Influence of rotating magnetic field on Maxwell saturated ferrofluid flow over a heated stretching sheet with heat generation/absorption

2019 ◽  
Vol 20 (5) ◽  
pp. 502 ◽  
Author(s):  
Aaqib Majeed ◽  
Ahmed Zeeshan ◽  
Farzan Majeed Noori ◽  
Usman Masud
Keyword(s):  
Magnetic Field ◽  
Temperature Field ◽  
Velocity Field ◽  
Differential Equations ◽  
Heat Transport ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Fluid Motion ◽  
Numerical Procedure ◽  
The Impact

This article is focused on Maxwell ferromagnetic fluid and heat transport characteristics under the impact of magnetic field generated due to dipole field. The viscous dissipation and heat generation/absorption are also taken into account. Flow here is instigated by linearly stretchable surface, which is assumed to be permeable. Also description of magneto-thermo-mechanical (ferrohydrodynamic) interaction elaborates the fluid motion as compared to hydrodynamic case. Problem is modeled using continuity, momentum and heat transport equation. To implement the numerical procedure, firstly we transform the partial differential equations (PDEs) into ordinary differential equations (ODEs) by applying similarity approach, secondly resulting boundary value problem (BVP) is transformed into an initial value problem (IVP). Then resulting set of non-linear differentials equations is solved computationally with the aid of Runge–Kutta scheme with shooting algorithm using MATLAB. The flow situation is carried out by considering the influence of pertinent parameters namely ferro-hydrodynamic interaction parameter, Maxwell parameter, suction/injection and viscous dissipation on flow velocity field, temperature field, friction factor and heat transfer rate are deliberated via graphs. The present numerical values are associated with those available previously in the open literature for Newtonian fluid case (γ 1 = 0) to check the validity of the solution. It is inferred that interaction of magneto-thermo-mechanical is to slow down the fluid motion. We also witnessed that by considering the Maxwell and ferrohydrodynamic parameter there is decrement in velocity field whereas opposite behavior is noted for temperature field.

scholarly journals Impact of Activation Energy in Darcy-Forchheimer Flow of Cross Nanofluid over a Radial Stretching Surface with Viscous Dissipation and Joule Heating

2021 ◽  
Vol 39 (5) ◽  
pp. 1557-1566
Author(s):  
Cherlacola Srinivas Reddy ◽  
Besthapu Prabhakar
Keyword(s):  
Activation Energy ◽  
Temperature Field ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Graphical Representation ◽  
Energy Parameter ◽  
System Of Nonlinear Equations ◽  
The Impact ◽  
Forchheimer Flow

This framework analyzes the impact of activation energy (AE) and binary chemical reaction (BCR) in Darcy-Forchheimer flow of cross fluid with nanoparticles due to radially stretched surface. Moreover slip, joule heating and viscous dissipation aspects have been considered. Ordinary differential equations acquired from the modelled governing partial differential equations with the assistance of suitable transformations. Further the system of nonlinear equations is computed numerically by Runge-Kutta-Fehlberg method cum shooting technique. Graphical representation has been given to analyze the velocity, temperature and concentration fields with the effect of various pertinent parameters. It is evident that inertia coefficient declines the velocity. Velocity decays for larger Weissenberg number while opposite trend observed in temperature field. Temperature field rises for augmented values of Eckert number. Concentration increases with increase of energy parameter.

Forced convection in 3D Maxwell nanofluid flow via Cattaneo–Christov theory with Joule heating

2021 ◽  
pp. 095440892199963
Author(s):  
Awais Ahmed ◽  
Masood Khan ◽  
Mahnoor Sarfraz ◽  
Jawad Ahmed ◽  
Zahoor Iqbal
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Joule Heating ◽  
Energy Transport ◽  
Fluid Motion ◽  
Analytical Technique ◽  
Maxwell Nanofluid ◽  
Homotopy Analysis ◽  
Non Linear System ◽  
The Impact

In this article, an investigation of the thermal and solutal energy transport in the 3 D flow of Maxwell nanofluid through a porous medium under the influence of the magnetic field is performed. The heat generation source and chemical reaction are also taken in account as a controlling agent for the heat and mass transport in the Maxwell liquid. A novel idea of Cattaneo-Christov theory and Buongiorno model for nanofluid is employed under the impact of Joule heating for the present analysis. The governing partial differential equations (PDEs) are transformed into a non-linear system of ordinary differential equations (ODEs) by using flow similarities. The solution of similar ODEs is constructed through a well known semi-analytical technique which is the homotopy analysis method. The results of the investigation are explored in the form of graphs. It is observed that higher values of magnetic field decline the flow field. The temperature and concentration distributions decrease with the higher magnitude of thermal and solutal relaxation time phenomena, respectively. Moreover, the temperature field enhances when the Brownian motion of nanoparticles increases in flow while the concentration profile decreases. Also, it is found that the increase in resistive heating boosts up the thermal energy transport in the fluid motion.

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.

scholarly journals Heat Induction by Viscous Dissipation Subjected to Symmetric and Asymmetric Boundary Conditions on a Small Oscillating Flow in a Microchannel

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 499 ◽  
Author(s):  
Chih Tso ◽  
Chee Hor ◽  
Gooi Chen ◽  
Chee Kok
Keyword(s):  
Temperature Field ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Lower Plate ◽  
Brinkman Number ◽  
Energy Equations ◽  
Oscillation Rate

The heat induced by viscous dissipation in a microchannel fluid, due to a small oscillating motion of the lower plate, is investigated for the first time. The methodology is by applying the momentum and energy equations and solving them for three cases of standard thermal boundary conditions. The first two cases involve symmetric boundary conditions of constant surface temperature on both plates and both plates insulated, respectively. The third case has the asymmetric conditions that the lower plate is insulated while the upper plate is maintained at constant temperature. Results reveal that, although the fluid velocity is only depending on the oscillation rate of the plate, the temperature field for all three cases show that the induced heating is dependent on the oscillation rate of the plate, but strongly dependent on the parameters Brinkman number and Prandtl number. All three cases prove that the increasing oscillation rate or Brinkman number and decreasing Prandtl number, when it is less than unity, will significantly increase the temperature field. The present model is applied to the synovial fluid motion in artificial hip implant and results in heat induced by viscous dissipation for the second case shows remarkably close agreement with the experimental literature.

scholarly journals Numerical Investigation for Radiative Transport in Magnetized Flow of Nanofluids due to Moving Surface

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Hassan Waqas ◽  
Shan Ali Khan ◽  
Metib Alghamdi ◽  
Taseer Muhammad
Keyword(s):  
Magnetic Field ◽  
Temperature Field ◽  
Heat Generation ◽  
Biomedical Engineering ◽  
Schmidt Number ◽  
Stretching Sheet ◽  
Concentration Field ◽  
Flow Properties ◽  
Similarity Transformations ◽  
Water Based

In this article, we examined the magnetized flow of ethylene glycol- 50 − 50 % water-based nanoliquids comprising molybdenum disulfide ( MoS 2 ) across a stretching sheet. Flow properties were examined under the impacts of magnetic field and thermal radiation. The behavior of heat generation/absorption is also accounted. Similarity transformations are used on the system of PDEs to get nondimensional ODEs. The obtained nondimensional ODEs are solved with the help of the Runge–Kutta–Fehlberg method via computational software MATHEMATICA. The behavior of prominent parameters for velocity and thermal profiles is plotted graphically and discussed in detail. It is depicted that the temperature field is upgraded with increase in the heat generation/absorption parameter. Furthermore, a larger Schmidt number causes reduction in the concentration field. The current formulated model may be useful in biomedical engineering, biotechnology, nanotechnology, biosensors, crystal growth, plastic industries, and mineral and cleaning oil manufacturing.

scholarly journals Nonlinear translational symmetric equilibria relevant to the L–H transition

2012 ◽  
Vol 79 (3) ◽  
pp. 257-265 ◽  
Author(s):  
Ap. KUIROUKIDIS ◽  
G. N. THROUMOULOPOULOS
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Plasma Flow ◽  
Sufficient Condition ◽  
Sheared Flow ◽  
Equilibrium Configurations ◽  
Shafranov Equation ◽  
The Impact ◽  
The Magnetic Field

AbstractNonlinear z-independent solutions to a generalized Grad–Shafranov equation (GSE) with up to quartic flux terms in the free functions and incompressible plasma flow non-parallel to the magnetic field are constructed quasi-analytically. Through an ansatz, the GSE is transformed to a set of three ordinary differential equations and a constraint for three functions of the coordinate x, in Cartesian coordinates (x,y), which then are solved numerically. Equilibrium configurations for certain values of the integration constants are displayed. Examination of their characteristics in connection with the impact of nonlinearity and sheared flow indicates that these equilibria are consistent with the L–H transition phenomenology. For flows parallel to the magnetic field, one equilibrium corresponding to the H state is potentially stable in the sense that a sufficient condition for linear stability is satisfied in an appreciable part of the plasma while another solution corresponding to the L state does not satisfy the condition. The results indicate that the sheared flow in conjunction with the equilibrium nonlinearity plays a stabilizing role.

scholarly journals Effect of magnetic field, heat generation and absorption on nanofluid flow over a nonlinear stretching sheet

2020 ◽  
Vol 11 ◽  
pp. 976-990
Author(s):  
Santoshi Misra ◽  
Govardhan Kamatam
Keyword(s):  
Magnetic Field ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Partial Slip ◽  
Nanoparticle Suspension ◽  
Dimensionless Parameters ◽  
Similarity Transformations ◽  
Highly Nonlinear ◽  
Layer Flow ◽  
The Impact

The study of magnetohydrodynamic flow of a nanoparticle suspension under the influence of varied dimensionless parameters has been the focus of research in contemporary times. This work models the effect of magnetic field, heat generation and absorption parameter in a steady, laminar, two-dimensional boundary layer flow of a nanofluid over a permeable stretching sheet at a given surface temperature and partial slip. The highly nonlinear governing equations are solved numerically using similarity transformations with suitable boundary conditions and converted to ordinary differential equations. A computational model is setup using FORTRAN, where a relevant Adam’s predictor–corrector method is employed to solve the equations. The impact of the dimensionless parameters, including the Brownian motion, thermophoresis, magnetic field, heat generation and absorption parameters, on the velocity, temperature and nanoparticle concentration of fluid flow are analysed systematically.

scholarly journals MHD Slip Flow of Casson Fluid along a Nonlinear Permeable Stretching Cylinder Saturated in a Porous Medium with Chemical Reaction, Viscous Dissipation, and Heat Generation/Absorption

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 531 ◽  
Author(s):  
Ullah ◽  
Abdullah Alkanhal ◽  
Shafie ◽  
Nisar ◽  
Khan ◽  
...  
Keyword(s):  
Porous Medium ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Heat Generation ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Casson Fluid ◽  
Similarity Solutions ◽  
Local Similarity ◽  
The Impact

The aim of the present analysis is to provide local similarity solutions of Casson fluid over a non-isothermal cylinder subject to suction/blowing. The cylinder is placed inside a porous medium and stretched in a nonlinear way. Further, the impact of chemical reaction, viscous dissipation, and heat generation/absorption on flow fields is also investigated. Similarity transformations are employed to convert the nonlinear governing equations to nonlinear ordinary differential equations, and then solved via the Keller box method. Findings demonstrate that the magnitude of the friction factor and mass transfer rate are suppressed with increment in Casson parameter, whereas heat transfer rate is found to be intensified. Increase in the curvature parameter enhanced the flow field distributions. The magnitude of wall shear stress is noticed to be higher with an increase in porosity and suction/blowing parameters.

scholarly journals Impact of Nonlinear Thermal Radiation and the Viscous Dissipation Effect on the Unsteady Three-Dimensional Rotating Flow of Single-Wall Carbon Nanotubes with Aqueous Suspensions

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 207 ◽  
Author(s):  
Muhammad Jawad ◽  
Zahir Shah ◽  
Saeed Islam ◽  
Jihen Majdoubi ◽  
I. Tlili ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Carbon Nanotubes ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Temperature Profile ◽  
Viscous Dissipation ◽  
Single Wall Carbon Nanotubes ◽  
Nonlinear Thermal Radiation ◽  
Aqueous Suspensions ◽  
The Impact

The aim of this article is to study time dependent rotating single-wall electrically conducting carbon nanotubes with aqueous suspensions under the influence of nonlinear thermal radiation in a permeable medium. The impact of viscous dissipation is taken into account. The basic governing equations, which are in the form of partial differential equations (PDEs), are transformed to a set of ordinary differential equations (ODEs) suitable for transformations. The homotopy analysis method (HAM) is applied for the solution. The effect of numerous parameters on the temperature and velocity fields is explanation by graphs. Furthermore, the action of significant parameters on the mass transportation and the rates of fiction factor are determined and discussed by plots in detail. The boundary layer thickness was reduced by a greater rotation rate parameter in our established simulations. Moreover, velocity and temperature profiles decreased with increases of the unsteadiness parameter. The action of radiation phenomena acts as a source of energy to the fluid system. For a greater rotation parameter value, the thickness of the thermal boundary layer decreases. The unsteadiness parameter rises with velocity and the temperature profile decreases. Higher value of augments the strength of frictional force within a liquid motion. For greater and ; the heat transfer rate rises. Temperature profile reduces by rising values of .

MHD mixed convection stagnation-point flow of a viscoelastic fluid towards a stretching sheet in a porous medium with heat generation and radiation

2015 ◽  
Vol 93 (5) ◽  
pp. 532-541 ◽  
Author(s):  
M. Modather M. Abdou ◽  
E. Roshdy EL-Zahar ◽  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Viscoelastic Fluid ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Heat Transfer Characteristics

An analysis was carried out to study the effect of thermal radiation on magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid near the stagnation point of a vertical stretching sheet in a porous medium with internal heat generation–absorption. The flow is generated because of linear stretching of the sheet and influenced by the uniform magnetic field that is applied horizontally in the flow region. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically using an accurate implicit finite difference scheme. A comparison of the obtained results with previously published numerical results is done and the results are found to be in good agreement. The effects of the viscoelastic fluid parameter, magnetic field parameter, nonuniform heat source–sink, and the thermal radiation parameter on the heat transfer characteristics are presented graphically and discussed. The values of the skin friction coefficient and the local Nusselt number are tabulated for both cases of assisting and opposing flows.

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