scholarly journals Effect of magnetic field and heat source on Upper-convected-maxwell fluid in a porous channel

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 917-928 ◽  
Author(s):  
Zeeshan Khan ◽  
Haroon Ur Rasheed ◽  
Tawfeeq Abdullah Alkanhal ◽  
Murad Ullah ◽  
Ilyas Khan ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Maxwell Fluid ◽  
Deborah Number ◽  
Physical Parameters ◽  
Fluid Temperature

Abstract The effect of magnetic field on the flow of the UCMF (Upper-Convected-Maxwell Fluid) with the property of a heat source/sink immersed in a porous medium is explored. A shrinking phenomenon along with the permeability of the wall are considered. The governing equations for the motion and transfer of heat of the UC MF along with boundary conditions are converted into a set of coupled nonlinear mathematical equations. Appropriate similarity transformations are used to convert the set of nonlinear partial differential equations into nonlinear ordinary differential equations. The modeled ordinary differential equations have been solved by the Homotopy Analysis Method (HAM). The convergence of the series solution is established. For the sake of comparison, numerical (ND-Solve method) solutions are also obtained. Special attention is given to how the non-dimensional physical parameters of interest affect the flow of the UCMF. It is observed that with the increasing Deborah number the velocity decreases and the temperature inside the fluid increases. The results show that the velocity and temperature distribution increases with a porous medium. It is also observed that the magnetic parameter has a decelerating effect on velocity while the temperature profiles increases in the entire domain. Due to the increase in Prandtl number the temperature profile increases. It is also observed that the heat source enhance the thermal conductivity and increases the fluid temperature while the heat sink provides a decrease in the fluid temperature.

scholarly journals Flow over Exponentially Stretching Sheet through Porous Medium with Heat Source/Sink

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
I. Swain ◽  
S. R. Mishra ◽  
H. B. Pattanayak
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Heat Source ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Mass Transfer Effect ◽  
Exponentially Stretching Sheet ◽  
Exponentially Stretching ◽  
Source Sink

An attempt has been made to study the heat and mass transfer effect in a boundary layer MHD flow of an electrically conducting viscous fluid subject to transverse magnetic field on an exponentially stretching sheet through porous medium. The effect of thermal radiation and heat source/sink has also been discussed in this paper. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and then solved numerically using a fourth-order Runge-Kutta method with a shooting technique. Graphical results are displayed for nondimensional velocity, temperature, and concentration profiles while numerical values of the skin friction local Nusselt number and Sherwood number are presented in tabular form for various values of parameters controlling the flow system.

Magnetohydrodynamic Mixed Convective Flow Due to a Vertical Plate With Induced Magnetic Field

2018 ◽  
Vol 10 (6) ◽  
Author(s):  
R. Nandkeolyar ◽  
M. Narayana ◽  
S. S. Motsa ◽  
P. Sibanda
Keyword(s):  
Magnetic Field ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Linearization Method ◽  
Fluid Temperature ◽  
Magnetic Field Effects ◽  
Induced Magnetic Field ◽  
Partial Differential

The steady hydromagnetic flow of a viscous, incompressible, perfectly conducting, and heat absorbing fluid past a vertical flat plate under the influence of an aligned magnetic field is studied. The flow is subject to mixed convective heat transfer. The fluid is assumed to have a reasonably high magnetic Prandtl number which causes significant-induced magnetic field effects. Such fluid flows find application in many magnetohydrodynamic devices including MHD power-generation. The effects of viscous dissipation and heat absorption by the fluid are investigated. The governing nonlinear partial differential equations are converted into a set of nonsimilar partial differential equations which are then solved using a spectral quasi-linearization method (SQLM). The effects of the important parameters on the fluid velocity, induced magnetic field, fluid temperature and as well as on the coefficient of skin-friction and the Nusselt number are discussed qualitatively.

Ohmic and viscous dissipation effects on micropolar non-Newtonian nanofluid Al2O3 flow through a non-Darcy porous media

2022 ◽  
pp. 1-13
Author(s):  
Nabil T. Eldabe ◽  
Mohamed Y. Abou zeid ◽  
Sami M. El Shabouri ◽  
Tarek N. Salama ◽  
Aya M. Ismael
Keyword(s):  
Magnetic Field ◽  
Heat Source ◽  
Numerical Solutions ◽  
Tangential Velocity ◽  
Darcy Number ◽  
Physical Parameters ◽  
Fluid Temperature ◽  
High Concentration ◽  
Ohmic Dissipation ◽  
Similarity Transformations

Inclined uniform magnetic field and mixed convention effects on micropolar non-Newtonian nanofluid Al2O3 flow with heat transfer are studied. The heat source, both viscous and ohmic dissipation and temperature micropolarity properties are considered. We transformed our system of non-linear partial differential equations into ordinary equations by using suitable similarity transformations. These equations are solved by making use of Rung–Kutta–Merson method in a shooting and matching technique. The numerical solutions of the tangential velocity, microtation velocity, temperature and nanoparticle concentration are obtained as functions of the physical parameters of the problem. Moreover, we discussed the effects of these parameters on the numerical solutions and depicted graphically. It is obvious that these parameters control the fluid flow. It is noticed that the tangential velocity magnifies with an increase in the value of Darcy number. Meanwhile, the value of the tangential velocity reduces with the elevation in the value of the magnetic field parameter. On the other hand, the elevation in the value of Brownian motion parameter leads to a reduction in the value of fluid temperature. Furthermore, increasing in the value of heat source parameter makes an enhancement in the value of nanoparticles concentration. The current study has many accomplishments in several scientific areas like medical industry, medicine, and others. Therefore, it represents the depiction of gas or liquid motion over a surface. When particles are moving from areas of high concentration to areas of low concentration.

Entropy Generation on Maxwell Fluid Flow Past an Inclined Stretching Plate with Slip and Convective Surface Conditon: Darcy-Forchheimer Model

2019 ◽  
Vol 26 ◽  
pp. 62-83
Author(s):  
Tunde Abdulkadir Yusuf ◽  
Jacob Abiodun Gbadeyan
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Entropy Generation ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Entropy Generation Rate ◽  
Physical Parameters ◽  
Convective Boundary ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study the effect of entropy generation on two dimensional magnetohydrodynamic (MHD) flow of a Maxwell fluid over an inclined stretching sheet embedded in a non-Darcian porous medium with velocity slip and convective boundary condition is investigated. Darcy-Forchheimer based model was employed to describe the flow in the porous medium. The non-linear thermal radiation is also taken into account. Similarity transformation is used to convert the non-linear partial differential equations to a system of non-linear ordinary differential equations. The resulting transformed equations are then solved using the Homotopy analysis method (HAM). Influence of various physical parameters on the dimensionless velocity profile, temperature profile and entropy generation are shown graphically and discussed in detail while the effects of these physical parameters on velocity gradient and temperature gradient are aided with the help of Table. Furthermore, comparison of some limiting cases of this model was made with existing results. The results obtained are found to be in good agreement with previously published results. Moreover, increase in local inertial coefficient parameter is found to decrease the entropy generation rate.

Radiative Flow of Jeffrey Fluid Through a Convectively Heated Stretching Cylinder

2014 ◽  
Vol 31 (1) ◽  
pp. 69-78 ◽  
Author(s):  
T. Hayat ◽  
S. Asad ◽  
A. Alsaedi ◽  
F. E. Alsaadi
Keyword(s):  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Convective Boundary Condition ◽  
Deborah Number ◽  
Temperature Fields ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Stretching Cylinder ◽  
Series Solutions ◽  
Convective Boundary

AbstractTwo-dimensional flow of Jeffrey fluid by an inclined stretching cylinder with convective boundary condition is studied. In addition the combined effects of thermal radiation and viscous dissipation are taken into consideration. The developed nonlinear partial differential equations are reduced into the ordinary differential equations by suitable transformations. The governing equations are solved for the series solutions. The convergence of the series solutions for velocity and temperature fields is carefully analyzed. The effects of various physical parameters such as ratio of relaxation to retardation times, Deborah number, radiation parameter, Biot number, curvature parameter, local Grashof number, Prandtl number, Eckert number and angle of inclination are examined through graphical and numerical results of the velocity and temperature distributions.

MHD Reacting and Radiating 3-D Flow of Maxwell Fluid Past a Stretching Sheet with Heat Source/Sink and Soret Effects in a Porous Medium

2018 ◽  
Vol 387 ◽  
pp. 145-156 ◽  
Author(s):  
Sure Geethan Kumar ◽  
S. Vijaya Kumar Varma ◽  
Putta Durga Prasad ◽  
Chakravarthula S.K. Raju ◽  
Oluwole Daniel Makinde ◽  
...  
Keyword(s):  
Porous Medium ◽  
Heat Source ◽  
Stretching Sheet ◽  
Soret Effect ◽  
Linear Equations ◽  
Maxwell Fluid ◽  
Deborah Number ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Source Sink

In this study, we numerically investigate the hydromagnetic three dimensional flow of a radiating Maxwell fluid over a stretching sheet embedded in a porous medium with heat source/sink, first ordered chemical reaction and Soret effect. The corresponding boundary layer equations are reduced into set of non-linear ordinary differential equations by means of similarity transformations. The resulting coupled non-linear equations are solved numerically by employing boundary value problem default solver in MATLAB bvp4c package. The obtained results are presented and discussed through graphs and tables. It is noticed that the Deborah number reduces the velocity fields and improves the temperature and concentration fields. Nomenclature

scholarly journals Diffusion-thermo and thermal-diffusion effects with inclined magnetic field on unsteady MHD slip flow over a permeable vertical plate

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
T. L. Oyekunle ◽  
S. A. Agunbiade
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Thermal Diffusion ◽  
Vertical Plate ◽  
Perturbation Technique ◽  
Slip Flow ◽  
Physical Parameters ◽  
Inclined Magnetic Field ◽  
Fluid Properties

AbstractIn this study, various fluid physical quantities effects such as diffusion-thermo, thermal-diffusion, thermal radiation, viscous dissipation, inclined magnetic field on unsteady MHD slip flow over a permeable vertical plate are considered. The coupled and nonlinear partial differential governing equations consisting of momentum, energy and species equations are reduced to ordinary differential equations using perturbation technique. The resulted coupled, nonlinear ordinary differential equations are solved by using collocation method with the aid of assumed Legendre polynomial. The impacts of different physical parameters on fluid properties are discussed and presented both graphically and tabularly. Both Dufour and Soret have the tendency of enhancing velocity profiles.

Three-dimensional biomagnetic Maxwell fluid flow over a stretching surface in presence of heat source/sink

2019 ◽  
Vol 12 (03) ◽  
pp. 1950036 ◽  
Author(s):  
M. G. Murtaza ◽  
M. Ferdows ◽  
J. C. Misra ◽  
E. E. Tzirtzilakis
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Numerical Method ◽  
Heat Generation ◽  
Velocity Component ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Maxwell Fluid ◽  
Deborah Number ◽  
Numerical Results

The present paper deals with the study of three-dimensional boundary layer flow of biomagnetic Maxwell fluid over a plane horizontal surface stretched linearly along two mutually perpendicular directions. Basic principles of magnetohydrodynamics (MHD) and ferro-hydrodynamics (FHD) have been employed. The effect of heat generation/absorption has been taken into consideration. The study is theoretical and is conducted by using a combination of approximate and numerical techniques. By using the method of similarity transformation, the governing nonlinear partial differential equations are converted into a set of coupled ordinary differential equations. In the sequel, a suitable numerical method has been developed to solve the coupled differential equations. The accuracy of the numerical method has been checked by comparing the numerical results with those of an earlier study reported in available literatures. Effects of various parameters involved in the study, viz. the magnetohydrodynamic and ferromagnetic parameters, Deborah number, stretching ratio and heat generation on the fluid flow profiles are investigated and the results have been presented graphically. Variations of the skin friction, heat transfer rate and relative wall pressure with change in hydrodynamic and ferromagnetic parameters have also been illustrated. It is found that due to the influence of the Kelvin force, the velocity component in [Formula: see text]-direction is greater than the corresponding one in the hydrodynamic case, but the opposite is true for the velocity component in the [Formula: see text]-direction. We also found that the temperature of the fluid for hydrodynamic flow is greater than that for MHD or FHD flow. It is even greater for BFD flows. The numerical results of the study reveal that the characteristics of blood flow are significantly affected by the presence of a magnetic field.

scholarly journals Hydromagnetic Dissipative and Radiative Graphene Maxwell Nanofluid Flow Past a Stretched Sheet-Numerical and Statistical Analysis

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1929 ◽  
Author(s):  
Syed M. Hussain ◽  
Rohit Sharma ◽  
Manas R. Mishra ◽  
Sattam S. Alrashidy
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Physical Parameters ◽  
Maxwell Nanofluid ◽  
Nusselt Numbers ◽  
Highly Nonlinear ◽  
Numeric Data ◽  
The Relationship ◽  
The Magnetic Field

The key objective of this analysis is to examine the flow of hydromagnetic dissipative and radiative graphene Maxwell nanofluid over a linearly stretched sheet considering momentum and thermal slip conditions. The appropriate similarity variables are chosen to transform highly nonlinear partial differential equations (PDE) of mathematical model in the form of nonlinear ordinary differential equations (ODE). Further, these transformed equations are numerically solved by making use of Runge-Kutta-Fehlberg algorithm along with the shooting scheme. The significance of pertinent physical parameters on the flow of graphene Maxwell nanofluid velocity and temperature are enumerated via different graphs whereas skin friction coefficients and Nusselt numbers are illustrated in numeric data form and are reported in different tables. In addition, a statistical approach is used for multiple quadratic regression analysis on the numerical figures of wall velocity gradient and local Nusselt number to demonstrate the relationship amongst heat transfer rate and physical parameters. Our results reveal that the magnetic field, unsteadiness, inclination angle of magnetic field and porosity parameters boost the graphene Maxwell nanofluid velocity while Maxwell parameter has a reversal impact on it. Finally, we have compared our numerical results with those of earlier published articles under the restricted conditions to validate our solution. The comparison of results shows an excellent conformity among the results.

scholarly journals Effects of Mass Suction on MHD Boundary Layer Flow and Heat Transfer over a Porous Shrinking Sheet with Heat Source/Sink

2019 ◽  
Vol 8 (10) ◽  
pp. 263-266 ◽  
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Shrinking Sheet ◽  
Dynamic Framework ◽  
Mhd Boundary Layer ◽  
Source Sink

An examination is made to think about the impacts of the mass suction on the steady flow of 2-D magneto-hydrodynamic (MHD) boundary layer flows and heat transfer past on a shrinking sheet with source/sink. In the dynamic framework, an-uniform magnetic field acts perpendicular to the plane of flow. The governing non-dimensional partial differential equations are changed into nonlinear ordinary differential equations (ODE’s) using similarity transformations. The so derived ordinary differential equations are solved numerically by using the MAT LAB solver bvp5c. From the keen examinations it is found that the velocity inside the boundary layer increments with increment of wall mass suction, magnetic field and reportedly the thickness of the momentum layer diminishes. There is a reduction in temperature as increases the Prandtl number. With heat source specifications, Hartmann number, heat sink parameter & the temperature increments are seen. Moreover, for strong heat source heat assimilation at the sheet happens.

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