scholarly journals Finite Element Simulation of Multiple Slip Effects on MHD Unsteady Maxwell Nanofluid Flow over a Permeable Stretching Sheet with Radiation and Thermo-Diffusion in the Presence of Chemical Reaction

Processes ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 628 ◽  
Author(s):  
Bagh Ali ◽  
Yufeng Nie ◽  
Shahid Ali Khan ◽  
Muhammad Tariq Sadiq ◽  
Momina Tariq
Keyword(s):  
Finite Element ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Numerical Solution ◽  
Skin Friction ◽  
Stretching Sheet ◽  
Skin Friction Coefficient ◽  
Nanofluid Flow ◽  
Maxwell Nanofluid ◽  
Slip Effects

The aim of the present study is to investigate the multiple slip effects on magnetohydrodynamic unsteady Maxwell nanofluid flow over a permeable stretching sheet with thermal radiation and thermo-diffusion in the presence of chemical reaction. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations with the aid of appropriate similarity variables, and the transformed equations are then solved numerically by using a variational finite element method. The effects of various physical parameters on the velocity, temperature, solutal concentration, and nanoparticle concentration profiles as well as on the skin friction coefficient, rate of heat transfer, and Sherwood number for solutal concentration are discussed by the aid of graphs and tables. An exact solution of flow velocity, skin friction coefficient, and Nusselt number is compared with the numerical solution obtained by FEM and also with numerical results available in the literature. A good agreement between the exact and numerical solution is observed. Also, to justify the convergence of the finite element numerical solution, the calculations are carried out by reducing the mesh size. The present investigation is relevant to high-temperature nanomaterial processing technology.

scholarly journals Finite Element Analysis of Thermo-Diffusion and Multi-Slip Effects on MHD Unsteady Flow of Casson Nano-Fluid over a Shrinking/Stretching Sheet with Radiation and Heat Source

2019 ◽  
Vol 9 (23) ◽  
pp. 5217 ◽  
Author(s):  
Liaqat Ali ◽  
Xiaomin Liu ◽  
Bagh Ali ◽  
Saima Mujeed ◽  
Sohaib Abdal
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Medium ◽  
Heat Source ◽  
Numerical Solution ◽  
Skin Friction ◽  
Stretching Sheet ◽  
Physical Parameters ◽  
Nano Fluid ◽  
Slip Effects

In this article, we probe the multiple-slip effects on magnetohydrodynamic unsteady Casson nano-fluid flow over a penetrable stretching sheet, sheet entrenched in a porous medium with thermo-diffusion effect, and injection/suction in the presence of heat source. The flow is engendered due to the unsteady time-dependent stretching sheet retained inside the porous medium. The leading non-linear partial differential equations are transmuted in the system of coupled nonlinear ordinary differential equations by using appropriate transformations, then the transformed equations are solved by using the variational finite element method numerically. The velocity, temperature, solutal concentration, and nano-particles concentration, as well as the rate of heat transfer, the skin friction coefficient, and Sherwood number for solutal concentration, are presented for several physical parameters. Next, the effects of these various physical parameters are conferred with graphs and tables. The exact values of flow velocity, skin friction, and Nusselt number are compared with a numerical solution acquired with the finite element method (FEM), and also with numerical results accessible in literature. In the end, we rationalize the convergence of the finite element numerical solution, and the calculations are carried out by reducing the mesh size.

Flow and Heat Transfer in a Newtonian Nanoliquid due to a Curved Stretching Sheet

2017 ◽  
Vol 72 (9) ◽  
pp. 833-842 ◽  
Author(s):  
Pradeep Ganapathi Siddheshwar ◽  
Meenakshi Nerolu ◽  
Igor Pažanin
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Skin Friction Coefficient ◽  
Variable Coefficients

AbstractFlow of a Newtonian nanoliquid due to a curved stretching sheet and heat transfer in it is studied. The governing nonlinear partial differential equations are reduced to nonlinear ordinary differential equations with variable coefficients by using a similarity transformation. The flow characteristics are studied using plots of flow velocity components and the skin-friction coefficient as a function of suction-injection parameter, curvature, and volume fraction. Prescribed surface temperature and prescribed surface heat flux are considered for studying the temperature distribution in the flow. The thermophysical properties of 20 nanoliquids are considered in the investigation by modeling them through the use of phenomenological laws and mixture theory. The results of the corresponding problem involving a plane stretching sheet is obtained as a particular case of those obtained in the present paper. Skin friction coefficient and Nusselt number are evaluated and it is observed that skin friction coefficient decreases with concentration of nanoparticles in the absence as well as presence of suction where as Nusselt number increases with increase in concentration of nanoparticles in a dilute range.

scholarly journals A Simplified Finite Difference Method (SFDM) for EMHD Powell–Eyring Nanofluid Flow Featuring Variable Thickness Surface and Variable Fluid Characteristics

2020 ◽  
Vol 2020 ◽  
pp. 1-22
Author(s):  
M. Irfan ◽  
M. Asif Farooq ◽  
T. Iqra ◽  
A. Mushtaq ◽  
Z. H. Shamsi
Keyword(s):  
Friction Coefficient ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Skin Friction ◽  
Variable Thickness ◽  
Difference Method ◽  
Skin Friction Coefficient ◽  
Nanofluid Flow ◽  
Flow Variables

We study constant and variable fluid properties together to investigate their effect on MHD Powell–Eyring nanofluid flow with thermal radiation and heat generation over a variable thickness sheet. The similarity variables assist in having ordinary differential equations acquired from partial differential equations (PDEs). A novel numerical procedure, the simplified finite difference method (SFDM), is developed to calculate the physical solution. The SFDM described here is simple, efficient, and accurate. To highlight its accuracy, results of the SFDM are compared with the literature. The results obtained from the SFDM are compared with the published results from the literature. This gives a good agreed solution with each other. The velocity, temperature, and concentration distributions, when drawn at the same time for constant and variable physical features, are observed to be affected against incremental values of the flow variables. Furthermore, the impact of contributing flow variables on the skin friction coefficient (drag on the wall) and local Nusselt (heat transfer rate on the wall) and Sherwood numbers (mass transfer on the wall) is illustrated by data distributed in tables. The nondimensional skin friction coefficient experiences higher values for constant flow regimes especially in comparison with changing flow features.

scholarly journals Analyzing the impact of induced magnetic flux and Fourier’s and Fick’s theories on the Carreau-Yasuda nanofluid flow

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Seemab Bashir ◽  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Yu-Ming Chu ◽  
Seifedine Kadry
Keyword(s):  
Activation Energy ◽  
Nusselt Number ◽  
Brownian Motion ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Chemical Reaction ◽  
Skin Friction Coefficient ◽  
Nanofluid Flow ◽  
Stretching Ratio

AbstractThe current study analyzes the effects of modified Fourier and Fick's theories on the Carreau-Yasuda nanofluid flow over a stretched surface accompanying activation energy with binary chemical reaction. Mechanism of heat transfer is observed in the occurrence of heat source/sink and Newtonian heating. The induced magnetic field is incorporated to boost the electric conductivity of nanofluid. The formulation of the model consists of nonlinear coupled partial differential equations that are transmuted into coupled ordinary differential equations with high nonlinearity by applying boundary layer approximation. The numerical solution of this coupled system is carried out by implementing the MATLAB solver bvp4c package. Also, to verify the accuracy of the numerical scheme grid-free analysis for the Nusselt number is presented. The influence of different parameters, for example, reciprocal magnetic Prandtl number, stretching ratio parameter, Brownian motion, thermophoresis, and Schmidt number on the physical quantities like velocity, temperature distribution, and concentration distribution are addressed with graphs. The Skin friction coefficient and local Nusselt number for different parameters are estimated through Tables. The analysis shows that the concentration of nanoparticles increases on increasing the chemical reaction with activation energy and also Brownian motion efficiency and thermophoresis parameter increases the nanoparticle concentration. Opposite behavior of velocity profile and the Skin friction coefficient is observed for increasing the stretching ratio parameter. In order to validate the present results, a comparison with previously published results is presented. Also, Factors of thermal and solutal relaxation time effectively contribute to optimizing the process of stretchable surface chilling, which is important in many industrial applications.

scholarly journals MHD VISCOUS NANOFLUID FLOW WITH BASE FLUIDS’ WATER AND KEROSENE IN THE PRESENCE OF A TEMPERATURE GRADIENT DEPENDENT HEAT SINK WITH PRESCRIBED HEAT FLUX

2018 ◽  
Vol 48 (2) ◽  
pp. 139-144
Author(s):  
K. SARITHA ◽  
S. PALANIAMMAL
Keyword(s):  
Heat Flux ◽  
Friction Coefficient ◽  
Temperature Gradient ◽  
Differential Equations ◽  
Skin Friction ◽  
Heat Sink ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Flux Boundary Condition

MHD viscous nanofluid flow with viscous dissipation and thermal radiation in the presence of a temperature gradient dependent heat sink is analyzed. Hence, this work mainly deals nano fluids with nanoparticles Cu, Ag, Al, Al2O3 and TiO2 and with base fluids’ water and kerosene. Prescribed heat flux boundary condition is employed on the porous surface. Suitable similarity transformations are introduced for converting nonlinear partial differential equations into the nonlinear ordinary differential equations and then solved by analytically. The influence of various physical parameters over the velocity and temperature of nanofluids Cu-water and Cu-kerosene are examined by using graphs. Skin friction coefficient and Nusselt number of various nanofluids tabulated and analyzed. It is found that skin friction coefficient and heat transfer rate of kerosene based nanofluid is higher than the water based nanofluid in the presence of considered physical effects.

scholarly journals Second Law Analysis of Dissipative Nanofluid Flow over a Curved Surface in the Presence of Lorentz Force: Utilization of the Chebyshev–Gauss–Lobatto Spectral Method

Nanomaterials ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 195 ◽  
Author(s):  
Muhammad Afridi ◽  
Muhammad Qasim ◽  
Abderrahim Wakif ◽  
Abid Hussanan
Keyword(s):  
Silver Nanoparticles ◽  
Friction Coefficient ◽  
Entropy Production ◽  
Skin Friction ◽  
Spectral Method ◽  
Lorentz Force ◽  
Entropy Generation ◽  
Copper Nanoparticles ◽  
Skin Friction Coefficient ◽  
Nanofluid Flow

The primary objective of the present work is to study the effects of heat transfer and entropy production in a nanofluid flow over a curved surface. The influences of Lorentz force and magnetic heating caused by the applied uniform magnetic field and energy dissipation by virtue of frictional heating are considered in the problem formulation. The effects of variable thermal conductivity are also encountered in the present model. The dimensional governing equations are reduced to dimensionless form by introducing the similarity transformations. The dimensionless equations are solved numerically by using the Chebyshev–Gauss–Lobatto spectral method (CGLSM). The rate of increase/increase in the local Nusselt number and skin friction coefficient are estimated by using a linear regression model. The expression for dimensionless entropy production is computed by employing the solutions obtained from dimensionless momentum and energy equations. Various graphs are plotted in order to examine the effects of physical flow parameters on velocity, temperature, and entropy production. The increase in skin friction coefficient with magnetic parameter is high for nanofluid containing copper nanoparticles as compared to silver nanoparticles. The analysis reveals that velocity, temperature, and entropy generation decrease with the rising value of dimensionless radius of curvature. Comparative analysis also reveals that the entropy generation during the flow of nanofluid containing copper nanoparticles is greater than that of containing silver nanoparticles.

Entropy generation analysis in flow of thixotropic nanofluid

2019 ◽  
Vol 29 (12) ◽  
pp. 4507-4530 ◽  
Author(s):  
Muhammad Ijaz Khan ◽  
Salman Ahmad ◽  
Tasawar Hayat ◽  
M. Waleed Ahmad Khan ◽  
Ahmed Alsaedi
Keyword(s):  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Entropy Generation ◽  
Hartmann Number ◽  
Convective Boundary Condition ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Content Type ◽  
Flow Variables

Purpose The purpose of this paper is to address entropy generation in flow of thixotropic nonlinear radiative nanoliquid over a variable stretching surface with impacts of inclined magnetic field, Joule heating, viscous dissipation, heat source/sink and chemical reaction. Characteristics of nanofluid are described by Brownian motion and thermophoresis effect. At surface of the sheet zero mass flux and convective boundary condition are considered. Design/methodology/approach Considered flow problem is mathematically modeled and the governing system of partial differential equations is transformed into ordinary ones by using suitable transformation. The transformed ordinary differential equations system is figure out by homotopy algorithm. Outcomes of pertinent flow variables on entropy generation, skin friction, concentration, temperature, velocity, Bejan, Sherwood and Nusselts numbers are examined in graphs. Major outcomes are concluded in final section. Findings Velocity profile increased versus higher estimation of material and wall thickness parameter while it decays through larger Hartmann number. Furthermore, skin friction coefficient upsurges subject to higher values of Hartmann number and magnitude of skin friction coefficient decays via materials parameters. Thermal field is an increasing function of Hartmann number, radiation parameter, thermophoresis parameter and Eckert number. Originality/value The authors have discussed entropy generation in flow of thixotropic nanofluid over a variable thicked surface. No such consideration is yet published in the literature.

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.

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 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.

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