scholarly journals Numerical Analysis with Keller-Box Scheme for Stagnation Point Effect on Flow of Micropolar Nanofluid over an Inclined Surface

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1379 ◽  
Author(s):  
Rafique ◽  
Anwar ◽  
Misiran ◽  
Khan ◽  
Seikh ◽  
...  
Keyword(s):  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Nonlinear Differential Equations ◽  
Stagnation Region ◽  
Similarity Transformations ◽  
Box Scheme ◽  
Mass Fluxes ◽  
Micropolar Nanofluid ◽  
Inclined Surface

The prime aim of this paper is to probe the flow of micropolar nanofluid towards an inclined stretching surface adjacent to the stagnation region with Brownian motion and thermophoretic impacts. The chemical reaction and heat generation or absorption are also taken into account. The energy and mass transport of the micropolar nanofluid flow towards an inclined surface are discussed. The numerical solution is elucidated for the converted non-linear ordinary differential equation from the set of partial nonlinear differential equations via compatible similarity transformations. A converted system of ordinary differential equations is solved via the Keller-box scheme. The stretching velocity and external velocity are supposed to change linearly by the distance from the stagnation point. The impacts of involved parameters on the concerned physical quantities such as skin friction, Sherwood number, and energy exchange are discussed. These results are drawn through the graphs and presented in the tables. The energy and mass exchange rates show a direct relation with the stagnation point. In the same vein, skin friction diminishes with the growth of the stagnation factor. Heat and mass fluxes show an inverse correspondence with the inclination factor.

scholarly journals Keller-Box Simulation for the Buongiorno Mathematical Model of Micropolar Nanofluid Flow over a Nonlinear Inclined Surface

Processes ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 926 ◽  
Author(s):  
Khuram Rafique ◽  
Muhammad Imran Anwar ◽  
Masnita Misiran ◽  
Ilyas Khan ◽  
Asiful H. Seikh ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Similarity Transformations ◽  
Flow Parameters ◽  
Box Scheme ◽  
Micropolar Nanofluid ◽  
Brownian Motion And Thermophoresis ◽  
Buongiorno Model ◽  
Inclined Surface ◽  
Physical Quantities

Brownian motion and thermophoresis diffusions are the fundamental ideas of abnormal upgrading in thermal conductivity via binary fluids (base fluid along with nanoparticles). The influence of Brownian motion and thermophoresis are focused on in the Buongiorno model. In this problem, we considered the Buongiorno model with Brownian motion and thermophoretic effects. The nonlinear ordinary differential equations are recovered from the partial differential equations of the boundary flow via compatible similarity transformations and then employed to the Keller-box scheme for numerical results. The physical quantities of our concern including skin friction, Nusselt number, and Sherwood number along with velocity, temperature and concentration profile against involved effects are demonstrated. The impacts of the involved flow parameters are drawn in graphs and tabulated forms. The inclination effect shows an inverse relation with the velocity field. Moreover, the velocity profile increases with the growth of the buoyancy effect.

scholarly journals Axisymmetric Stagnation Flow of a Micropolar Nanofluid in a Moving Cylinder

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
S. Nadeem ◽  
Abdul Rehman ◽  
K. Vajravelu ◽  
Jinho Lee ◽  
Changhoon Lee
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Flow ◽  
Finite Radius ◽  
Similarity Transformations ◽  
Moving Cylinder ◽  
Micropolar Nanofluid ◽  
Homotopy Analysis ◽  
Flow Phenomena

An analysis is carried out for axisymmetric stagnation flow of a micropolar nanofluid in a moving cylinder with finite radius. The coupled nonlinear partial differential equations of the problem are simplified with the help of similarity transformations and the resulting coupled nonlinear differential equations are solved analytically by homotopy analysis method (HAM). The features of the flow phenomena, inertia, heat transfer, and nanoparticles are analyzed and discussed.

On both MHD and slip effect in micropolar hybrid nanofluid past a circular cylinder under stagnation point region

2019 ◽  
Vol 97 (4) ◽  
pp. 392-399 ◽  
Author(s):  
S. Nadeem ◽  
Nadeem Abbas
Keyword(s):  
Circular Cylinder ◽  
Differential Equations ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Hybrid Nanofluid ◽  
Shooting Technique ◽  
Slip Effects ◽  
Highly Nonlinear ◽  
Micropolar Nanofluid ◽  
Heat Transfer Improvement

The physical model of the micropolar hybrid nanofluid flow with magnetohydrodynamic and thermal slip effects is considered. The flow of three-dimensional stagnation point of micropolar hybrid nanofluid past a circular cylinder is also taken into account. The flow model is controlled through partial differential equations. These equations are highly nonlinear in character and reduce to ordinary differential equations through applying the suitable similarity transformation. The reduced system is solved numerically using the shooting technique. The mutual effects are presented using graphs while comparative numerical results are presented in the tables. The diverse physical parts of the issue have been talked about. This study aims to investigate the solid nano-sized particle on the surface of a circular cylinder having sinusoidal variation. These nanosized particles are used to analyze the heat transfer improvement of micropolar hybrid nanofluid as compared to micropolar nanofluid.

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 NUMERICAL SIMULATION OF MHD STAGNATION POINT FLOW TOWARDS A HEATED AXISYMMETRIC SURFACE

2011 ◽  
Vol 52 (3) ◽  
pp. 301-308
Author(s):  
MUHAMMAD ASHRAF ◽  
M. ANWAR KAMAL
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Stagnation Point ◽  
Applied Magnetic Field ◽  
Nonlinear Differential Equations ◽  
Transverse Magnetic ◽  
Stagnation Point Flow ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Axisymmetric Surface

AbstractThe problem of stagnation point flow with heat transfer of an electrically conducting fluid impinging normally on a permeable axisymmetric surface in the presence of a uniform transverse magnetic field is analysed. The governing nonlinear differential equations and their associated boundary conditions are reduced to dimensionless form using suitable similarity transformations. Comparison with previously published work shows good agreement. Effects of the injection–suction parameter, magnetic parameter and Prandtl number on the flow and thermal fields are presented. The investigations show that the wall shear stress and heat transfer rate from the surface increase with increased applied magnetic field. An increase in the velocity and thermal boundary layer thicknesses is observed with an increase in the wall injection, while the velocity and thermal boundary layers become thinner when increasing the wall suction and applied magnetic field.

scholarly journals A New Numerical Solution of Maxwell Fluid over a Shrinking Sheet in the Region of a Stagnation Point

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
S. S. Motsa ◽  
Y. Khan ◽  
S. Shateyi
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Nonlinear Partial Differential Equations ◽  
Maxwell Fluid ◽  
Shrinking Sheet ◽  
Two Dimensional ◽  
Similarity Transformations ◽  
The Mathematical Model ◽  
Successive Linearisation Method ◽  
Fluid Parameters

The mathematical model for the incompressible two-dimensional stagnation flow of a Maxwell fluid towards a shrinking sheet is proposed. The developed equations are used to discuss the problem of being two dimensional in the region of stagnation point over a shrinking sheet. The nonlinear partial differential equations are transformed to ordinary differential equations by first-taking boundary-layer approximations into account and then using the similarity transformations. The obtained equations are then solved by using a successive linearisation method. The influence of the pertinent fluid parameters on the velocity is discussed through the help of graphs.

scholarly journals Unsteady Stagnation Point Flow of Hybrid Nanofluid Past a Convectively Heated Stretching/Shrinking Sheet with Velocity Slip

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1649
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Velocity Slip ◽  
Slip Condition ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Unsteady stagnation point flow in hybrid nanofluid (Al2O3-Cu/H2O) past a convectively heated stretching/shrinking sheet is examined. Apart from the conventional surface of the no-slip condition, the velocity slip condition is considered in this study. By incorporating verified similarity transformations, the differential equations together with their partial derivatives are changed into ordinary differential equations. Throughout the MATLAB operating system, the simplified mathematical model is clarified by employing the bvp4c procedure. The above-proposed approach is capable of producing non-uniqueness solutions when adequate initial assumptions are provided. The findings revealed that the skin friction coefficient intensifies in conjunction with the local Nusselt number by adding up the nanoparticles volume fraction. The occurrence of velocity slip at the boundary reduces the coefficient of skin friction; however, an upward trend is exemplified in the rate of heat transfer. The results also signified that, unlike the parameter of velocity slip, the increment in the unsteady parameter conclusively increases the coefficient of skin friction, and an upsurge attribution in the heat transfer rate is observed resulting from the increment of Biot number. The findings are evidenced to have dual solutions, which inevitably contribute to stability analysis, hence validating the feasibility of the first solution.

Radiative Heat and Mass Transfer Analysis of Micropolar Nanofluid Flow of Casson Fluid Between Two Rotating Parallel Plates With Effects of Hall Current

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Zahir Shah ◽  
Saeed Islam ◽  
Hamza Ayaz ◽  
Saima Khan
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Hall Current ◽  
Nonlinear Differential Equations ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Micropolar Nanofluid ◽  
The Impact

The present research aims to examine the micropolar nanofluid flow of Casson fluid between two parallel plates in a rotating system with effects of thermal radiation. The influence of Hall current on the micropolar nanofluids have been taken into account. The fundamental leading equations are transformed to a system of nonlinear differential equations using appropriate similarity variables. An optimal and numerical tactic is used to get the solution of the problem. The convergence and comparison have been shown numerically. The impact of the Hall current, Brownian movement, and thermophoresis phenomena of Casson nanofluid have been mostly concentrated in this investigation. It is found that amassed Hall impact decreases the operative conductivity which intends to increase the velocity field. The temperature field enhances with larger values of Brownian motion thermophoresis effect. The impacts of the Skin friction coefficient, heat flux, and mass flux have been deliberate. The skin friction coefficient is observed to be larger for k=0, as compared to the case of k=0.5. Furthermore, for conception and visual demonstration, the embedded parameters have been deliberated graphically.

scholarly journals Analysis of Chemical Reaction on MHD Micropolar Fluid Flow over a Shrinking Sheet near Stagnation Point with Nanoparticles and External Heat

2021 ◽  
Vol 39 (1) ◽  
pp. 262-268
Author(s):  
Krishnandan Verma ◽  
Debozani Borgohain ◽  
Bishwaram Sharma
Keyword(s):  
Stagnation Point ◽  
Chemical Reaction ◽  
Micropolar Fluid ◽  
Numerical Data ◽  
Mhd Flow ◽  
Heat Transfer Process ◽  
External Heat ◽  
Shrinking Sheet ◽  
Similarity Transformations ◽  
Micropolar Nanofluid

The present study investigates numerically MHD flow near the stagnation point of micropolar fluid through a shrinking sheet containing nanoparticles under the influence of chemical reaction and external heat. The study is an attempt to investigate the flow behaviour of micropolar nanofluid because of its importance in heat transfer process in industries as well as cooling systems. The governing equations are converted to nonlinear ordinary differential equations by implementing similarity transformations. Numerical results are investigated in the form of figures and tables by using MATLAB built in solver bvp4c for various dimensionless parameters. The impacts of external heat parameter on temperature and chemical reaction factor on concentration of the nanofluid are illustrated in the form of graphs. It is observed that the temperature of the nanofluid and nanoparticle volume distributions increase when Biot number attain larger values. Rise in Thermophoretic parameter increases the nanoparticles concentration in the boundary layer. Numerical data are presented for Nusselt number and Sherwood number.

scholarly journals Magnetohydrodynamic stagnation point on a Casson nanofluid flow over a radially stretching sheet

2020 ◽  
Vol 11 ◽  
pp. 1303-1315
Author(s):  
Ganji Narender ◽  
Kamatam Govardhan ◽  
Gobburu Sreedhar Sarma
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Radiation Effects ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Casson Nanofluid ◽  
Similarity Transformations ◽  
Program Language ◽  
The Impact

This article proposes a numerical model to investigate the impact of the radiation effects in the presence of heat generation/absorption and magnetic field on the magnetohydrodynamics (MHD) stagnation point flow over a radially stretching sheet using a Casson nanofluid. The nonlinear partial differential equations (PDEs) describing the proposed flow problem are reduced to a set of ordinary differential equations (ODEs) via suitable similarity transformations. The shooting technique and the Adams–Moulton method of fourth order are used to obtain the numerical results via the computational program language FORTRAN. Nanoparticles have unique thermal and electrical properties which can improve heat transfer in nanofluids. The effects of pertinent flow parameters on the nondimensional velocity, temperature and concentration profiles are presented. Overall, the results show that the heat transfer rate increases for higher values of the radiation parameter in a Casson nanofluid.

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