scholarly journals RHEOLOGY OF POWER LAW FLUID FLOW AROUND A STAGNATION POINT IN POROUS MEDIUM WITH ENERGY DISSIPATION

2021 ◽  
Vol 51 (4) ◽  
pp. 223-228
Author(s):  
Debasish Dey ◽  
Bhagyashree Mahanta
Keyword(s):  
Porous Medium ◽  
Shear Stress ◽  
Energy Dissipation ◽  
Differential Equations ◽  
Prandtl Number ◽  
Stagnation Point ◽  
Power Law ◽  
Linear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Permeability Parameter

An investigation on two-dimensional stagnation point flow past a stretching or shrinking surface in a porous medium with energy dissipation using power law model is carried out in this paper. By applying some similarity transformations, the governing partial differential equations are converted to non-linear ordinary differential equations. Consequently, numerical calculations of these equations are done by using MATLAB built- in bvp4c method. Impact of various parameters such as Prandtl number, permeability parameter and magnetic parameter are depicted graphically on velocity and temperature distributions. Also, the numerical values for velocity gradient and shear stress are shown in tabular form. From the analysis, it is noted that Prandtl number helps in reducing the shear stress, Also, as the power law parameter increases, a decrease in velocity is observed.

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 Thermal Diffusion and Diffusion Thermo Effects on the Viscous Fluid Flow with Heat and Mass Transfer through Porous Medium over a Shrinking Sheet

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Nabil Eldabe ◽  
Mahmoud Abu Zeid
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Shear Stress ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Transfer Parameter ◽  
Mass Transfer Parameter ◽  
Permeability Parameter

The motion of the viscous, incompressible fluid through a porous medium with heat and mass transfer over a shrinking sheet is investigated. The cross-diffusion effect between temperature and concentration is considered. This phenomenon is modulated mathematically by a set of partial differential equations which govern the continuity, momentum, heat, and mass. These equations are transformed to a set of ordinary differential equations by using similarity solutions. The analytical solutions of these equations are obtained. The velocity, temperature, and concentration of the fluid as well as the heat and mass transfer with shear stress at the sheet are obtained as a function of the physical parameters of the problem. The effects of Prandtl number, mass transfer parameter, the wall shrinking parameter, the permeability parameter, and Dufour and Soret numbers on temperature and concentration are studied. Also, the effects of mass transfer parameter, permeability parameter, and shrinking strength on the velocity and shear stress are discussed. These effects are illustrated graphically through a set of figures.

Radiative MHD Stagnation-Point Flow with Heat Transfer Past a Permeable Stretching/Shrinking Sheet in a Porous Medium

2017 ◽  
Vol 11 ◽  
pp. 110-128
Author(s):  
Shoeb R. Sayyed ◽  
B.B. Singh ◽  
Nasreen Bano
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Nonlinear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Energy Equations

In the present study, an analytical analysis has been carried out to investigate the MHD stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet in a porous medium in the presence of thermal radiation. Similarity transformations have been employed to simplify the momentum and energy equations into coupled nonlinear ordinary differential equations. The resulting nonlinear ordinary differential equations are then solved analytically through BVPh 2.0 Mathematica package based on homotopy analysis method (HAM). Effects of various parameters such as Prandtl number, permeability parameter, magnetic parameter, suction/blowing parameter, stretching/shrinking parameter, radiation parameter and wall temperature exponent on velocity and/or temperature profiles are explored and discussed graphically. Our results have been compared with the available literature and have been found in excellent agreement. This study may have applications in metallurgy industry and aerodynamic extrusion of plastic sheet.

Mixed Convection Flow of a Micropolar Fluid Past a Vertical Stretching Surface in a Thermally Stratified Porous Medium with Thermal Radiation

2013 ◽  
Vol 29 (3) ◽  
pp. 461-470 ◽  
Author(s):  
Mostafa A.A. Mahmoud ◽  
Shimaa E. Waheed
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Micropolar Fluid ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Linear Ordinary Differential Equations ◽  
Permeability Parameter

AbstractThis paper is concerned with the effect of thermally stratification on the steady, two-dimensional mixed convection flow of a micropolar fluid past a vertical stretching permeable surface saturated in porous medium taking into account the effect of thermal radiation. The governing system of partial differential equations describing the problem are converted into a system of non-linear ordinary differential equations using similarity transformation. The resulting system of coupled nonlinear ordinary differential equations is solved numerically using the Chebyshev spectral method. The numerical results for the velocity, the micro-rotation and the temperature are displayed graphically showing the effects of various parameters like the buoyancy parameter, the radiation parameter, the stratification parameter, the permeability parameter and the suction/injection parameter. Moreover, the numerical values of the local skinfriction coefficient, the wall couple stress and the local Nusselt number for these parameters are also tabulated and discussed.

Multiple Solutions of an Unsteady Stagnation-Point Flow with Melting Heat Transfer in a Darcy–Brinkman Porous Medium

2016 ◽  
Vol 0 (0) ◽  
Author(s):  
M Khalid Aurangzaib ◽  
Bhattacharyya Krishnendu ◽  
Shafie Sharidan
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Stagnation Point ◽  
Multiple Solutions ◽  
Melting Heat ◽  
Similarity Transformations ◽  
Melting Heat Transfer ◽  
Self Similar ◽  
Layer Flow

AbstractThe characteristics of the unsteady boundary layer flow with melting heat transfer near a stagnation-point towards a flat plate embedded in a DarcyBrinkman porous medium with thermal radiation are investigated. The governing partial differential equations are transformed into self-similar ordinary differential equations by similarity transformations. The transformed self-similar equations are solved numerically using bvp4c from Matlab for several values of the flow parameters. The study reveals that the multiple solutions exist for the decelerating (

scholarly journals Analytical and Numerical Study on Magnetoconvection Stagnation-Point Flow in a Porous Medium with Chemical Reaction, Radiation, and Slip Effects

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
H. Niranjan ◽  
S. Sivasankaran ◽  
M. Bhuvaneswari
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Study ◽  
Slip Parameter ◽  
Similarity Transformations ◽  
Slip Effects ◽  
Homotopy Analysis ◽  
Chemically Reacting ◽  
Fourth Order Method

We investigate the effects of slip and radiation on magnetoconvection flow of a chemically reacting fluid near a stagnation-point towards a vertical plate embedded in a porous medium analytically and numerically. The governing partial differential equations are diminished into the coupled ordinary differential equations by similarity transformations. Then they are solved analytically by homotopy analysis method and solved numerically by shooting method with RK fourth-order method. In this study, the analytical and numerical results are compared for many combinations of parameters. The rates of heat and mass transfer are calculated. The velocity profile near the plate overshoots on increasing the slip parameter. The concentration and temperature are decreasing on increasing the slip 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.

Similarity Solutions of the MHD Stagnation-Point Flow over a Power-Law Stretching Sheet

2011 ◽  
Vol 52-54 ◽  
pp. 1895-1900
Author(s):  
Jing Zhu ◽  
Lian Cun Zheng ◽  
Xue Hui Chen
Keyword(s):  
Stagnation Point ◽  
Power Law ◽  
Stretching Sheet ◽  
Velocity Ratio ◽  
Similarity Solutions ◽  
Stagnation Point Flow ◽  
Electrically Conducting ◽  
Power Law Exponent ◽  
Permeability Parameter ◽  
Scaling Group Of Transformations

A similarity analysis is performed for a steady laminar boundary layer stagnation-point flow of an electrically conducting fluid in a porous medium subject to a transverse non-uniform magnetic field past a non-linear stretching sheet. A scaling group of transformations is applied to get the invariants. Using the invariants, a third order ordinary differential equation corresponding to the momentum is obtained. We show the existence and uniqueness of convex and concave solutions for the power law exponent, according to the values of magnetic parameter, permeability parameter and velocity ratio parameter.

Thermally and chemically reacted MHD Maxwell nanofluid flow past an inclined permeable stretching surface

2021 ◽  
pp. 095440892110507
Author(s):  
Amar B. Patil ◽  
Vishwambhar S. Patil ◽  
Pooja P. Humane ◽  
Nalini S. Patil ◽  
Govind R. Rajput
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Linear Ordinary Differential Equations ◽  
Maxwell Nanofluid ◽  
Similarity Transformations ◽  
Flow Past ◽  
Chemically Reacting ◽  
The Impact

The present work deals with chemically reacting unsteady magnetohydrodynamic Maxwell nanofluid flow past an inclined permeable stretching surface embedded in a porous medium with thermal radiation. The formulated governing partial differential equations conveying the flow model of Maxwell with Buongiorno modeled nanofluid is transformed into the system of highly non-linear ordinary differential equations via suitable similarity transformations; those equations are transmuted into an initial value problem and then solved numerically by a shooting approach with Runge–-Kutta fourth-order schema. To obtain the physical insight of the flow situation, the influence of associated parameters on the velocity, temperature, and concentration profiles is sketched graphically with the aid of MATLAB software. Furthermore, engineering quantities of interest are interpreted graphically. The computed numerical results are compared to estimate the validity of the achieved results; it has been found out that the computed results are highly accurate. The impact of the Maxwell parameter and inclination angle of the sheet on the velocity field is observed in decaying. Both thermal and solutal energy transport are progressive in nature as the Maxwell parameter and thermophoresis parameter grows, and a reverse trend is observed for Prandtl number.

scholarly journals Numerical Analysis with Keller-Box Scheme for Stagnation Point Effect on Flow of Micropolar Nanofluid over an Inclined Surface

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1379 ◽  
Author(s):  
Rafique ◽  
Anwar ◽  
Misiran ◽  
Khan ◽  
Seikh ◽  
...  
Keyword(s):  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Nonlinear Differential Equations ◽  
Stagnation Region ◽  
Similarity Transformations ◽  
Box Scheme ◽  
Mass Fluxes ◽  
Micropolar Nanofluid ◽  
Inclined Surface

The prime aim of this paper is to probe the flow of micropolar nanofluid towards an inclined stretching surface adjacent to the stagnation region with Brownian motion and thermophoretic impacts. The chemical reaction and heat generation or absorption are also taken into account. The energy and mass transport of the micropolar nanofluid flow towards an inclined surface are discussed. The numerical solution is elucidated for the converted non-linear ordinary differential equation from the set of partial nonlinear differential equations via compatible similarity transformations. A converted system of ordinary differential equations is solved via the Keller-box scheme. The stretching velocity and external velocity are supposed to change linearly by the distance from the stagnation point. The impacts of involved parameters on the concerned physical quantities such as skin friction, Sherwood number, and energy exchange are discussed. These results are drawn through the graphs and presented in the tables. The energy and mass exchange rates show a direct relation with the stagnation point. In the same vein, skin friction diminishes with the growth of the stagnation factor. Heat and mass fluxes show an inverse correspondence with the inclination factor.

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