Effect of MHD and Injection through one side of a long vertical channel embedded in porous medium with transpiration cooling

2014 ◽  
Vol 4 (4) ◽  
Author(s):  
K. Govardhan ◽  
K. Kaladhar ◽  
G. Nagaraju ◽  
B. Balaswamy
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Similarity Transformation ◽  
Initial Conditions ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Transpiration Cooling ◽  
Transfer Rates ◽  
Predictor Corrector ◽  
Raphson Method

AbstractThis paper examines the effect of MHD, and injection through one side of a long vertical channel embedded in porous medium with transpiration cooling. The governing nonlinear partial differential equations have been transformed by similarity transformation into a set of ordinary differential equations, which are solved numerically by Adam-moultan Predictor-Corrector method with Newton-Raphson Method for missing initial conditions. Proflles of dimensionless velocity, temperature and concentration are shown graphically for different parameters entering into the analysis. Also the effects of the pertinent parameters on the heat transfer rates are tabulated. An analysis of the results obtained shows that the flow field is influenced appreciably by emerging parameters of the present study.

scholarly journals Boundary Layer Flow Over a Vertical Cylinder Embedded in a Porous Medium Moving with non Linear Velocity

2021 ◽  
Vol 16 ◽  
pp. 32-36
Author(s):  
Tarek G. Emam
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Similarity Transformation ◽  
Initial Conditions ◽  
Vertical Cylinder ◽  
Linear Velocity ◽  
Self Similarity ◽  
Layer Flow ◽  
Nonlinear Velocity

In this work, we consider a steady flow of an incompressible fluid over a cylinder which is semi-infinite. The cylinder is embedded in a porous medium and is considered to move vertically with nonlinear velocity. A system of ordinary differential equations is obtained from the partial differential equations governing the motion using a self-similarity transformation. Such system of ordinary differential equations is solved numerically after obtaining the missed initial conditions. The problem has been solved analytically for the linear velocity case. Numerical and analytical results for such case are given to validate the numerical method used.

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.

Barycentric Jacobi Spectral Method for Numerical Solutions of the Generalized Burgers-Huxley Equation

2017 ◽  
Vol 18 (1) ◽  
pp. 67-81 ◽  
Author(s):  
Edson Pindza ◽  
M. K. Owolabi ◽  
K.C. Patidar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Point Of View ◽  
Partial Differential ◽  
Computational Point ◽  
Exponential Time Differencing ◽  
Predictor Corrector ◽  
Numerical Approaches

AbstractNumerical solutions of nonlinear partial differential equations, such as the generalized and extended Burgers-Huxley equations which combine effects of advection, diffusion, dispersion and nonlinear transfer are considered in this paper. Such system can be divided into linear and nonlinear parts, which allow the use of two numerical approaches. Barycentric Jacobi spectral (BJS) method is employed for the spatial discretization, the resulting nonlinear system of ordinary differential equation is advanced with a fourth-order exponential time differencing predictor corrector. Comparative numerical results for the values of options are presented. The proposed method is very elegant from the computational point of view. Numerical computations for a wide variety of problems, show that the present method offers better accuracy and efficiency in comparison with other previous methods. Moreover the method can be applied to a wide class of nonlinear partial differential equations.

Impact of Entropy Generation on Stagnation-Point Flow of Sutterby Nanofluid: A Numerical Analysis

2016 ◽  
Vol 71 (9) ◽  
pp. 837-848 ◽  
Author(s):  
Ehtsham Azhar ◽  
Z. Iqbal ◽  
E.N. Maraj
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Entropy Generation ◽  
Computational Analysis ◽  
Similarity Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Physical Parameters ◽  
Stretching Plate

AbstractThe present article dicusses the computational analysis of entropy generation for the stagnation-point flow of Sutterby nanofluid over a linear stretching plate. The Sutterby fluid is chosen to study the effect for three major classes of non-Newtonian fluids, i.e. pseudoplastic, Newtonian, and dilatant. The effects of pertinent physical parameters are examined under the approximation of boundary layer. The system of coupled nonlinear partial differential equations is simplified by incorporating suitable similarity transformation into a system of non-linear-coupled ordinary differential equations. Entropy generation analysis is conducted numerically, and the results are displayed through graphs and tables. Significant findings are listed in the closing remarks.

scholarly journals Dirichlet series and analytical solutions of MHD viscous flow with suction / blowing

2017 ◽  
Vol 2 (2) ◽  
pp. 341-350 ◽  
Author(s):  
Vishwanath B. Awati
Keyword(s):  
Differential Equations ◽  
Viscous Flow ◽  
Dirichlet Series ◽  
Analytical Solutions ◽  
Similarity Transformation ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Incompressible Viscous Flow ◽  
Approximate Analytical Solutions

AbstractThis paper presents Dirichlet series and approximate analytical solutions of magnetohydrodynamic (MHD) flow due to a suction / blowing caused by boundary layer of an incompressible viscous flow. The governing nonlinear partial differential equations of momentum equations are reduced into a set of nonlinear ordinary differential equations (ODE) by using a classical similarity transformation along with appropriate boundary conditions. Both nonlinearity and infinite interval demand novel mathematical tools for their analysis. We use elegant fast converging Dirichlet series and approximate analytical solutions (method of stretching of variables) of these nonlinear differential equations. These methods have advantages over pure numerical methods for obtaining derived quantities accurately for various values of the parameters involved at a stretch and also they are valid in much larger parameter domains as compared with DTM-Padé and classical numerical schemes.

BIOCONVECTION IN A NON-DARCY POROUS MEDIUM SATURATED WITH A NANOFLUID AND OXYTACTIC MICRO-ORGANISMS

2014 ◽  
Vol 07 (01) ◽  
pp. 1450005 ◽  
Author(s):  
S. SHAW ◽  
P. K. KAMESWARAN ◽  
M. NARAYANA ◽  
P. SIBANDA
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Horizontal Plate ◽  
Nanoparticle Concentration ◽  
Transfer Rates ◽  
Similarity Transformations ◽  
Fluid Properties ◽  
Layer Flow ◽  
Micro Organisms

The aim of this paper is to present a continuum model for bioconvection of oxytactic micro-organisms in a non-Darcy porous medium and to investigate the effects of bioconvection and mixed convection on the steady boundary layer flow past a horizontal plate embedded in a porous medium filled with a water-based nanofluid. The governing partial differential equations for momentum, heat, oxygen and micro-organism conservation are reduced to a set of nonlinear ordinary differential equations using similarity transformations that are numerically solved using a built-in MATLAB ODE solver. The effects of the bioconvection parameters on the nanofluid fluid properties, nanoparticle concentration and the density of the micro-organism are analyzed. A comparative analysis of our results with those previously reported in the literature is given. Among the significant findings in this study is that bioconvection parameters highly influence heat, mass and motile micro-organism transfer rates.

scholarly journals Serious Solutions for Unsteady Axisymmetric Flow over a Rotating Stretchable Disk with Deceleration

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 96 ◽  
Author(s):  
Sadiq
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Similarity Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Axisymmetric Flow ◽  
Analysis Method ◽  
Highly Nonlinear ◽  
Homotopy Analysis ◽  
Rotating Stretchable Disk ◽  
Comparison Table

In this article, the author has examined the unsteady flow over a rotating stretchable disk with deceleration. The highly nonlinear partial differential equations of viscous fluid are simplified by existing similarity transformation. Reduced nonlinear ordinary differential equations are solved by homotopy analysis method (HAM). The convergence of HAM solutions is also obtained. A comparison table between analytical solutions and numerical solutions is also presented. Finally, the results for useful parameters, i.e., disk stretching parameters and unsteadiness parameters, are found.

Double Diffusive Convection in Flow Couple Stress Nanofluid in a Permeable Wall Vertical Channel in the Presence of a Magnetic Field

2019 ◽  
Vol 26 ◽  
pp. 30-44
Author(s):  
Noureddine Messaoudi ◽  
Mohamed Nadjib Bouaziz ◽  
Hamza Ali Agha
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Couple Stress ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Strong Impact

In this work, the flow of a couple stress nanofluid in a vertical channel with heat and mass transfer in the presence of a magnetic field and taking account the Brownian motion, the thermophoresis as well as the effect of Soret and Dufour was simulated numerically using Matlab following the code bvp4c. The nonlinear partial differential equations governing this particular flow are transformed into a system of ordinary differential equations via the similarity technique. The influence of the parameters describing the behavior of the problem studied on the velocity, temperature, concentration and volume fraction fields of the nanoparticles, as well as on the coefficient of friction, Nusselt and Sherwood numbers, were highlighted for the end of the study. understand their effect on heat and mass transfer. The rheology of the nanofluid and the magnetic field have a strong impact on the velocity and temperature profiles, while the parameters of Brownian motion and thermophoresis promote heat transfer.

Instability of Variable Thermal Conductivity Magnetohydrodynamic Nanofluid Flow in a Vertical Porous Channel of Varying Width

2017 ◽  
Vol 378 ◽  
pp. 85-101
Author(s):  
Md. Sarwar Alam ◽  
Oluwole Daniel Makinde ◽  
Md. Abdul Hakim Khan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Entropy Generation ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Porous Wall ◽  
Variable Thermal Conductivity ◽  
Physical Parameters

A numerical investigation is performed into the heat transfer and entropy generation of a variable thermal conductivity magnetohydrodynamic flow of Al2O3-water nanofluid in a vertical channel of varying width with right porous wall, which enable the fluid to enter. The effects of the Lorentz force, buoyancy force, viscous dissipation and Joule heating are considered and modeled using the transverse momentum and energy balance equations respectively. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using appropriate similarity transformations and then solved numerically using power series with Hermite-Padé approximation method. A stability analysis has been performed for the local rate of shear stress and Nusselt number that indicates the existence of dual solution branches. Numerical results are achieved for the fluid velocity, temperature as well as the rate of heat transfer at the wall and the entropy generation of the system. The present results are original and new for the flow and heat transfer past a channel of varying width in a nanofluid which shows that the physical parameters have significant effects on the flow field.

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