence, uniqueness, and duality of the solutions of self-similar equations numerically. Dual solutions of velocity, temperature and concentration profiles are reported for different values of the each parameter involved for two types of nanoparticles, namely copper (Cu) and gold (Au) in the water-based fluid. It is found that the dual solutions exist for negative values of unsteady parameter A, whereas for positive values of unsteady parameter, the solution is unique. The results also indicate that the nanoparticle volume fraction reduces the skin friction coefficient, the heat transfer rate as well as mass transfer rate. Further, due to increase of thermophoresis parameter, the concentration inside the boundary layer reduces and the mass transfer rate enhances. In addition, to validate the present numerical results, comparison with published results is made and found to be in excellent agreement.

scholarly journals A Stability Analysis for Magnetohydrodynamics Stagnation Point Flow with Zero Nanoparticles Flux Condition and Anisotropic Slip

Energies ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1268 ◽  
Author(s):  
Najiyah Khashi’ie ◽  
Norihan Md Arifin ◽  
Roslinda Nazar ◽  
Ezad Hafidzuddin ◽  
Nadihah Wahi ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Brownian Motion ◽  
Stability Analysis ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Numerical Study ◽  
Mass Transfer Rate ◽  
Similarity Solutions ◽  
Stagnation Point Flow ◽  
Flux Condition

The numerical study of nanofluid stagnation point flow coupled with heat and mass transfer on a moving sheet with bi-directional slip velocities is emphasized. A magnetic field is considered normal to the moving sheet. Buongiorno’s model is utilized to assimilate the mixed effects of thermophoresis and Brownian motion due to the nanoparticles. Zero nanoparticles’ flux condition at the surface is employed, which indicates that the nanoparticles’ fraction are passively controlled. This condition makes the model more practical for certain engineering applications. The continuity, momentum, energy and concentration equations are transformed into a set of nonlinear ordinary (similarity) differential equations. Using bvp4c code in MATLAB software, the similarity solutions are graphically demonstrated for considerable parameters such as thermophoresis, Brownian motion and slips on the velocity, nanoparticles volume fraction and temperature profiles. The rate of heat transfer is reduced with the intensification of the anisotropic slip (difference of two-directional slip velocities) and the thermophoresis parameter, while the opposite result is obtained for the mass transfer rate. The study also revealed the existence of non-unique solutions on all the profiles, but, surprisingly, dual solutions exist boundlessly for any positive value of the control parameters. A stability analysis is implemented to assert the reliability and acceptability of the first solution as the physical solution.

scholarly journals Stagnation-point flow past a shrinking sheet in a nanofluid

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Roslinda Nazar ◽  
Mihaela Jaradat ◽  
Norihan Arifin ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Nonlinear System ◽  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Shrinking Sheet

AbstractIn this paper, the stagnation-point flow and heat transfer towards a shrinking sheet in a nanofluid is considered. The nonlinear system of coupled partial differential equations was transformed and reduced to a nonlinear system of coupled ordinary differential equations, which was solved numerically using the shooting method. Numerical results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ, the shrinking parameter λand the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It was found that nanoparticles of low thermal conductivity, TiO2, have better enhancement on heat transfer compared to nanoparticles Al2O3 and Cu. For a particular nanoparticle, increasing the volume fraction φ results in an increase of the skin friction coefficient and the heat transfer rate at the surface. It is also found that solutions do not exist for larger shrinking rates and dual solutions exist when λ < −1.0.

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.

On the Self Diffusion of Water Vapour

1985 ◽  
Vol 199 (2) ◽  
pp. 159-164 ◽  
Author(s):  
F Bakhtar ◽  
K Zidi
Keyword(s):  
Mass Transfer ◽  
Transfer Rate ◽  
Pressure Range ◽  
Large Range ◽  
Mass Transfer Rate ◽  
Transport Processes ◽  
The Self ◽  
Large Droplet ◽  
Number Range ◽  
Self Diffusion

Calculated values of the coefficient of self diffusion of steam, based on a theoretical model and covering the pressure range 0.07–27 bar, are presented. By considering the equilibrium vapour pressure surrounding a large droplet placed in its own vapour, its temperature, and hence the temperature field, have been estimated. From the heat transfer rate, the rate of mass transfer and consequently the coefficient of self diffusion have been deduced. The calculations are repeated over a large range of conditions and the results correlated. Application to the nett mass transfer rate is next considered. By drawing comparisons with the case of a droplet in the free molecule regime and other transport processes, an expression covering the whole Knudsen number range is developed.

Effects of hydromagnetic and chemical reaction over a stagnation point flow of horizontal stretching/shrinking cylinder in Ag-CuO/water hybrid nanofluid

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nur Adilah Liyana Aladdin ◽  
Norfifah Bachok
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Mass Transfer ◽  
Skin Friction ◽  
Stagnation Point ◽  
Chemical Reaction ◽  
Transfer Rate ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid ◽  
Content Type

Purpose This paper aims to explore on stagnation point flow of Ag-CuO/water over a horizontal stretching/shrinking cylinder by adding the effect of chemical reaction, B together with the magnetic field, M. Design/methodology/approach A set of reduced ordinary differential equations from the governing equations of partial differential equations is obtained through similarities requirements. The resulting equations are solved using bvp4c in MATLAB2019a. The impact of various physical parameters such as curvature parameter, ϒ, chemical reaction rate, B, magnetic field, M and Schmidt numbers, Sc on shear stress, f′′0 local heat flux, -θ′(0) and mass transfer, -∅′(0) also for velocity, f′(η), temperature, θ(η) and concentration, ∅(η) profiles have been plotted and briefly discussed. In this work, some vital characteristics such as local skin friction, Cf, local Nusselt number, Nux and local Sherwood number, Shx are chosen for physical and numerical analysis. Findings The findings expose that the duality of solutions appears in a shrinking region ( ε < 0). The value of skin friction, heat transfer rate and mass transfer rate reduction for existing of M, but in contrary result obtain for larger ϒ, B and Sc. Furthermore, the hybrid nanofluid demonstrates better heat transfer compared to nanofluid. Practical implications The hybrid nanofluid has widened its applications such as in electronic cooling, manufacturing, automotive, heat exchanger, solar energy, heat pipes and biomedical, as their efficiency in the heat transfer field is better compared to nanofluid. Originality/value The findings on stagnation point flow of Ag-CuO/water over a horizontal stretching/shrinking cylinder with the effect of chemical reaction, B and magnetic field, M is new and the originality is preserved for the benefits of future researchers.

scholarly journals Non-Similar Comutational Solutions for Double-Diffusive MHD Transport Phenomena for Non-Newtnian Nanofluid From a Horizontal Circular Cylinder

2019 ◽  
Vol 8 (1) ◽  
pp. 470-485 ◽  
Author(s):  
V. Ramachandra Prasad ◽  
S. Abdul gaffar ◽  
B. Rushi Kumar
Keyword(s):  
Mass Transfer ◽  
Circular Cylinder ◽  
Differential Equations ◽  
Skin Friction ◽  
Heat And Mass Transfer ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Physical Parameters

Abstract This article aims to study theoretically the combined magneto hydrodynamic flows of casson viscoplastic nanofluid from a horizontal isothermal circular cylinder in non-Darcy porous medium. The impacts of Brownian motion and thermophoresis are consolidated and studied. The governing partial differential equations are converted into nonlinear ordinary differential equations using suitable non-similarity transformation and are solved numerically using Keller-Box finite difference technique. The numerical method is validated with previous published work and the results are found to be in excellent agreement. Numerical results for velocity, temperature, concentration along with skin friction coefficient, heat and mass transfer rate are discussed for various values of physical parameters. It is observed that velocity, heat and mass transfer rate are increased with increasing casson fluid parameter whereas temperature, concentration and skin friction are decreased. Velocity is reduced with increasing Forchheimer parameter whereas temperature and nano-particle concentration are both enhanced. An increase in magnetic parameter is seen to increase temperature and concentration whereas velocity, skin friction heat and mass transfer rate are decreased. The present model finds applications in electric-conductive nano-materials of potential use in aviation and different enterprises, energy systems and thermal enhancement of industrial flow processes.

scholarly journals Dual solutions for unsteady flow of Powell-Eyring fluid past an inclined stretching sheet

2016 ◽  
Vol 13 (1) ◽  
pp. 89-99 ◽  
Author(s):  
P. M. Krishna ◽  
N. Sandeep ◽  
J. V. R. Reddy ◽  
V. Sugunamma
Keyword(s):  
Mass Transfer ◽  
Unsteady Flow ◽  
Friction Factor ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Transfer Rate ◽  
Stretching Sheet ◽  
Mass Transfer Rate ◽  
Dual Solutions ◽  
Source Sink

This paper deals with the heat and mass transfer in unsteady flow of Powell-Eyring fluid past an inclined stretching sheet in the presence of radiation, non-uniform heat source/sink and chemical reaction with suction/injection effects. The governing equations are reduced into system of ordinary differential equations using similarity transformation and solved numerically using Runge-Kutta based shooting technique. Results display the influence of governing parameters on the flow, heat and mass transfer, friction factor, local Nusselt and Sherwood numbers. Comparisons are made with the existed studies. Present results have an excellent agreement with the existed studies. Results indicate that an increase in the chemical reaction parameter depreciates the friction factor, heat transfer rate and enhances the mass transfer rate. Dual solutions exist only for certain range of suction/injection parameters.

Unsteady three-dimensional stagnation point magnetohydrodynamic flow of bionanofluid with variable properties

2018 ◽  
Vol 232 (4) ◽  
pp. 123-134
Author(s):  
Md Faisal Md Basir ◽  
Mohammed Jashim Uddin ◽  
Ahmad Izani Md Ismail
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Transport Properties ◽  
Stagnation Point ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Mass Transfer Rate ◽  
Three Dimensional ◽  
Magnetohydrodynamic Flow ◽  
Nanoparticle Volume Fraction

Unsteady three-dimensional laminar stagnation point forced convective boundary layer magnetohydrodynamic flow of a bionanofluid with variable transport properties is studied theoretically and numerically. Thermal convective and zero mass flux boundary conditions are incorporated in this study. The transport properties are assumed to be a function of nanoparticle volume fraction to get physically realistic results. The dimensional boundary layer equations along with the coupled boundary conditions are transformed via similarity transformations into a system of ordinary differential equations. The transformed equations are solved numerically using the Runge–Kutta–Fehlberg fourth-, fifth-order numerical method. The effect of selected governing parameters, namely, viscosity, thermal conductive, mass diffusivity, microorganism diffusivity, magnetic field and bioconvection Schmidt number, on the dimensionless velocity, temperature, nanoparticle volume fraction, microorganism, skin friction coefficient, heat transfer rate, mass transfer rate and microorganism transfer rate, is illustrated graphically and interpreted in detail. Comparisons with previous works are carried out for some limiting cases and found to be in good agreement.

scholarly journals Unsteady Stagnation Point Flow and Heat Transfer over a Stretching/Shrinking Sheet with Suction or Injection

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
M. Suali ◽  
N. M. A. Nik Long ◽  
N. M. Ariffin
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Similarity Transformation ◽  
Skin Friction Coefficient ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer ◽  
Suction Or Injection

The unsteady stagnation point flow and heat transfer over a stretching/shrinking sheet with suction/injection is studied. The governing partial differential equations are converted into nonlinear ordinary differential equations using a similarity transformation and solved numerically. Both stretching and shrinking cases are considered. Results for the skin friction coefficient, local Nusselt number, velocity, and temperature profiles are presented for different values of the governing parameters. It is found that the dual solutions exist for the shrinking case, whereas the solution is unique for the stretching case. Numerical results show that the range of dual solutions increases with mass suction and decreases with mass injection.

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