scholarly journals Boundary layer flow of magneto-micropolar nanofluid flow with Hall and ion-slip effects using variable thermal diffusivity

2017 ◽  
Vol 65 (3) ◽  
pp. 383-390 ◽  
Author(s):  
M. Bilal ◽  
S. Hussain ◽  
M. Sagheer
Keyword(s):  
Thermal Diffusivity ◽  
Differential Equations ◽  
Skin Friction Coefficient ◽  
Nanofluid Flow ◽  
Similarity Transformations ◽  
Slip Effects ◽  
Micropolar Nanofluid ◽  
Ion Slip ◽  
Layer Flow ◽  
Linear Differential

AbstractIn the present article, magneto-micropolar nanofluid flow with suction or injection in a porous medium over a stretching sheet for the heat and mass transfer is analyzed numerically. Both Hall and ion-slip effects are considered along with variable thermal diffusivity. The governing partial differential equations are transformed to ordinary differential equations using usual similarity transformations. These coupled non-linear differential equations are solved using the shooting method. Effects of prominent parameter on velocities, temperature and concentration are discussed graphically. Numerical values of skin-friction coefficient, local Nusselt number and local Sherwood number are also tabulated and discussed.

scholarly journals Numerical Study on Micropolar Nanofluid Flow over an Inclined Surface by Means of Keller-Box

2019 ◽  
pp. 1-21 ◽  
Author(s):  
Khuram Rafique ◽  
Muhammad Imran Anwar ◽  
Masnita Misiran
Keyword(s):  
Differential Equations ◽  
Numerical Study ◽  
Nonlinear Partial Differential Equations ◽  
Nanofluid Flow ◽  
Heat And Mass Exchange ◽  
Buongiorno’S Model ◽  
Similarity Transformations ◽  
Keller Box Method ◽  
Micropolar Nanofluid ◽  
Layer Flow

In this paper, micropolar nanofluid boundary layer flow over a linear inclined stretching surface with the magnetic effect is investigated. Buongiorno’s model utilized in this study for the thermal efficiencies of the fluid flow in the presence of Brownian motion and thermophoresis properties. The nonlinear problem for micropolar nanofluid flow over an inclined sheet is established to study the heat and mass exchange phenomenon by considering portent flow parameters to strengthen the boundary layers. The governing nonlinear partial differential equations are changed to nonlinear ordinary differential equations by using suitable similarity transformations and then solved numerically by applying the Keller-Box method. A comparison of the setup results in the absence of the incorporated impacts is performed with the accessible results and perceived in a decent settlement. Numerical and graphical outcomes are additionally presented in tables and diagrams.

Impact of Convective Boundary Condition on Heat and Mass Transfer of Nanofluid Flow Over a Thin Needle Filled with Carbon Nanotubes

2020 ◽  
Vol 9 (4) ◽  
pp. 282-292
Author(s):  
P. Sreedevi ◽  
P. Sudarsana Reddy
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Convective Boundary Condition ◽  
Skin Friction Coefficient ◽  
Nanofluid Flow ◽  
Finite Element Scheme ◽  
Convective Boundary ◽  
Non Linear ◽  
Layer Flow ◽  
Linear Differential

In the current study, we have scrutinized the sway of non-linear thermal radiation and Biot number on boundary layer flow along a continuously moving thin needle filled with carbon based nanotubes by considering water as regular fluid. The main system of partial differential equations is first reduced to the system of ordinary non-linear differential equations with the help of similarity conversion technique. The transmuted boundary layer ordinary differential equations are answered numerically by implementing Finite element scheme. The influence of pertinent constraints involved on heat, hydro-dynamic and solutal boundary layers are analysed in depth and the outcomes are revealed through plots. Moreover, the effect of these parameters on the values of Sherwood number, Nusselt number and skin-friction coefficient is also inspected and the results are exposed through tables. It is seen that velocity sketches depreciates with improving values of size of the needle parameter.

scholarly journals Inclusion of Viscous Dissipation on the Boundary Layer Flow of Cu-TiO2 Hybrid Nanofluid over Stretching/Shrinking Sheet

2021 ◽  
Vol 88 (2) ◽  
pp. 64-79
Author(s):  
Yap Bing Kho ◽  
Rahimah Jusoh ◽  
Mohd Zuki Salleh ◽  
Muhammad Khairul Anuar Mohamed ◽  
Zulkhibri Ismail ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Layer Flow

The effects of viscous dissipation on the boundary layer flow of hybrid nanofluids have been investigated. This study presents the mathematical modelling of steady two dimensional boundary layer flow of Cu-TiO2 hybrid nanofluid. In this research, the surface of the model is stretched and shrunk at the specific values of stretching/shrinking parameter. The governing partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the employment of the appropriate similarity transformations. Then, Matlab software is used to generate the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are acquired through the exact guessing values. It is observed that the second solution adhere to less stableness than first solution after performing the stability analysis test. The existence of viscous dissipation in this model is dramatically brought down the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter enhances the magnitude of the reduced skin friction coefficient while the augmentation of concentration of copper and titanium oxide nanoparticles show different modes.

scholarly journals Finite Element Simulation of Multi-Slip Effects on Unsteady MHD Bioconvective Micropolar Nanofluid Flow Over a Sheet with Solutal and Thermal Convective Boundary Conditions

Coatings ◽  
2019 ◽  
Vol 9 (12) ◽  
pp. 842 ◽  
Author(s):  
Liaqat Ali ◽  
Xiaomin Liu ◽  
Bagh Ali ◽  
Saima Mujeed ◽  
Sohaib Abdal
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fluid Velocity ◽  
Mesh Size ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Micropolar Nanofluid ◽  
Layer Flow ◽  
Buoyancy Ratio

In this article, the intention is to explore the flow of a magneto-hydrodynamic (MHD) bioconvective micro-polar Nanofluid restraining microorganism. The numerical solution of 2-D laminar bioconvective boundary layer flow of micro-polar nanofluids are presented. The phenomena of multi-slip, convective thermal and Solutal boundary conditions have been integrated. A system of non-linear partial differential equations are transformed into the system of coupled nonlinear ordinary differential equations by applying appropriate transformations, the transformed equations are then solved by applying the variational finite element method (FEM). The fascinating features of assorted velocity parameter, microrotation, temperature, microorganism compactness, solutal and nanoparticles concentration have been inspected. The rate of heat transfer, the skin friction coefficient, couple stress and Sherwood number for microorganisms have also been discussed graphically and numerically. The investigations illustrated that increase in material parameters causes a reduction in microorganism compactness, concentration and temperature. As a result of enhancement in the unsteadiness parameter, the fluid velocity, concentration of microorganisms and the temperature are observed to be declines. Energy and microorganism compactness profile affected by the improvement in the buoyancy ratio parameter. As the improvement in results of buoyancy ratio parameter effects on improvement in the energy and the microorganism compactness profile while the velocity profile is condensed. In the end, rationalized convergence of the finite element solution has been inspected; the computations are found out via depreciating the mesh size.

scholarly journals Analytical solution of MHD free convective flow of couple stress fluid in an annulus with Hall and ion-slip effects

2011 ◽  
Vol 16 (4) ◽  
pp. 477-487 ◽  
Author(s):  
Darbhashayanam Srinivasacharya ◽  
Kolla Kaladhar
Keyword(s):  
Differential Equations ◽  
Couple Stress ◽  
Circular Cylinders ◽  
Couple Stress Fluid ◽  
Electrically Conducting ◽  
Linear Partial Differential Equations ◽  
Similarity Transformations ◽  
Slip Effects ◽  
Homotopy Analysis ◽  
Ion Slip

This paper presents the Hall and Ion-slip effects on electrically conducting couple stress fluid flow between two circular cylinders in the presence of a temperature dependent heat source. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations and then solved using homotopy analysis method (HAM). The effects of the magnetic parameter, Hall parameter, Ion-slip parameter and couple stress fluid parameter on velocity and  temperature are discussed and shown graphically.

scholarly journals A Numerical Approach for an Unsteady Tangent Hyperbolic Nanofluid Flow past a Wedge in the Presence of Suction/Injection

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
U. Shahzad ◽  
M. Mushtaq ◽  
S. Farid ◽  
K. Jabeen ◽  
R.M.A. Muntazir
Keyword(s):  
Differential Equations ◽  
Graphical Representation ◽  
Numerical Technique ◽  
Darcy Number ◽  
Numerical Approach ◽  
Nanofluid Flow ◽  
Similarity Transformations ◽  
Flow Past ◽  
Layer Flow ◽  
The Impact

The analysis of unsteady tangent hyperbolic nanofluid flow past a wedge with injection-suction, because of its beneficial uses, has gained a lot of attention. The present study is mainly concerned with tangent hyperbolic nanofluid (non-Newtonian nanofluid). First, we have converted the system of partial differential equations (PDEs) to a system of ordinary differential equations (ODEs) with the help of appropriate similarity transformations. Boundary conditions are also transformed by utilizing suitable similarity transformation. Now, for the obtained ODEs, we have used the numerical technique bvp 4 c and investigated the velocity, temperature, and concentration profiles. The accuracy of the flow model is validated by applying MAPLE d-solve command having good agreement while comparing the numerical results obtained by bvp4c for both suction and injection cases. The effects of distinct dimensionless parameters on the various profiles are being analyzed. The novel features such as thermophoresis and Brownian motion are also discussed to investigate the characteristics of heat and mass transfer. Graphical representation of the impact of varying parameters and the solution method for the abovementioned model is thoroughly discussed. It was observed that suction or injection can play a key role in controlling boundary layer flow and brings stability in the flow. It was also noticed that by increasing the Darcy number, velocity profile increases in both injection-suction cases.

scholarly journals Unsteady Transport Phenomena of Hybrid Al2O3-Cu/H2O Nanofluid Past a Shrinking Slender Cylinder

2021 ◽  
Vol 50 (12) ◽  
pp. 3753-3764
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Theoretical Investigations ◽  
Suitable Form ◽  
Layer Flow

Theoretical investigations of unsteady boundary layer flow gain interest due to its relatability to practical settings. Thus, this study proposes a unique mathematical model of the unsteady flow and heat transfer in hybrid nanofluid past a permeable shrinking slender cylinder. The suitable form of similarity transformations is adapted to simplify the complex partial differential equations into a solvable form of ordinary differential equations. A built-in bvp4c function in MATLAB software is exercised to elucidate the numerical analysis for certain concerning parameters, including the unsteadiness and curvature parameters. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The present analysis further observed dual solutions that exist in the system of equations. Notable findings showed that by increasing the nanoparticles volume fraction, the skin friction coefficient increases in accordance with the heat transfer rate. In contrast, the decline of the unsteadiness parameter demonstrates a downward trend toward the heat transfer performance.

scholarly journals Brownian Motion and Thermophoretic Diffusion Effects on Micropolar Type Nanofluid Flow with Soret and Dufour Impacts over an Inclined Sheet: Keller-Box Simulations

Energies ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 4191 ◽  
Author(s):  
Khuram Rafique ◽  
Muhammad Imran Anwar ◽  
Masnita Misiran ◽  
Ilyas Khan ◽  
Asiful H. Seikh ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Soret Effect ◽  
Nanofluid Flow ◽  
Soret And Dufour Effects ◽  
Similarity Transformations ◽  
Stretching Factor ◽  
Micropolar Nanofluid ◽  
Nonlinear Stretching ◽  
Physical Quantities

The principal objective of the current study is to analyze the Brownian motion and thermophoretic impacts on micropolar nanofluid flow over a nonlinear inclined stretching sheet taking into account the Soret and Dufour effects. The compatible similarity transformations are applied to obtain the nonlinear ordinary differential equations from the partial differential equations. The numerical solution of the present study obtained via the Keller-Box technique. The physical quantities of interest are skin friction, Sherwood number, and heat exchange, along with several influences of material parameters on the momentum, temperature, and concentration are elucidated and clarified with diagrams. A decent settlement can be established in the current results with previously published work in the deficiency of incorporating effects. It is found that the growth of the inclination and nonlinear stretching factor decreases the velocity profile. Moreover, the growth of the Soret effect reduces the heat flux rate and wall shear stress.

scholarly journals Impact of hall and ion slip in a thermally stratified nanofluid flow comprising Cu and Al2O3 nanoparticles with nonuniform source/sink

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Nosheen Gul ◽  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Seifedine Kadry ◽  
Yu-Ming Chu
Keyword(s):  
Differential Equations ◽  
Skin Friction Coefficient ◽  
Solid Particles ◽  
Alumina Nanoparticles ◽  
Al2o3 Nanoparticles ◽  
Practical Applications ◽  
Slip Effects ◽  
Study Results ◽  
Ion Slip ◽  
Source Sink

Abstract Nanofluids play a pivotal role in the heat transport phenomenon and are essential in the cooling process of small gadgets like computer microchips and other related applications in microfluidics. Having such amazing applications of nanofluids, we intend to present a theoretical analysis of the thermally stratified 3D flow of nanofluid containing nano solid particles (Cu and Al2O3) over a nonlinear stretchable sheet with Ion and Hall slip effects. Moreover, the features of buoyance effect and non-uniform heat source/skin are also analyzed. For the study of numerically better results, Tawari and Das model is adopted here. For the conversion of the system of partial differential equations into ordinary differential equations, apposite transformations are engaged and are tackled by utilizing the bvp4c scheme of MATLAB software. The effects of dimensionless parameters on velocity and temperature profiles are depicted with the help of graphs. Additionally, the Skin friction coefficient and Nusselt number for the practical applications are examined in the tabular form. Verification of the current study by comparing it with an already published work in a special case is also a part of this study. Results show that the thermal performance of copper nanoparticles is more than alumina nanoparticles. An upsurge in the temperature of nanofluid is observed when the strength of the magnetic field is enhanced. However, the temperature of partially ionized nanofluid is significantly lowered because of the collisions of electrons and ions.

Two-Phase Flow of Fluid-Particle Interaction over a Stretching Sheet in the Presence of Magnetic Field

2019 ◽  
Vol 20 (6) ◽  
pp. 651-659
Author(s):  
J. Hasnain ◽  
Z. Abbas ◽  
M. Sajid
Keyword(s):  
Differential Equations ◽  
Stretching Sheet ◽  
Perturbation Technique ◽  
Particle Interaction ◽  
Skin Friction Coefficient ◽  
Second Grade ◽  
Two Phase ◽  
Similarity Transformations ◽  
Keller Box Method ◽  
Layer Flow

AbstractThis article presents a theoretical study of magnetohydrodynamic boundary layer flow of a dusty viscoelastic fluid over a porous stretching sheet. The basic steady equations of the viscoelastic second grade fluid and dust phases are in the form of partial differential equations. A set of coupled nonlinear ordinary differential equations is obtained by using suitable similarity transformations. The approximate first order solutions of the resulting equations are obtained using the perturbation technique. The results are also verified with the well-known finite difference technique known as Keller box method. The physical insight of the involved parameters on the velocity of both fluid and dust phases and the skin-friction coefficient is shown through graphs and tables and discussed in detail. The study shows that an increased effective viscosity increases the velocity of both fluid and particle phase.

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