scholarly journals Unsteady Tangent Hyperbolic Fluid on Radiated Exponentially Porous Surface

2019 ◽  
Vol 9 (1S5) ◽  
pp. 230-234
Keyword(s):  
Differential Equations ◽  
Stretching Sheet ◽  
Nonlinear Differential Equations ◽  
Governing Equations ◽  
Shooting Technique ◽  
Runge Kutta Method ◽  
Tangent Hyperbolic Fluid ◽  
Porosity Effect ◽  
Exponentially Stretching ◽  
Parameter Values

This analysis refers the radiation and porosity effects on unsteady hyperbolic tangent fluid over exponentially stretching sheet. Using similarity transformation the governing equations which are partial differential equations in nature have been modified into nonlinear differential equations (ODE), and then we obtained the solution by shooting technique along with Runge-Kutta method. The dimensional less velocity and temperature have been represented graphically. We have found local Nusselt number and friction factor for distant dimensional less physical parameter values, and they displayed in table. At the end of the analysis we conclude that magnetic field decreases velocity of hyper tangent fluid and porosity effect decreases velocity of hyper tangent fluid. Further the radiation enriches temperature profile in injection case than suction case. This conclusion tells us injection case is useful in temperature transportation than suction case.

Theoretical treatment of bio-convective Maxwell nanofluid over an exponentially stretching sheet

2020 ◽  
Vol 98 (8) ◽  
pp. 732-741 ◽  
Author(s):  
Muhammad Naveed Khan ◽  
Sohail Nadeem
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Skin Friction ◽  
Stretching Sheet ◽  
Theoretical Treatment ◽  
Shooting Technique ◽  
Maxwell Nanofluid ◽  
Exponentially Stretching Sheet ◽  
Two Dimensional Flow ◽  
Exponentially Stretching

The heat and mass transfer of unsteady two-dimensional flow of a bio-convective non-Newtonian Maxwell nanofluid past an exponentially stretching sheet is presented. A viscous dissipation and external magnetic field along multiple slip conditions and chemical reactions are incorporated. The governing partial differential equations are reduced to the system of ordinary differential equations by applying suitable transformations. Using the bvp4c -shooting technique, we were able to solve the boundary value problem. The influence of the obtained parameters are deliberated graphically on the velocity, concentration, temperature, and microorganism profile. The tabulated values of skin friction, Nusselt number, mass flux rate, and microorganism rate along various parameters are computed and examined. The findings show that the value of the skin friction, Nusselt number, Sherwood number, and microorganism number decline due to enhancement in the time relaxation parameter.

scholarly journals Mathematical analysis of bio-convective micropolar nanofluid

2019 ◽  
Vol 6 (3) ◽  
pp. 233-242 ◽  
Author(s):  
Sohail Nadeem ◽  
Muhammad Naveed Khan ◽  
Noor Muhammad ◽  
Shafiq Ahmad
Keyword(s):  
Differential Equations ◽  
Microbial Fuel Cells ◽  
Shooting Method ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Convection Flow ◽  
Micropolar Nanofluid ◽  
Exponentially Stretching ◽  
Micro Organisms

Abstract The present investigation concentrates on three dimensional unsteady forced bio-convection flow of a viscous fluid. An incompressible flow of a micropolar nanofluid encloses micro-organisms past an exponentially stretching sheet with magnetic field is analyzed. By employing convenient transformation the partial differential equations are converted into the ordinary differential equations which are non-linear. By using shooting method to solved these equations numerically. The influence of the determining parameters on the velocity, temperature, micro-rotation, nanoparticle volume fraction, microorganism are incorporated. The skin friction, heat transfer rate, and the microorganism rate are analyzed. The results depicts that the value of the wall shear stress and Nusselt number are declined while an enhancement take place in the microorganism number. The slip parameters increases the velocity, thermal energy, and microorganism number consequentially. The present investigation are important in improving achievement of microbial fuel cells.

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.

scholarly journals Mixed convection of micropolar fluid on a permeable stretching surface of another quiescent fluid

2020 ◽  
Vol 16 (4) ◽  
pp. 487-492
Author(s):  
Nurazleen Abdul Majid ◽  
Nurul Farahain Mohammad ◽  
Abdul Rahman Mohd Kasim ◽  
Sharidan Shafie
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Mixed Convection ◽  
Micropolar Fluid ◽  
Research Subjects ◽  
Governing Equations ◽  
Stretching Surface ◽  
Shooting Technique ◽  
Micropolar Fluid Flow ◽  
Quiescent Fluid

In recent decades, micropolar fluid has been one of the major interesting research subjects due to the numerous applications such as blood, paint, body fluid, polymers, colloidal fluid and suspension fluid. However, the behavior of micropolar fluid flow over a permeable stretching surface of another quiescent fluid with a heavier density of micropolar fluid under the condition of mixed convection is still unknown. Thus, the current work aims to investigate numerically the mixed convection of micropolar fluid flow over a permeable stretching surface of another quiescent fluid. In this research, the similarity transformation is implemented to reduce the boundary layer governing equations from partial differential equations to a system of nonlinear ordinary differential equations. Then, this model is solved numerically using shooting technique with Runge-Kutta-Gill method and applied in Jupyter Notebook using Python 3 language. The behavior of micropolar fluid in terms of velocity, skin friction, microrotation and temperature are analyzed.

scholarly journals Rotating flow of nanofluid due to exponentially stretching surface: An optimal study

2019 ◽  
Vol 13 ◽  
pp. 174830261988136 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Muhammad Hamid ◽  
Muhammad Usman ◽  
Afshan Kanwal ◽  
Tamour Zubair ◽  
...  
Keyword(s):  
Transfer Rate ◽  
Stretching Sheet ◽  
Cuo Nanoparticles ◽  
Shear Stresses ◽  
Stretching Surface ◽  
Physical Problems ◽  
Runge Kutta Method ◽  
Exponentially Stretching Surface ◽  
Effects Of Rotation ◽  
Exponentially Stretching

In this article, the presented study is based on a modification in Gegenbauer wavelets method. The modeled problem is presented to analyze the phenomena of transfer of heat of rotating nanofluids in which the flow is produced by an exponentially stretching sheet. The purpose of this study is to examine the simultaneous effects of rotation of nanofluid and exponentially stretching on the shear stresses and heat transfer rate, cooling proficiency of water-based nanofluids containing Ag, Cu, Al2O3, TiO2, and CuO nanoparticles, and modification in Gegenbauer wavelets method to obtain the numerical solution of the said problem. A comparative analysis is presented among the outcomes obtained by modified Gegenbauer wavelets method, Runge–Kutta method of order-4, and already existing methods. The comparison shows that this modification is extremely efficient, and proposed technique could be extended for other physical problems.

scholarly journals Dynamics of Gaussian spikes on Gaussian laser beam in relativistic plasma

2009 ◽  
Vol 27 (4) ◽  
pp. 587-593 ◽  
Author(s):  
A. Singh ◽  
M. Aggarwal ◽  
T.S. Gill
Keyword(s):  
Differential Equations ◽  
Laser Beam ◽  
Nonlinear Differential Equations ◽  
Beam Width ◽  
Main Beam ◽  
Gaussian Laser Beam ◽  
Runge Kutta Method ◽  
Self Focusing ◽  
Gaussian Perturbation ◽  
Paraxial Ray

AbstractIn the present paper, we have investigated the growth of a Gaussian perturbation superimposed on a Gaussian laser beam. The nonlinearity we have considered is of relativistic type. We have setup the nonlinear differential equations for beam width parameter of the main beam, growth and width of the laser spike by using the WKB and paraxial ray approximation. These are coupled ordinary differential equations and therefore these are simultaneously solved numerically using the Runge Kutta method. It has been observed from the analysis that self-focusing/defocusing of the main beam and the spike determine the growth dynamic of the spike.

Application of GDQ method in nonlinear analysis of a flexible manipulator undergoing large deformation

2013 ◽  
Vol 227 (12) ◽  
pp. 2671-2685 ◽  
Author(s):  
Mohammad R Fazel ◽  
Majid M Moghaddam ◽  
Javad Poshtan
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equation ◽  
Flexible Manipulator ◽  
Runge Kutta Method ◽  
Highly Nonlinear ◽  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
Generalized Differential

Analysis of a flexible manipulator as an initial value problem, due to its large deformations, involves nonlinear ordinary differential equations of motion. In the present work, these equations are solved through the general Frechet derivatives and the generalized differential quadrature (GDQ) method directly. The results so obtained are compared with those of the fourth-order Runge–Kutta method. It is seen that both the results match each other well. Further considering the same manipulator as a boundary value problem, its governing equation is a highly nonlinear partial differential equation. Again applying the general Frechet derivatives and the GDQ method, it is seen that the results are in good match with the linear theory. In both cases, the general Frechet derivatives are introduced and successfully used for linearization. The results of the present study indicate that the GDQ method combined with the general Frechet derivatives can be successfully used for the solution of nonlinear differential equations.

scholarly journals Effect of Viscous Dissipation and Thermoporesis on the Flow Over an Exponentially Stretching Sheet

2019 ◽  
Vol 24 (2) ◽  
pp. 425-438 ◽  
Author(s):  
D. Srinivasacharya ◽  
P. Jagadeeshwar
Keyword(s):  
Viscous Dissipation ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Convective Boundary Condition ◽  
Local Similarity ◽  
Governing Equations ◽  
Convective Boundary ◽  
Exponentially Stretching ◽  
Physical Quantities ◽  
Sheet Stretching

Abstract This article analyses the influence of viscous dissipation and thermoporesis effects on the viscous fluid flow over a porous sheet stretching exponentially by applying convective boundary condition. The numerical solutions to the governing equations are evaluated using a local similarity and non-similarity approach along with a successive linearisation procedure and Chebyshev collocation method. The influence of the pertinent parameters on the physical quantities are displayed through graphs.

Stochastic Nonlinear Vibration of Fluid-Loaded Double-Walled Carbon Nanotubes

2013 ◽  
Vol 284-287 ◽  
pp. 362-366
Author(s):  
Tai Ping Chang
Keyword(s):  
Carbon Nanotubes ◽  
Differential Equations ◽  
Nonlinear Vibration ◽  
Nonlinear Differential Equations ◽  
Mean Value ◽  
Stochastic Dynamic ◽  
Governing Equations ◽  
The Mean ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

This paper investigates the stochastic dynamic behaviors of nonlinear vibration of the fluid-loaded double-walled carbon nanotubes (DWCNTs) by considering the effects of the geometric nonlinearity and the nonlinearity of van der Waals (vdW) force. The nonlinear governing equations of the fluid-conveying DWCNTs are formulated based on the Hamilton’s principle. The Young’s modulus of elasticity of the DWCNTs is assumed as stochastic with respect to the position to actually describe the random material properties of the DWCNTs. By utilizing the perturbation technique, the nonlinear governing equations of the fluid-conveying can be decomposed into two sets of nonlinear differential equations involving the mean value of the displacement and the first variation of the displacement separately. Then we adopt the harmonic balance method in conjunction with Galerkin’s method to solve the nonlinear differential equations successively. Some statistical dynamic response of the DWCNTs such as the mean values and standard deviations of the amplitude of the displacement are computed. It is concluded that the mean value and standard deviation of the amplitude of the displacement increase nonlinearly with the increase of the frequencies.

The Flow of Radiated Carreau Dusty Fluid over Exponentially Stretching Sheet with Partial Slip at the Wall

2018 ◽  
Vol 16 ◽  
pp. 96-108 ◽  
Author(s):  
H.B. Santosh ◽  
Mahesha ◽  
Chakravarthula S.K. Raju ◽  
Oluwole Daniel Makinde
Keyword(s):  
Stretching Sheet ◽  
Velocity Slip ◽  
Partial Slip ◽  
Exponentially Stretching Sheet ◽  
Flow And Heat Transfer ◽  
Runge Kutta Method ◽  
Nuclear Heat ◽  
Exponentially Stretching ◽  
Source Sink ◽  
The Impact

In this study, we addressed the impact of magnetic field on fluid flow and heat transfer of an in compressible Carreau fluid over exponentially stretching sheet in addition with fluid and dust particle suspension. Thermal radiation and non-uniform heat source/sink were included to develop heat transport phenomena. Dusty fluids have various applications such as processing of material, nuclear heat treatment, cooling process, treatment of waste water etc. The relevant governing equations are converted into ordinary differential equation using similarity transformation the transformed ordinary differential equations are then solved numerically by shooting technique along with Runge-Kutta method The effect of certain parameters on the dimensionless velocity and temperature are presented graphically. The physical quantities of the flow such as the friction factor and Local Nusselt number were calculated. It was found from the study that the velocity slip parameter increases the temperature profiles.

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