Numerical Simulation of Non-Axisymmetric Homann's Stagnation-Point Flow of Nanofluid

2020 ◽  
Vol 9 (1) ◽  
pp. 47-55
Author(s):  
I. Ahmad ◽  
M. R. Jagwal ◽  
M. Sajid
Keyword(s):  
Brownian Motion ◽  
Stagnation Point ◽  
Shooting Method ◽  
Mass Transfer Rate ◽  
Numerical Results ◽  
Stagnation Point Flow ◽  
Solid Boundary ◽  
Point Problem ◽  
Shear Stresses ◽  
Outer Potential

This paper addresses numerical results for nanofluid near Homann's non-axisymmetric stagnation-point flow. The nanofluids model shows Brownian motion and thermophoresis effects. Recently, Weidman modify the Homann's stagnation-point problem to non-axisymmetric on rigid surface by superposing additional periodic terms to outer potential flow. The numerical results for couple differential system are obtained by means of shooting method. The solution is achieved for diverse values of involved parameter and ratio γ = b/a (b is shear and a is strain rate), which ranges from (–∞, ∞). The distributions for shear stresses, heat and mass transfer rate, temperature and nanoparticle concentration compared to their large- asymptotic behaviors also presented. For nanofluids, properties may vary considerably near solid boundary due to thermophoresis and Brownian motion of the fluid particles. These effects can result in decreasing viscosity within the boundary layer for heated fluids, thus leading to heat transfer enhancement.

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.

Stagnation-point flow towards a stretching/shrinking sheet in a nanofluid using Buongiorno's model

2016 ◽  
Vol 231 (2) ◽  
pp. 172-180 ◽  
Author(s):  
Syahira Mansur ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Stagnation Point ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Numerical Results ◽  
Stagnation Point Flow ◽  
Problem Solver ◽  
Shrinking Sheet ◽  
Lower Branch ◽  
Buongiorno’S Model ◽  
Brownian Motion Parameter

The stagnation point flow of a nanofluid towards a permeable stretching/shrinking sheet using the Buongiorno's model is studied. Numerical results are obtained using boundary value problem solver bvp4c in MATLAB for several values of the governing parameters. The numerical results show that dual (upper and lower branch) solutions exist for the shrinking case, while for the stretching case, the solution is unique. A stability analysis is performed to determine the physical realizable in practice of the dual solutions. It is found that the skin friction decreases when the sheet is stretched, but increases when the suction effect is increased. It is also found that increasing the thermophoresis parameter reduces the heat transfer rate at the surface, while increasing the Brownian motion parameter increases the mass transfer rate at the surface.

scholarly journals A Numerical Approach to Slip Flow of a Micropolar Fluid above A Flat Permeable Contracting Surface

2021 ◽  
Vol 26 (2) ◽  
pp. 173-185
Author(s):  
R. Parthiban ◽  
G. Palani ◽  
Seema Tinker ◽  
R. P. Sharma
Keyword(s):  
Mathematical Modeling ◽  
Stagnation Point ◽  
Micropolar Fluid ◽  
Couple Stress ◽  
Slip Flow ◽  
Numerical Approach ◽  
Numerical Results ◽  
Polar Liquid ◽  
Stagnation Point Flow ◽  
Physical Quantities

Abstract A plain linear penetrable contracting sheet with slip over a micro-polar liquid with a stagnation-point flow is analyzed. Through similarity mapping, the mathematical modeling statements are transformed as ODE’s and numerical results are found by shooting techniques. The varying impacts of physical quantities on the momentum, micro-rotation, and temperature were demonstrated through graphs. The computed measures including shear and couple stress with distinct measures of factors involved in this proposed problem are presented through a table.

scholarly journals Dual similarity solutions of MHD stagnation point flow of Casson fluid with effect of thermal radiation and viscous dissipation: stability analysis

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Viscous Dissipation ◽  
Shooting Method ◽  
Casson Fluid ◽  
Similarity Solutions ◽  
Stagnation Point Flow ◽  
Stretching Surfaces

Abstract In this paper, the rate of heat transfer of the steady MHD stagnation point flow of Casson fluid on the shrinking/stretching surface has been investigated with the effect of thermal radiation and viscous dissipation. The governing partial differential equations are first transformed into the ordinary (similarity) differential equations. The obtained system of equations is converted from boundary value problems (BVPs) to initial value problems (IVPs) with the help of the shooting method which then solved by the RK method with help of maple software. Furthermore, the three-stage Labatto III-A method is applied to perform stability analysis with the help of a bvp4c solver in MATLAB. Current outcomes contradict numerically with published results and found inastounding agreements. The results reveal that there exist dual solutions in both shrinking and stretching surfaces. Furthermore, the temperature increases when thermal radiation, Eckert number, and magnetic number are increased. Signs of the smallest eigenvalue reveal that only the first solution is stable and can be realizable physically.

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.

Two-dimensional oblique stagnation-point flow towards a stretching surface in a viscoelastic fluid

Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Iqbal Husain ◽  
Fotini Labropulu ◽  
Ioan Pop
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Stagnation Point ◽  
Shooting Method ◽  
Stagnation Point Flow ◽  
Two Dimensional ◽  
Stretching Surface ◽  
Finite Difference Technique ◽  
Walters B Fluid

AbstractIn this paper, the steady two-dimensional stagnation-point flow of a viscoelastic Walters’ B’ fluid over a stretching surface is examined. It is assumed that the fluid impinges on the wall obliquely. Using similarity variables, the governing partial differential equations are transformed into a set of two non-dimensional ordinary differential equations. These equations are then solved numerically using the shooting method with a finite-difference technique.

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 Chemical Reaction Effects on Stretching/Shrinking Vertical Surface in Stagnation Point Flow

2019 ◽  
Vol 8 (12S2) ◽  
pp. 719-723
Keyword(s):  
Stagnation Point ◽  
Chemical Reaction ◽  
Vertical Surface ◽  
Numerical Results ◽  
Dual Solutions ◽  
Stagnation Point Flow

The effects of chemical reaction on nanofluid vertical surface were considered on the flow of stagnation point. The numerical results were obtained by MATLAB to observe the impacts of the parameter of chemical reaction to the governing parameters. The results are graphically portrayed to observe the presence of dual solutions. The validation of the results is compared to the previous study and tends to give a favorable argument.

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