An Analytic Solution for Electrical Magneto-Hydrodynamics Darcy–Forchheimer Three Dimensional Non-Newtonian Nanofluid Flow with Convective Boundary Conditions

2020 ◽  
Vol 9 (4) ◽  
pp. 257-268
Author(s):  
Gossaye Aliy Adem
Keyword(s):  
Brownian Motion ◽  
Velocity Profile ◽  
Electric Field ◽  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Velocity Slip ◽  
Slip Parameter ◽  
Convective Boundary ◽  
Strongly Nonlinear ◽  
Biot Numbers

In this article, the treatment of three-dimensional non-Newtonian Williamson fluid has been carried out under examination. Using the standard transformation, the governing equations are converted into universal similarity equations which have been solved by the optimal homotopy asymptotic method. We observed that the method is effective, reliable, consistent and efficient in solving strongly nonlinear differential equations. The influence of embedded parameters on the fluid flow has discovered graphically and using table. The velocity profile in the x-direction is increased with magnetic and electric field parameters and decreased with the increased stretching parameter, coefficient of inertia, velocity slip parameter L1 and porosity parameters. The velocity profile in the y-direction is increased with magnetic and electric field parameters, the distended stretching parameter, while reduced with the velocity slip parameter L2, coefficient of inertia, and porosity parameters. The temperature profile is increased with the radiation, thermophoresis and Brownian motion parameters, and Biot number. The profile of concentration is rising with the enlarged Biot numbers and thermophoresis parameter, while reduced with the Brownian motion parameter.

Spectral Simulation to Investigate the Effects of Active Passive Controls of Nanoparticles on the Radiative Nanofluidic Transport Over a Spinning Disk

2020 ◽  
Vol 13 (3) ◽  
Author(s):  
Nilankush Acharya
Keyword(s):  
Brownian Motion ◽  
Mass Transport ◽  
Three Dimensional ◽  
Velocity Slip ◽  
Rotating Disk ◽  
Thermal Slip ◽  
Slip Parameter ◽  
Spectral Simulation ◽  
Discussion Section ◽  
Passive Flow

Abstract The present investigation deals with the flow dynamics and heat transport of the nanofluid flow over a rotating disk. The flow is considered to be laminar and steady. Active–passive controls of tiny nanoparticles influenced by the Brownian motion and thermophoretic migration are included to reveal the variations in the hydrothermal behaviour. Thermal radiation, velocity slip, and thermal slip are also introduced to model the flow. The foremost governing equations are converted into its dimensionless form after applying the requisite similarity transformation. The spectral quasi-linearization method (SQLM) has been employed to extract the numeric outcomes of the flow. Effects of the underlying parameters on the flow and heat-mass transport are revealed through graphs and tables. Several three-dimensional (3D) and streamlines plots are depicted to enrich the Result and Discussion section. Results assured that the velocities in every direction reduce for velocity slip parameter and magnetic parameter. Temperature increases for thermophoresis and Brownian motion, but reduces for velocity and thermal slip parameter. Active flow reveals high temperature than passive flow. The Brownian motion and thermophoresis provide dual scenario for concentration profile. Heat and mass transport always sustain high magnitude for passive flow.

Computational Study of Three-Dimensional Stagnation Point Nanofluid Bioconvection Flow on a Moving Surface With Anisotropic Slip and Thermal Jump Effect

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
M. J. Uddin ◽  
W. A. Khan ◽  
A. I. Md. Ismail ◽  
O. Anwar Bég
Keyword(s):  
Nusselt Number ◽  
Skin Friction ◽  
Stagnation Point ◽  
Local Nusselt Number ◽  
Local Density ◽  
Three Dimensional ◽  
Velocity Slip ◽  
Slip Parameter ◽  
Moving Surface ◽  
Local Skin

The effects of anisotropic slip and thermal jump on the three-dimensional stagnation point flow of nanofluid containing microorganisms from a moving surface have been investigated numerically. Anisotropic slip takes place on geometrically striated surfaces and superhydrophobic strips. Zero mass flux of nanoparticles at the surface is applied to achieve practically applicable results. Using appropriate similarity transformations, the transport equations are reduced to a system of nonlinear ordinary differential equations with coupled boundary conditions. Numerical solutions are reported by means of very efficient numerical method provided by the symbolic code Maple. The influences of the emerging parameters on the dimensionless velocity, temperature, nanoparticle volumetric fraction, density of motile microorganism profiles, as well as the local skin friction coefficient, the local Nusselt number, and the local density of the motile microorganisms are displayed graphically and illustrated in detail. The computations demonstrate that the skin friction along the x-axis is enhanced with the velocity slip parameter along the y-axis. The converse response is observed for the dimensionless skin friction along the y-axis. The heat transfer rate is increased with greater velocity slip effects but depressed with the thermal slip parameter. The local Nusselt number is increased with Prandtl number and decreased with the thermophoresis parameter. The local density for motile microorganisms is enhanced with velocity slip parameters and depressed with the bioconvection Lewis number, thermophoresis, and Péclet number. Numerical results are validated where possible with published results and excellent correlation is achieved.

scholarly journals MHD Partial Slip Flow and Heat Transfer of Nanofluids through a Porous Medium Over a Stretching Sheet with Convective Boundary Condition

2020 ◽  
Vol 12 (1) ◽  
pp. 39-59
Author(s):  
Yohannes Yirga
Keyword(s):  
Heat Transfer ◽  
Volume Fraction ◽  
Slip Flow ◽  
Velocity Slip ◽  
Partial Slip ◽  
Slip Parameter ◽  
Convective Boundary ◽  
Porosity Parameter ◽  
Flow And Heat Transfer ◽  
Convective Parameter

This paper investigates the boundary layer analysis for magnetohydrodynamic partial slip flow and heat transfer of nanofluids through porous media over a stretching sheet with convective boundary condition. Four types of nanoparticles, namely copper, alumina, copper oxide and titanium oxide in the ethylene glycol (50%, i.e., Pr = 29.86) and water (i.e., Pr = 6.58) based fluids are studied. The governing highly nonlinear and coupled partial differential equations are solved numerically using fourth order Runge-Kutta method with shooting techniques. The velocity and temperature profiles are obtained and utilized to compute the skin friction coefficient and local Nusselt number for different values of the governing parameters viz. nanoparticle volume fraction parameter, magnetic field parameter, porosity parameter, velocity slip parameter and convective parameter. It is found that the velocity distribution of the nanofluids is a decreasing function of the magnetic parameter, porosity parameter, and velocity slip parameter. However, temperature of the nanofluids is an increasing function of magnetic field parameter, nanoparticle volume fraction parameter, porosity parameter, velocity slip parameter and convective parameter. The flow and heat transfer characteristics of the four nanofluids are compared. Moreover, comparison of the numerical results is made with previously published works for special cases and an excellent agreement is found.  Keywords: Magnetohydrodynamics, Partial Slip, Porous medium, Convective boundary, Nanofluid.

Activation energy impact on radiated magneto-Sisko nanofluid flow over a stretching and slipping cylinder: entropy analysis

2020 ◽  
Vol 16 (5) ◽  
pp. 1085-1115
Author(s):  
S. Sarkar ◽  
R.N. Jana ◽  
S. Das
Keyword(s):  
Activation Energy ◽  
Mass Transfer ◽  
Brownian Motion ◽  
Boundary Conditions ◽  
Entropy Generation ◽  
Velocity Slip ◽  
Stretching Cylinder ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Content Type

PurposeThe purpose of this article is to analyze the heat and mass transfer with entropy generation during magnetohydrodynamics (MHD) flow of non-Newtonian Sisko nanofluid over a linearly stretching cylinder under the influence of velocity slip, chemical reaction and thermal radiation. The Brownian motion, thermophoresis and activation energy are assimilated in this nanofluid model. Convective boundary conditions on heat and mass transfer are considered. The physical model may have diverse applications in several areas of technology underlying thermohydrodynamics including supercritical fluid extraction, refrigeration, ink-jet printing and so on.Design/methodology/approachThe dimensional governing equations are nondimensionalized by using appropriate similarity variables. The resulting boundary value problem is converted into initial value problem using the method of superposition and numerically computed by employing well-known fourth-order Runge–Kutta–Fehlberg approach along with shooting technique (RKF4SM). The quantitative impacts of emerging physical parameters on the velocity, temperature, concentration, skin friction coefficient, Nusselt number, Sherwood number, entropy generation rate and Bejan number are presented graphically and in tabular form, and the salient features are comprehensively discussed.FindingsFrom graphical outcomes, it is concluded that the slip parameters greatly influence the flow characteristics. Fluid temperature is elevated with rising radiation parameter and thermal Biot number. Nanoparticle concentration is reported in decreasing form with activation energy parameter. Entropy is found to be an increasing function of magnetic field, Brownian motion and material parameters. The entropy is less generated for shear-thinning fluid compared to shear-thickening as well as Newtonian fluids in the system.Originality/valueTill now no study has been documented to explore the impact of binary chemical reaction with Arrhenius activation energy on entropy generation in an MHD boundary layer flow of non-Newtonian Sisko nanofluid over a linear stretching cylinder with velocity slip and convective boundary conditions.

scholarly journals An optimal analysis for Darcy–Forchheimer three-dimensional Williamson nanofluid flow over a stretching surface with convective conditions

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983351 ◽  
Author(s):  
Abdullah Dawar ◽  
Zahir Shah ◽  
Saeed Islam ◽  
Waris Khan ◽  
Muhammad Idrees
Keyword(s):  
Heat Transfer ◽  
Brownian Motion ◽  
Fluid Flow ◽  
Velocity Profile ◽  
Flow Behavior ◽  
Three Dimensional ◽  
And Brownian Motion ◽  
Homotopy Analysis ◽  
Motion Parameters ◽  
The Impact

The augmented thermal conductivity is significant in betterment of heat transfer behavior of fluids. A number of other physical quantities such as density, viscosity, and specific heat play the key role in fluid flow behavior. Investigators have shown that the nanofluids have not only superior heat conductivity but also have better convective heat transfer capability than the base fluids. In this article, the analysis of three-dimensional Williamson fluid has been carried out under investigation. The fluid flow is taken over a linear porous stretching sheet under the influence of thermal radiation. The transformed system of equations has been solved by homotopy analysis method. The impact of embedded parameters on the fluid flow has shown graphically. The velocity profile in x-direction is decreased with the augmented stretching, Williamson, coefficient of inertia, and porosity parameters. The velocity profile in y-direction is increased with the enlarged stretching parameter, while reduced with the augmented Williamson, coefficient of inertia, and porosity parameters. The temperature profile is increased with the enlarged stretching, radiation, thermophoresis, parameter and Brownian motion parameters, and Biot number while decreased with the increased Prandtl number. The concentration profile is increased with the increased thermophoresis parameter and Biot numbers, while decreased with the enlarged stretching and Brownian motion parameters.

scholarly journals Influence of Magnetohydrodynamic and Thermal Radiation Boundary Layer Flow of a Nanofluid Past a Stretching Sheet

2014 ◽  
Vol 6 (2) ◽  
pp. 257-272 ◽  
Author(s):  
M. G. Reddy
Keyword(s):  
Boundary Layer ◽  
Brownian Motion ◽  
Thermal Radiation ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Velocity Slip ◽  
Heat Radiation ◽  
Convective Boundary ◽  
Non Linear ◽  
Layer Flow

The problem of laminar fluid flow which results from a permeable stretching of a flat surface in a nanofluid with the effects of heat radiation, magnetic field, velocity slip and convective boundary conditions have been investigated. The transport equations used in the analysis took into account the effect of Brownian motion and thermophoresis parameters. The solution for the velocity, temperature and nanoparticle concentration depends on parameters viz. thermal radiation parameter R, magnetic parameter M, Prandtl number Pr, Lewis number Le, Brownian motion parameter Nb, thermophoresis parameter Nt, velocity slip parameter A convection and Biot numbe Bi. Similarity transformation is used to convert the governing non-linear boundary-layer equations into coupled higher order non-linear ordinary differential equations. These equations are numerically solved using fourth order Runge-Kutta method along with shooting technique. An analysis has been carried out to elucidate the effects of governing parameters corresponding to various physical conditions. Numerical results are obtained for distributions of velocity, temperature and concentration, as well as, for the skin friction, local Nusselt number and local Sherwood number for several values of governing parameters. Keywords: Nanofluid, Boundary layer flow; Stretching sheet; Thermal radiation; MHD; Velocity slip; Convective boundary. © 2014 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v6i2.17233 J. Sci. Res. 6 (2), 257-272 (2014)  

scholarly journals Stability Analysis of the Magnetized Casson Nanofluid Propagating through an Exponentially Shrinking/Stretching Plate: Dual Solutions

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1162 ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan ◽  
El-Sayed M. Sherif ◽  
Hany S. Abdo
Keyword(s):  
Brownian Motion ◽  
Stability Analysis ◽  
Mhd Flow ◽  
Dual Solutions ◽  
Convective Boundary ◽  
Suction Parameter ◽  
Casson Nanofluid ◽  
Stretching Surfaces ◽  
Stretching Plate ◽  
Biot Numbers

In this research, we intend to develop a dynamical system for the magnetohydrodynamic (MHD) flow of an electrically conducting Casson nanofluid on exponentially shrinking and stretching surfaces, in the presence of a velocity and concertation slip effect, with convective boundary conditions. There are three main objectives of this article, specifically, to discuss the heat characteristics of flow, to find multiple solutions on both surfaces, and to do stability analyses. The main equations of flow are governed by the Brownian motion, the Prandtl number, and the thermophoresis parameters, the Schmid and Biot numbers. The shooting method and three-stage Lobatto IIIa formula have been employed to solve the equations. The ranges of the dual solutions are f w c 1 ≤ f w and λ c ≤ λ , while the no solution ranges are f w c 1 > f w and λ c > λ . The results reveal that the temperature of the fluid increases with the extended values of the thermophoresis parameter, the Brownian motion parameter, and the Hartmann and Biot numbers, for both solutions. The presence of dual solutions depends on the suction parameter. In order to indicate that the first solution is physically relevant and stable, a stability analysis has been performed.

Thermo-Solutal Chemically Reacting Micropolar Fluid Past a Permeable Stretching Porous Sheet

2019 ◽  
Vol 392 ◽  
pp. 42-59 ◽  
Author(s):  
M.D. Shamshuddin ◽  
Thirupathi Thumma ◽  
S.R. Mishra
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Electric Field ◽  
Micropolar Fluid ◽  
Thermal Boundary Layer ◽  
Transverse Magnetic ◽  
Slip Parameter ◽  
Convective Boundary ◽  
Nonlinear Odes ◽  
Chemically Reacting

The boundary layer flow, heat and mass transfer over a permeable stretching sheet due to a chemically reacting micropolar fluid with slip and convective boundary conditions have been analyzed. Transverse magnetic field clubbed with electric field is also considered for the sake of brevity. Governing nonlinear coupled PDEs are transformed to nonlinear ODEs with the use of suitable similarity transformation. However, analytical solutions to these transformed equations are not useful therefore; numerical solution is carried out using Runge-Kutta fourth order with shooting technique. The characteristics of the embedded parameters are obtained and presented through graphs. Validation of the proposed work with earlier established results are shown in tables and these are in good agreement. From the careful observation the major outcomes are: induced magnetic field decelerates the flow, enhances the thickness of thermal boundary layer temperature whereas applied electric field decelerates the thickness of thermal boundary layer. Both electric field and slip parameter accelerates the angular momentum. Temperature and concentration magnitudes are accelerated at the sheet with an increase of slip parameter. Furthermore, Schmidt number and first order chemical reaction reduces the concentration boundary layer thickness. PACS Number: 05.45-a; 05.70-Ce.

scholarly journals Dual solutions for three-dimensional magnetohydrodynamic nanofluid flow with entropy generation

2019 ◽  
Vol 6 (4) ◽  
pp. 657-665 ◽  
Author(s):  
Hiranmoy Mondal ◽  
Mohammed Almakki ◽  
Precious Sibanda
Keyword(s):  
Brownian Motion ◽  
Entropy Generation ◽  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Linearization Method ◽  
Dissipation Function ◽  
Dual Solutions ◽  
Shrinking Sheet ◽  
Temperature Profiles ◽  
Residual Errors

Abstract This paper presents a formulation for simulating magnetohydrodynamic three-dimensional convective flow and heat transfer in a nanofluid by incorporating the complete viscous dissipation function in the energy equation. A novel feature of this investigation of entropy generation and dual solutions is the use of the spectral quasilinearization method to solve the conservation equations. The results are compared with exact solutions or higher order solutions and a good agreement is achieved. The accuracy is determined by calculation of residual errors and the method of solution is shown to produce smaller residual errors than those achieved by the fifth-order Runge-Kutta Fehlberg method for nonlinear differential equations. The dual solutions for different Prandtl number, and Brownian motion and thermophoresis parameters are shown graphically and discussed. It is found that the temperature profiles as well as thermal boundary layer thickness increase with the Brownian motion parameter for first and the second solutions. The temperature profiles increase with the thermophoresis parameter for the first and second solutions. The entropy generation increases with the Reynolds number. Highlights Combined effects of entropy generation and MHD nanofluid are proposed. Spectral quasi-linearization method (SQLM) is used for computer simulations. Use axisymmetric stretching/shrinking sheet for dual solution. Validate the accuracy and convergence using residual error analysis.

Sign in / Sign up

Export Citation Format

Share Document