scholarly journals FERROFLUID FLOW IN MAGNETIC FIELD ABOVE STRETCHING SHEET WITH SUCTION AND INJECTION

2020 ◽  
Vol 25 (3) ◽  
pp. 461-472 ◽  
Author(s):  
Gabriella Bognár ◽  
Krisztián Hriczó
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Skin Friction ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Transfer Coefficients ◽  
Linear Ordinary Differential Equations ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
The Impact

The aim of this paper is to investigate the boundary layer of ferrofluid flow induced by a permeable stretching sheet. Fluid is electrically non-conducting in the presence of non-uniform magnetic field. The governing non-linear partial differential equations are reduced to non-linear ordinary differential equations by applying a similarity transformation. Numerical solutions are obtained by using Maple. The effects of the magnetic field, the Reynolds number and the porosity on the velocity and thermal fields are investigated. The impact of the parameters on the skin friction and the local Nusselt number is numerically examined. The skin friction and heat transfer coefficients are decreasing with enhancing the stretching, the values of porosity and the ferromagnetic parameter.

MHD STAGNATION POINT FLOW OF HYPERBOLIC TANGENT FLUID WITH VISCOUS DISSIPATION AND CHEMICAL REACTION

2021 ◽  
Vol 21 (2) ◽  
pp. 569-588
Author(s):  
KINZA ARSHAD ◽  
MUHAMMAD ASHRAF
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Normal Velocity ◽  
Hyperbolic Tangent ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In the present work, two dimensional flow of a hyperbolic tangent fluid with chemical reaction and viscous dissipation near a stagnation point is discussed numerically. The analysis is performed in the presence of magnetic field. The governing partial differential equations are converted into non-linear ordinary differential equations by using appropriate transformation. The resulting higher order non-linear ordinary differential equations are discretized by finite difference method and then solved by SOR (Successive over Relaxation parameter) method. The impact of the relevant parameters is scrutinized by plotting graphs and discussed in details. The main conclusion is that the large value of magnetic field parameter and wiessenberg numbers decrease the streamwise and normal velocity while increase the temperature distribution. Also higher value of the Eckert number Ec results in increases in temperature profile.

Radiative Unsteady Rarefied Gaseous Flow Over a Stretching Sheet with Velocity Slip and Temperature Jump Effects

2020 ◽  
Vol 87 (3-4) ◽  
pp. 261
Author(s):  
Ram Prakash Sharma ◽  
N. Indumathi ◽  
S. Saranya ◽  
B. Ganga ◽  
A. K. Abdul Hakeem
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Gaseous Flow ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study a mathematical analysis has been carried out to scrutinize the unsteady boundary layer flow of an incompressible, rarefied gaseous flow over a vertical stretching sheet with velocity slip and thermal jump boundary conditions in the presence of thermal radiation. Using boundary layer approach and suitable similarity transformations, the governing partial differential equations with the boundary conditions are reduced to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved with the help of fourth order Runge-Kutta method with shooting technique. The results obtained for the velocity profile, temperature profile, skin friction coefficient and the reduced Nusselt number are described through graphs. It is predicted that the velocity and temperature profiles are lower for unsteady flow and has an opposite effect for steady flow.

Heat and Mass Transfer of a MHD Flows of An Oldroyd 8-Constant Nano-Fluid Through a Non-Darcy Porous Medium

2017 ◽  
Vol 14 (1) ◽  
pp. 321-329
Author(s):  
Abeer A Shaaban
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Prandtl Number ◽  
Heat And Mass Transfer ◽  
Induced Magnetic Field ◽  
Linear Ordinary Differential Equations ◽  
Nano Fluid ◽  
Non Linear

Explicit finite-difference method was used to obtain the solution of the system of the non-linear ordinary differential equations which transform from the non-linear partial differential equations. These equations describe the steady magneto-hydrodynamic flow of an oldroyd 8-constant non-Newtonian nano-fluid through a non-Darcy porous medium with heat and mass transfer. The induced magnetic field was taken into our consideration. The numerical formula of the velocity, the induced magnetic field, the temperature, the concentration, and the nanoparticle concentration distributions of the problem were illustrated graphically. The effect of the material parameters (α1 α2), Darcy number Da, Forchheimer number Fs, Magnetic Pressure number RH, Magnetic Prandtl number Pm, Prandtl number Pr, Radiation parameter Rn, Dufour number Nd, Brownian motion parameter Nb, Thermophoresis parameter Nt, Heat generation Q, Lewis number Le, and Sort number Ld on those formula were discussed specially in the case of pure Coutte flow (U0 = 1, d <inline-formula> <mml:math display="block"> <mml:mrow> <mml:mover accent="true"> <mml:mi>P</mml:mi> <mml:mo stretchy="true">^</mml:mo> </mml:mover> </mml:mrow> </mml:math> </inline-formula> /dx = 0). Also, an estimation of the global error for the numerical values of the solutions is calculated by using Zadunaisky technique.

scholarly journals Dual solutions for heat and mass transfer in chemically reacting radiative non-Newtonian fluid with aligned magnetic field

2017 ◽  
Vol 14 (1) ◽  
pp. 25-38 ◽  
Author(s):  
J. V. Ramana Reddy ◽  
V. Sugunamma ◽  
N. Sandeep
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Graphical Representation ◽  
Physical Parameters ◽  
Transfer Coefficients ◽  
Chemically Reacting ◽  
Aligned Magnetic Field

Through this paper we investigated the heat and mass transfer in chemically reacting radiative Casson fluid flow over a slandering/flat stretching sheet in a slip flow regime with aligned magnetic field. This study is carried out under the influence of non uniform heat source/sink. First we converted the governing equations of the flow into ordinary differential equations by making use of suitable similarity transformations. The obtained non-linear differential equations are solved numerically using Runge-Kutta based shooting technique. Further, graphical representation has been given to study the effects of various physical parameters on velocity, temperature and concentration fields. Also numerical computations has been carried out to investigate the influence of the physical parameters involved in the flow on skin friction, rate of heat and mass transfer coefficients. Through this investigation, it is observed that aligned angle, Casson parameter and velocity slip parameter have the tendency to control the velocity field. Also heat transfer rate in flat stretching sheet is higher than that of slendering stretching sheet. A good agreement of the present results with the existed literature has been observed. 

An Oscillatory Radiating Hydromagnetic Internal Heat Generating Fluid Flow Through a Vertcal Porous Channel with Slip and Temperature Jump

2018 ◽  
Vol 23 (2) ◽  
pp. 503-519 ◽  
Author(s):  
E.O. Titiloye ◽  
J.A. Gbadeyan ◽  
A.T. Adeosun
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Temperature Jump ◽  
Slip Flow ◽  
Internal Heat ◽  
Porous Channel ◽  
Linear Ordinary Differential Equations ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
Flow Through

Abstract The present study concerns the natural convective heat generating/absorbing, radiative magnetohydrodynamic, oscillatory fluid flow through a vertical porous channel with slip and temperature jump. The effect of Joule dissipation is taken into consideration while it is assumed that the flow is fully developed. The differential transforms method(DTM) is employed to solve the system of non-linear ordinary differential equations that is obtained from the non-linear partial differential equations governing the flow. Semi analytical solutions of the steady and unsteady part of the flow in the slip flow regime through a vertical porous channel are obtained. The effects of various flow parameters on the velocity and temperature profiles as well as Nusselt and skin friction are presented graphically and discussed. An excellent agreement between the results of this article and those available in the literature validated the presented approach.

A comparative study of Al2O3 and TiO2 nanofluid flow over a wedge with non-linear thermal radiation

2019 ◽  
Vol 30 (3) ◽  
pp. 1291-1317 ◽  
Author(s):  
Paluru Sreedevi ◽  
P. Sudarsana Reddy ◽  
Mikhail Sheremet
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Field Parameter ◽  
Convection Flow ◽  
Geothermal Systems ◽  
Content Type ◽  
Magnetic Field Parameter ◽  
Non Linear ◽  
The Impact

Purpose The purpose of this study is to analyze the impact of chemical reaction and thermal radiation on mixed convection flow, heat and mass transfer characteristics of nanofluid through a wedge occupied with water–TiO2 and water–Al2O3 made nanofluid by considering velocity, temperature and concentration slip conditions in present investigation. Design/methodology/approach Using acceptable similarity transformations, the prevailing partial differential equations have been altered into non-linear ordinary differential equations and are demonstrated by the diverse thermophysical parameters. The mathematical model is solved numerically by implementing Galarkin finite element method and the outcomes are shown in tables and graphs. Findings The temperature and concentration fields impede as magnetic field parameter improves in both water–Al2O3 and water–TiO2 nanofluid. While there is contradiction in the velocity field as the values of magnetic field parameter rises in both nanofluids. The non-dimensional velocity rate, rate of temperature and rate of concentration rise with improved values of Weissenberg number. Originality/value Nanofluid flows past wedge-shaped geometries have gained much consideration because of their extensive range of applications in engineering and science, such as, magnetohydrodynamics, crude oil extraction, heat exchangers, aerodynamics and geothermal systems. Virtually, these types of nanofluid flows happen in ground water pollution, aerodynamics, retrieval of oil, packed bed reactors and geothermal industries.

scholarly journals Numerical Study of Thermal-Diffusion and Diffusion-Thermo Effects on Mixed Convective Flow and Mass Transfer in the Presence of MHD over an Accelerating Surface

2020 ◽  
Vol 11 (4) ◽  
pp. 11487``-11498
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Thermal Diffusion ◽  
Variable Viscosity ◽  
Numerical Study ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Mixed Convective Flow ◽  
The Impact ◽  
And Diffusion

This study investigates the impact of MHD, variable viscosity, thermal-diffusion, and diffusion-thermo effects with the heat source on mixed convection of heat and mass transfer over an accelerating surface. The physical problem's governing equations involve a coupled non-linear partial differential equations, which are transformed to a coupled non-linear ordinary differential equations using a suitable similarity transformation. Numerical computation using shooting technique is adopted to study the physical characteristics of velocity, temperature, and concentration for various values of non-dimensional parameters like thermal diffusion parameter, diffusion-thermo parameter, viscosity parameter, Prandtl number, and strength of the magnetic field are involved in the problem. The obtained numerical results are found to be a good agreement with the earlier works.

scholarly journals MHD 3-dimensional nanofluid flow induced by a power-law stretching sheet with thermal radiation, heat and mass fluxes

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Sudipta Ghosh ◽  
Swati Mukhopadhyay ◽  
Kuppalapalle Vajravelu
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Two Phase ◽  
Mass Fluxes ◽  
First Case ◽  
Special Cases ◽  
Non Linear ◽  
Mass Transfers

AbstractIn this article, the three-dimensional Magnetohydrodynamics flow of a nanofluid over a horizontal non-linearly stretching sheet in bilateral directions under boundary layer approximation is addressed. A two-phase model has been used for the nanofluid. The influences of thermophoresis, Brownian motion and thermal radiation on heat and mass transfers are considered. Two different cases for the heat and mass transfers are studied. In the first case, uniform wall temperature and zero nanoparticles flux due to thermophoresis are considered. In the second case, prescribed heat and mass fluxes at the boundary are considered. By using the appropriate transformations, a system of non-linear partial differential equations along with the boundary conditions is transformed into coupled non-linear ordinary differential equations. Numerical solutions of the self-similar equations are obtained using a Runge–Kutta method with a shooting technique. Our results for special cases are compared with the available results in the literature, and the results are found to be in good agreement. It is observed that the pertaining parameters have significant effects on the characteristics of flow, heat and mass transfer. The results are presented and discussed in detail through illustrations.

scholarly journals Analysis of Ethylene Glycol (EG)-based ((Cu-Al2O3), (Cu-TiO2), (TiO2-Al2O3)) Hybrid Nanofluids for Optimal Car Radiator Coolant

2020 ◽  
pp. 34-50
Author(s):  
J. A. Okello ◽  
W. N. Mutuku ◽  
A. O. Oyem
Keyword(s):  
Differential Equations ◽  
Ethylene Glycol ◽  
Waste Heat ◽  
Cooling System ◽  
Integration Scheme ◽  
Shooting Technique ◽  
Linear Ordinary Differential Equations ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
Hybrid Nanofluids

Coolants are vital in any automotive since they manage the heat in the internal combustion of the engines by preventing corrosion in the cooling system as well as assist in eradicating the engine’s waste heat. This paper examines three different types of ethylene glycol-based hybrid nanofluids ((Cu-Al2O3), (Cu-TiO2), (TiO2-Al2O3)) to establish their cooling capabilities for industrial cooling applications. The vertical flow of these hybrid nanofluids combination through a semi-infinite convectively heated flat plate mimicking the flow of coolant in car radiator is modeled. The governing non-linear partial differential equations of fluid flow are transformed into a system of coupled non-linear ordinary differential equations using a suitable similarity transformation variables and the numerical solution executed using the shooting technique together with the fourth-order Runge-Kutta-Fehlberg integration scheme. The numerical simulation is executed using MATLAB and results are displayed graphically. The effects of pertinent parameters on velocity, temperature, skin friction, and local Nusselt number are investigated. From the study (Cu-Al2O3  hybrid nanocoolant leads to a rapid decrease in temperature at the boundary layer.

scholarly journals An Unsteady Flow and Melting Heat Transfer of a Nanofluid Over a Stretching Sheet Embedded in a Porous Medium

2019 ◽  
Vol 24 (2) ◽  
pp. 245-258 ◽  
Author(s):  
K. Ganesh Kumar ◽  
B.J. Gireesha ◽  
N.G. Rudraswamy ◽  
M.R. Krishnamurthy
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Unsteady Flow ◽  
Stretching Sheet ◽  
Physical Parameters ◽  
Local Skin ◽  
Melting Heat ◽  
Linear Ordinary Differential Equations ◽  
Melting Heat Transfer ◽  
Non Linear

Abstract An unsteady flow and melting heat transfer of a nanofluid over a stretching sheet was numerically studied by considering the effect of chemical reaction and thermal radiation. The governing non-linear partial differential equations describing the flow problem are reduced to a system of non-linear ordinary differential equations using the similarity transformations and solved numerically using the Runge–Kutta–Fehlberg fourth–fifth order method. Numerical results for concentration, temperature and velocity profiles are shown graphically and discussed for different physical parameters. Effect of pertinent parameters on momentum, temperature and concentration profiles along with local Sherwood number, local skin-friction coefficient and local Nusselt number are well tabulated and discussed.

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