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.

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 On a similarity solution of MHD boundary layer flow over a moving vertical cylinder

2006 ◽  
Vol 2006 ◽  
pp. 1-9
Author(s):  
Maryem Amkadni ◽  
Adnane Azzouzi
Keyword(s):  
Shooting Method ◽  
Similarity Transformation ◽  
Vertical Cylinder ◽  
Transverse Magnetic ◽  
Self Similarity ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Mhd Boundary Layer Flow

The steady flow of an incompressible electrically conducting fluid over a semi-infinite moving vertical cylinder in the presence of a uniform transverse magnetic field is analyzed. The partial differential equations governing the flow are reduced to an ordinary differential equation, using the self-similarity transformation. The analysis deals with the existence of an exact solution to the boundary value problem by a shooting method.

scholarly journals Radiative Boundary Layer Flow in Porous Medium due to Exponentially Shrinking Permeable Sheet

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Paresh Vyas ◽  
Nupur Srivastava
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Layer Flow ◽  
Radiative Heat ◽  
Saturated Porous Medium ◽  
Similarity Transformations ◽  
Layer Flow ◽  
Rosseland Approximation

This communication pertains to the study of radiative heat transfer in boundary layer flow over an exponentially shrinking permeable sheet placed at the bottom of fluid saturated porous medium. The porous medium has permeability of specified form. The fluid considered here is Newtonian, without phase change, optically dense, absorbing-emitting radiation but a nonscattering medium. The setup is subjected to suction to contain the vorticity in the boundary layer. The radiative heat flux in the energy equation is accounted by Rosseland approximation. The thermal conductivity is presumed to vary with temperature in a linear fashion. The governing partial differential equations are reduced to ordinary differential equations by similarity transformations. The resulting system of nonlinear ordinary differential equations is solved numerically by fourth-order Runge-Kutta scheme together with shooting method. The pertinent findings displayed through figures and tables are discussed.

scholarly journals Bioconvection of Nanofluid Past Stretching Sheet in a Porous Medium in Presence of Gyrotactic Microorganisms with Newtonian Heating

2018 ◽  
Vol 220 ◽  
pp. 01004
Author(s):  
Rashid Pourrajab ◽  
Aminreza Noghrehabadi
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Boussinesq Approximation ◽  
Newtonian Heating ◽  
Gyrotactic Microorganisms ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer ◽  
Layer Flow

In this study, the effect of Newtonian heating on the boundary layer flow and heat transfer over a stretching surface in a porous medium in the presence of gyrotactic microorganisms and nanoparticle fractions are analysed. The governing equations are reduced to a system of couple non-linear ordinary differential equations, subjected to the Boussinesq approximation and asymmetric heat conditions. The reduced governing ordinary differential equations are then solved numerically. The solutions obtained are graphically represented. The effects of the controlling parameters on the flow, heat, nanoparticle concentration and the density of motile microorganisms have been examined. The results of the present study show the flow velocity, heat and mass transfer and motile microorganism characteristics on the stretching sheet are strongly influenced by the bioconvection parameters and Newtonian.

scholarly journals A New Numerical Approach for the Laminar Boundary Layer Flow and Heat Transfer along a Stretching Cylinder Embedded in a Porous Medium with Variable Thermal Conductivity

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
S. Shateyi ◽  
G. T. Marewo
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Stretching Cylinder ◽  
Special Cases ◽  
Layer Flow

The study presents an axisymmetric laminar boundary layer flow of a viscous incompressible fluid and heat transfer over a stretching cylinder embedded in a porous medium. A suitable similarity transformation is employed to transform the partial differential equations corresponding to the momentum and heat equations into nonlinear ordinary differential equations. The resultant ordinary differential equations are then solved using a successive relaxation method (SRM). The effects of significant parameters on the velocity and temperature profiles have been analyzed graphically. The obtained results are also compared with previously published results in some special cases and were found to be in excellent agreement. The skin friction as well as the heat transfer rate at the surface are increased as the values of the curvature parameter increase.

Plumes Above Line Fires in a Cross-Wind

1994 ◽  
Vol 4 (4) ◽  
pp. 201 ◽  
Author(s):  
GN Mercer ◽  
RO Weber
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Conditions ◽  
Velocity Profiles ◽  
Ambient Wind ◽  
Leaf Scorch ◽  
Wind Velocities ◽  
Wind Profiles ◽  
Fire Characteristics ◽  
Temperature Time

A model for the plume above a line fire in a cross wind is constructed. This problem is shown to reduce to numerically solving a system of 6 coupled ordinary differential equations for given initial conditions that depend upon the fire characteristics. The model is valid above the flaming zone and takes inputs such as the width, velocity and temperature of the plume at a given height above the flaming zone, Different horizontal ambient wind velocities are allowed for and a comparison is made between some of these representative wind profiles. The plume trajectory, width, velocity and temperature are calculated for these different representative velocity profiles. This model has application to the calculation of temperature-time exposures of vegetation above line fires and hence can be used in models that predict effects such as leaf scorch and canopy stored seed death. On a larger scale it has application to the problem of tracking burning brands which can cause spotting ahead of the fire.

Mixed Convection Boundary Layer Flow Near the Lower Stagnation Point of a Cylinder Embedded in a Porous Medium Using a Thermal Nonequilibrium Model

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Haliza Rosali ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Boundary Layer Flow ◽  
Thermal Conductivity Ratio ◽  
Convection Boundary Layer ◽  
Convection Boundary ◽  
Layer Flow

The present paper analyzes the problem of two-dimensional mixed convection boundary layer flow near the lower stagnation point of a cylinder embedded in a porous medium. It is assumed that the Darcy's law holds and that the solid and fluid phases of the medium are not in thermal equilibrium. Using an appropriate similarity transformation, the governing system of partial differential equations are transformed into a system of ordinary differential equations, before being solved numerically by a finite-difference method. We investigate the dependence of the Nusselt number on the solid–fluid parameters, thermal conductivity ratio and the mixed convection parameter. The results indicate that dual solutions exist for buoyancy opposing flow, while for the assisting flow, the solution is unique.

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