Scrutinization of 2D and mixed convection flow of generalized Newtonian fluid with nanoparticles and magnetic field

2020 ◽  
Vol 98 (1) ◽  
pp. 65-75 ◽  
Author(s):  
Humara Sardar ◽  
Latif Ahmad ◽  
Masood Khan
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Skin Friction ◽  
Research Paper ◽  
Weissenberg Number ◽  
Convection Flow ◽  
Generalized Newtonian Fluid ◽  
Flux Boundary Condition ◽  
Buoyancy Parameter ◽  
Similar Solutions

In this research paper we focus on presenting the local non-similar solutions for two-dimensional steady and mixed convective flow of electrically conducting Carreau nanofluid under the influence of Brownian motion and thermophoresis effects. This research paper also presents the new mass flux boundary condition of nanoparticles. The governing partial differential equations are converted into ordinary differential equations by using the local non-similar transformations called the Sparrow–Quack–Boerner local non-similar method. A numerical approach is used to investigate the local non-similar solutions of the entire problem. Outcomes for the skin friction and rate of heat and mass transfer have been obtained and discussed for parametric variations of the buoyancy parameter ξ, magnetic parameter M, Weissenberg number We, viscosity ratio parameter β*, Brownian motion parameter Nb, thermophoresis parameter Nt, Prandtl number Pr, and Schmidt number Sc. From the obtained results a considerable increase in the skin friction coefficient is observed with an increase in buoyancy parameter ξ. Also, ξ shows relative growth for the momentum and concentration profiles.

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 HYDROMAGNETIC MIXED CONVECTION FLOW OF AN EXOTHERMIC FLUID IN A VERTICAL CHANNEL

2019 ◽  
Vol 1 (1) ◽  
pp. 19-37
Author(s):  
Abdulazeez Sheriff ◽  
Murtala Sani
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Mixed Convection ◽  
Ordinary Differential Equations ◽  
Skin Friction ◽  
Sherwood Number ◽  
Vertical Channel ◽  
Transformation Method ◽  
Convection Flow ◽  
Mixed Convection Flow

In this paper, Hydromagnetic mixed convection flow of an exothermic fluid in a vertical channel is considered. The dimensionless ordinary differential equations were solved using differential transformation method (DTM) to obtain the expression of velocity, temperature and concentration. From momentum, energy and mass equations.  The effect of Skin friction, Nusselt number and Sherwood number with various parameters on velocity, temperature and concentration are presented and discussed. The result indicated that the effect of t, is to increase the Skin friction while K increases it at upper plate and suppresses it at lower plate.

scholarly journals EFFECT OF CHEMICAL REACTION ON MIXED CONVECTION FLOW OF AN EXOTHERMIC FLUID IN A VERTICAL POROUS CHANNEL

2019 ◽  
Vol 1 (1) ◽  
pp. 38-58
Author(s):  
Murtala Sani ◽  
Abdulazeez Sheriff
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Mixed Convection ◽  
Skin Friction ◽  
Chemical Reaction ◽  
Sherwood Number ◽  
Transformation Method ◽  
Porous Channel ◽  
Convection Flow ◽  
Mixed Convection Flow

In this paper, effect of chemical reaction on mixed convection flow of an exothermic fluid in a vertical porous channel is considered. The dimensionless ordinary differential equations were solved using differential transformation method (DTM) to obtain the expression of velocity, temperature and concentration from momentum, energy and mass equations.  The effect of Skin friction, Nusselt number and Sherwood number with various parameters on velocity, temperature and concentration are presented and discussed. The result indicated that the velocity, temperature and concentration increases with the increase in suction/injection and mixed convection parameters.

scholarly journals Unsteady/Steady Natural Convection Flow of Reactive Viscous Fluid in a Vertical Annulus

2013 ◽  
Vol 18 (1) ◽  
pp. 73-83 ◽  
Author(s):  
B.K. Jha ◽  
A.K. Samaila ◽  
A.O. Ajibade
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Natural Convection ◽  
Differential Equations ◽  
Viscous Fluid ◽  
Skin Friction ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Vertical Annulus ◽  
Analytical Expressions

This paper presents both analytical and numerical analyses of a fully developed unsteady/steady natural convection flow of a reactive viscous fluid in an open ended vertical annulus. Analytical expressions for velocity, temperature, skin-friction and rate of heat transfer are obtained after simplifying and solving the governing differential equations with reasonable approximations. The interesting result found in this study is that an increase in non-dimensional time (t) , increases both temperature and velocity profiles until a steady-state value is attained. Subsequent results obtained by numerical calculations show excellent agreement with analytical results.

Magnetohydrodynamic, Thermal Radiation and Convective Boundary Effects of Free Convection Flow Past a Vertical Plate Embedded in a Porous Medium Saturated with a Nanofluid

2015 ◽  
Vol 31 (5) ◽  
pp. 607-616 ◽  
Author(s):  
H. Ali Agha ◽  
M. N. Bouaziz ◽  
S. Hanini
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Brownian Motion ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Heat And Mass Transfer ◽  
Vertical Plate ◽  
Volume Fraction ◽  
Convection Flow ◽  
Convective Boundary

AbstractA numerical analysis was performed to study the effects of combined magnetohydrodynamic and thermal radiation under convective boundary condition over a semi infinite vertical plate embedded in a non-Darcy porous medium. Coupled heat and mass transfer of free convective boundary layer with viscous nanofluid are considered. The model used for the nanofluid includes the effects of Brownian motion and thermophoresis mechanisms, while the Darcy-Forchheimer model is used for the porous medium. The governing partial differential equations are transformed into the ordinary differential equations using the similarity transformations. The accuracy of the method is observed by a comparison with other works reduced to a common case. Many results are tabulated and representative set is displayed graphically to illustrate the influence of the various parameters of interest on different profiles. Extensive numerical investigations show that the flow field, temperature, concentration and nanoparticle volume fraction shapes are significantly influenced by magnetic parameter, regular Lewis number, Brownian motion parameter, thermophoresis parameter, regular buoyancy ratio parameter and Biot number. Heat and mass transfer rates are significantly affected by the level of the applied magnetic field and the convective heat coefficient.

scholarly journals Consequence of Heat Transfer on Free Convection Flow of Casson Fluid with Hall Effect

2019 ◽  
Vol 8 (10S) ◽  
pp. 90-95
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Free Convection ◽  
Hall Effect ◽  
Skin Friction ◽  
Casson Fluid ◽  
Temperature Fields ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Fluid Parameter

Effect of heat transfer on free convection flow of Casson fluid over a vertical plate with Hall effect has been studied. A similarity analysis method was used to transform the system of partial differential equations describing the problem into an ordinary differential equations, Analytical solutions are obtained by solving the ODE to analyze the velocity and temperature fields. Variations of interesting parameters on the velocity, heat transfer and skin friction are observed by plotting graphs. Further, it was concluded that the Casson fluid parameter and hall parameter has an retarding influence on velocity profile and also in the skin friction.

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 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.

Global attracting sets of neutral stochastic functional integro-differential equations driven by a fractional Brownian motion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Bakka ◽  
S. Hajji ◽  
D. Kiouach
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Hurst Parameter ◽  
Fixed Point Principle ◽  
Stochastic Functional

Abstract By means of the Banach fixed point principle, we establish some sufficient conditions ensuring the existence of the global attracting sets of neutral stochastic functional integrodifferential equations with finite delay driven by a fractional Brownian motion (fBm) with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} in a Hilbert space.

Sign in / Sign up

Export Citation Format

Share Document