scholarly journals Magnetohydrodynamic Impact on Carreau Thin Film Couple Stress Nanofluid Flow over an Unsteady Stretching Sheet

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Taza Gul ◽  
Muhammad Rehman ◽  
Anwar Saeed ◽  
Imran Khan ◽  
Amir Khan ◽  
...  
Keyword(s):  
Thin Film ◽  
Brownian Motion ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Couple Stress ◽  
Fluid Velocity ◽  
Skin Friction Coefficient ◽  
Physical Factors ◽  
Fluid Temperature ◽  
Model Framework

A mathematical model of time-dependent thin-film flow of Carreau liquid over a stretching surface is studied in this investigation in the presence of couple stress and uniform magnetic field. To explain the properties of heat and mass transport phenomena, the influence of both thermophoresis and Brownian motion variables is used. For the conversion of the model framework (momentum, heat, and concentration expression with boundary conditions) into a set of ordinary differential equations, the appropriate transformation technique is followed. By using analytical tool, HomotopyAnalysis Method (HAM), the transformed model expressions are solved. For different estimations of the affected physical factors, the numerical results involving skin-friction coefficient, Nusselt number, Sherwood number, fluid velocity profile, thermal profile, and concentration profile are displayed graphically. Besides, the findings for skin-friction coefficient, Nu x , and ϕ η are given in the table format. In raising the fluid temperature, the effect of thermophoresis and magnetic parameters is beneficial. With the Brownian motion and Schmidt number, the solute concentration is found to reduce.

HEAT GENERATION AND ABSORPTION IN MHD FLOW OF CASSON FLUID PAST A STRETCHING WEDGE WITH VISCOUS DISSIPATION AND NEWTONIAN HEATING

2018 ◽  
Vol 80 (3) ◽  
Author(s):  
Imran Ullah ◽  
Sharidan Shafie ◽  
Ilyas Khan
Keyword(s):  
Heat Transfer ◽  
Skin Friction ◽  
Heat Transfer Rate ◽  
Heat Generation ◽  
Transfer Rate ◽  
Fluid Velocity ◽  
Mhd Flow ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Fluid Temperature

The dissipative flow of Casson fluid in the presence of heat generation and absorption is investigated. The flow is induced due to stretching wedge. The similarity transformations were used to to transformed the governing equations into ordinary differential equations. The transformed equations are solved numerically via Keller-box method. Numerical results for skin friction coefficient are compared and found in excellent agreement with published results. The effects of pertinent parameters on velocity and temperature profiles as well as skin friction and heat transfer rate are graphically displayed and analyzed. It is noticed that fluid velocity drops with the increase of Casson fluid and magnetic parameters when the wedge is stretching faster than free stream. It is also noted that the heat transfer rate at wedge surface reduces with the increase of Eckert number, whereas the reverse trend is noted in the case of Casson and radiation parameters. Moreover, with increasing of heat generation or absorption parameter the fluid temperature rises.

scholarly journals Unsteady Hydromagnetic Flow of Radiating Fluid Past a Convectively Heated Vertical Plate with the Navier Slip

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
O. D. Makinde ◽  
M. S. Tshehla
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Vertical Plate ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Skin Friction Coefficient ◽  
Newtonian Heating ◽  
Local Skin ◽  
Navier Slip

This paper investigates the unsteady hydromagnetic-free convection of an incompressible electrical conducting Boussinesq’s radiating fluid past a moving vertical plate in an optically thin environment with the Navier slip, viscous dissipation, and Ohmic and Newtonian heating. The nonlinear partial differential equations governing the transient problem are obtained and tackled numerically using a semidiscretization finite difference method coupled with Runge-Kutta Fehlberg integration technique. Numerical data for the local skin friction coefficient and the Nusselt number have been tabulated for various values of parametric conditions. Graphical results for the fluid velocity, temperature, skin friction, and the Nusselt number are presented and discussed. The results indicate that the skin friction coefficient decreases while the heat transfer rate at the plate surface increases as the slip parameter and Newtonian heating increase.

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 Mixed Convection Flow of Powell–Eyring Nanofluid near a Stagnation Point along a Vertical Stretching Sheet

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 364
Author(s):  
Nadhirah Abdul Halim ◽  
Noor Fadiya Mohd Noor
Keyword(s):  
Heat Transfer ◽  
Brownian Motion ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Mixed Convection ◽  
Skin Friction ◽  
Stagnation Point ◽  
Buoyancy Force ◽  
Skin Friction Coefficient ◽  
Transfer Rates

A stagnation-point flow of a Powell–Eyring nanofluid along a vertical stretching surface is examined. The buoyancy force effect due to mixed convection is taken into consideration along with the Brownian motion and thermophoresis effect. The flow is investigated under active and passive controls of nanoparticles at the surface. The associating partial differential equations are converted into a set of nonlinear, ordinary differential equations using similarity conversions. Then, the equations are reduced to first-order differential equations before further being solved using the shooting method and bvp4c function in MATLAB. All results are presented in graphical and tabular forms. The buoyancy parameter causes the skin friction coefficient to increase in opposing flows but to decrease in assisting flows. In the absence of buoyancy force, there is no difference in the magnitude of the skin friction coefficient between active and passive controls of the nanoparticles. Stagnation has a bigger influence under passive control in enhancing the heat transfer rate as compared to when the fluid is under active control. Assisting flows have better heat and mass transfer rates with a lower magnitude of skin friction coefficient as compared to opposing flows. In this case, the nanofluid parameters, the Brownian motion, and thermophoresis altogether reduce the overall heat transfer rates of the non-Newtonian nanofluid.

scholarly journals Stability Analysis on Magnetohydrodynamic Flow of Casson Fluid over a Shrinking Sheet with Homogeneous-Heterogeneous Reactions

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 652 ◽  
Author(s):  
Rusya Yahaya ◽  
Norihan Md Arifin ◽  
Siti Mohamed Isa
Keyword(s):  
Stability Analysis ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Fluid Velocity ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Heterogeneous Reactions ◽  
Shrinking Sheet ◽  
Local Skin

Two-dimensional magnetohydrodynamic (MHD) stagnation point flow of incompressible Casson fluid over a shrinking sheet is studied. In the present study, homogeneous-heterogeneous reactions, suction and slip effects are considered. Similarity variables are introduced to transform the governing partial differential equations into non-linear ordinary differential equations. The transformed equations and boundary conditions are then solved using the bvp4c solver in MATLAB. The local skin friction coefficient is tabulated for different values of suction and shrinking parameters. The profiles for fluid velocity and concentration for various parameters are illustrated. It was found that two solutions were obtained at certain ranges of parameters. Then, the bvp4c solver was used to perform stability analysis on the dual solutions. Based on the results, the first solution was more stable and physically meaningful than the other solution. The skin friction coefficient increased when suction increased, but decreased when the magnitude of shrinking parameter increased. Meanwhile, the velocity and concentration profile increased in the presence of a magnetic field. It is also noted that the higher the strength of the homogeneous-heterogeneous reactions, the lower the concentration of reactants.

MHD Blasius flow of radiative Williamson nanofluid over a vertical plate

2019 ◽  
Vol 33 (22) ◽  
pp. 1950245 ◽  
Author(s):  
Aamir Hamid ◽  
Hashim ◽  
Masood Khan ◽  
Metib Alghamdi
Keyword(s):  
Brownian Motion ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Vertical Plate ◽  
Flow Characteristics ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Buoyancy Parameter ◽  
Source Sink ◽  
The Mathematical Model

The flow characteristics of Williamson nanofluids flow caused by a permeable vertical plate are investigated in this research. Influence of magnetic field on mixed convection flow in the presence of thermal radiation and heat source/sink is further studied. To develop the mathematical model of Williamson nanofluids, we employ the Brownian motion and thermophoresis impacts. By using Sparrow–Quack–Boerner local nonsimilarity method, the governing equations are transformed into a set of ordinary differential equations. Additionally, the obtained equations are numerically tackled by employing an efficient Runge–Kutta–Fehlberg method with MATLAB. The effect of emerging parameters on dimensionless velocity, temperature and concentration as well as the skin friction coefficient, the local Nusselt number and a local Sherwood number are explored with the help of graphs. The results indicate that as the value of buoyancy parameter increases, the nanofluid temperature and concentration decrease, whereas the velocity distribution increases. Further, the skin friction coefficient is increased with the higher buoyancy parameter. On the other hand, the rate of heat transfer is decreased by Brownian motion parameter. A comparison with the previous data in the literature shows good agreement with the obtained results.

scholarly journals Study of ramped temperature influence on MHD convective chemically reactive and absorbing fluid past an exponentially accelerated vertical porous plate

2018 ◽  
Vol 15 (2) ◽  
pp. 107-125
Author(s):  
M C Raju ◽  
S Harinath Reddy ◽  
Dr. E. Keshava Reddy
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Vertical Plate ◽  
Fluid Velocity ◽  
Porous Plate ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Governing Equations ◽  
Laplace Transform Technique ◽  
The Impact

A systematic study has been performed on MHD convective chemically reactive and absorbing fluid along an exponentially accelerated vertical plate with the impact of Hall current by considering ramped temperature. Laplace transform technique is applied to obtain exact solutions of the non-dimensional governing equations for fluid velocity, temperature and concentration. Based on these solutions, the expressions for skin friction coefficient, Nusselt number and Sherwood number are also derived. The consequences of diverse physical parameters on flow quantities are examined thoroughly with graphical representations. The numerical values for skin friction coefficient, rate of heat transfer and rate of mass transfer are recorded and analyzed.

Impact of viscosity variation on oblique flow of Cu–H2O nanofluid

2017 ◽  
Vol 232 (5) ◽  
pp. 622-631 ◽  
Author(s):  
R Tabassum ◽  
Rashid Mehmood ◽  
O Pourmehran ◽  
NS Akbar ◽  
M Gorji-Bandpy
Keyword(s):  
Heat Flux ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Solid Volume Fraction ◽  
Local Heat ◽  
Skin Friction Coefficient ◽  
Viscosity Parameter ◽  
Local Heat Flux

The dynamic properties of nanofluids have made them an area of intense research during the past few decades. In this article, flow of nonaligned stagnation point nanofluid is investigated. Copper–water based nanofluid in the presence of temperature-dependent viscosity is taken into account. The governing nonlinear coupled ordinary differential equations transformed by partial differential equations are solved numerically by using fourth-order Runge–Kutta–Fehlberg integration technique. Effects of variable viscosity parameter on velocity and temperature profiles of pure fluid and copper–water nanofluid are analyzed, discussed, and presented graphically. Streamlines, skin friction coefficients, and local heat flux of nanofluid under the impact of variable viscosity parameter, stretching ratio, and solid volume fraction of nanoparticles are also displayed and discussed. It is observed that an increase in solid volume fraction of nanoparticles enhances the magnitude of normal skin friction coefficient, tangential skin friction coefficient, and local heat flux. Viscosity parameter is found to have decreasing effect on normal and tangential skin friction coefficients whereas it has a positive influence on local heat flux.

Low-Reynolds-Number Turbulent Boundary Layers in Zero and Favorable Pressure Gradients

1983 ◽  
Vol 27 (03) ◽  
pp. 147-157 ◽  
Author(s):  
A. J. Smits ◽  
N. Matheson ◽  
P. N. Joubert
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Low Reynolds

This paper reports the results of an extensive experimental investigation into the mean flow properties of turbulent boundary layers with momentum-thickness Reynolds numbers less than 3000. Zero pressure gradient and favorable pressure gradients were studied. The velocity profiles displayed a logarithmic region even at very low Reynolds numbers (as low as Rθ = 261). The results were independent of the leading-edge shape, and the pin-type turbulent stimulators performed well. It was found that the shape and Clauser parameters were a little higher than the correlation proposed by Coles [10], and the skin friction coefficient was a little lower. The skin friction coefficient behavior could be fitted well by a simple power-law relationship in both zero and favorable pressure gradients.

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