scholarly journals Approximate Analytical study of unsteady Hybrid nanofluid in the presences of magnetic field with convective boundary condition over a stretching surface

2021 ◽  
Author(s):  
Ali Rehman ◽  
Waris khan
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Analytical Solution ◽  
Convective Boundary Condition ◽  
Skin Friction Coefficient ◽  
Nonlinear Ordinary Differential Equation ◽  
Hybrid Nanofluid ◽  
Stretching Surface ◽  
Convective Boundary

Abstract The objective of this researcher paper is to study the analytical solution of unsteady hybrid nanofluid in the presences of magnetic field over a stretching surface. By using similarity transformation the major partial differential equation is converted to a set of nonlinear ordinary differential equation .the analytical method (OHAM) is used to find the approximate analytical solution of the nonlinear ordinary differential equation The BVPh 2.0 package function of MATHEMATICA is used to obtained the numerical results the result of important parameter such as, magnetic parameter, Prandtl number, Eckert number and surface convection parameter for both velocity and temperature profile are plotted and discuss. The BVPh 2.0 package is used to obtained the converges of the problem up to 25 iterations. The skin friction coefficient and Nusselt is explained in table form.

scholarly journals Saturation of the magnetorotational instability by stable magnetoacoustic modes

2012 ◽  
Vol 8 (S294) ◽  
pp. 365-366
Author(s):  
Edward Liverts ◽  
Yuri Shtemler ◽  
Michael Mond ◽  
Orkan M. Umurhan ◽  
Dmitry V. Bisikalo
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Axial Magnetic Field ◽  
Nonlinear Ordinary Differential Equation ◽  
Amplitude Equation ◽  
Magnetorotational Instability ◽  
Zero Eigenvalue ◽  
Magnetoacoustic Waves ◽  
Linearized System

AbstractThe magnetorotational instability (MRI) of thin, vertically-isothermal Keplerian discs, under the influence of an axial magnetic field is investigated near the instability threshold. The nonlinear interaction of Alfven-Coriolis (MRI) modes with stable magnetoacoustic waves is considered. The transition of the Alfven-Coriolis modes to instability occurs when the linearized system has zero eigenvalue of multiplicity two. As a result the nonlinear ordinary differential equation that describes the evolution of the amplitude of the MRI mode near the threshold is of second order. Solutions of that amplitude equation reveal that the MRI is saturated to bursty periodical oscillations due to the transfer of energy to the stable magnetosonic modes.

scholarly journals Radiative Magnetohydrodynamics Casson Nanofluid Flow and Heat and Mass Transfer past on Nonlinear Stretching Surface

2021 ◽  
Author(s):  
Gurrala Thirupathi ◽  
Kamatam Govardhan ◽  
Ganji Narender
Keyword(s):  
Differential Equations ◽  
Velocity Slip ◽  
Convective Boundary Condition ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Convective Boundary ◽  
Casson Nanofluid ◽  
Order Four

The magnetohydrodynamics (MHD) stagnation point Casson nanofluid flow towards stretching surface with velocity slip and convective boundary condition has been investigated in this article. Effects of thermal radiation, viscous dissipation, heat source and chemical reaction have also been incorporated. Using appropriate similarity transformation Partial Differential Equations (PDEs) are converted into Ordinary Differential Equations (ODEs) and shooting technique along with Adams–Moulton method of order four has been used to obtain the numerical results. Different physical parameters effects on velocity, temperature and concentration of nanofluid flow have been presented graphically and discussed in detail. Numerical values of the skin friction coefficient, Nusselt number and Sherwood number are also and discussed.

Design of evolutionary cubic spline intelligent solver for nonlinear Painlevé-I transcendent

2021 ◽  
Author(s):  
Sharafat Ali ◽  
Iftikhar Ahmad ◽  
Muhammad Asif Zahoor Raja ◽  
Siraj ul Islam Ahmad ◽  
Muhammad Shoaib
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Genetic Algorithms ◽  
Statistical Analysis ◽  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Process Variation ◽  
Nonlinear Ordinary Differential Equation ◽  
Second Derivative ◽  
Search Technique

In this research paper, an innovative bio-inspired algorithm based on evolutionary cubic splines method (CSM) has been utilized to estimate the numerical results of nonlinear ordinary differential equation Painlevé-I. The computational mechanism is used to support the proposed technique CSM and optimize the obtained results with global search technique genetic algorithms (GAs) hybridized with sequential quadratic programming (SQP) for quick refinement. Painlevé-I is solved by the proposed technique CSM-GASQP. In this process, variation of splines is implemented for various scenarios. The CSM-GASQP produces an interpolated function that is continuous upto its second derivative. Also, splines proved to be stable than a single polynomial fitted to all points, and reduce wiggles between the tabulated points. This method provides a reliable and excellent procedure for adaptation of unknown coefficients of splines by searching globally exploiting the performance of GA-SQP algorithms. The convergence, exactness and accuracy of the proposed scheme are examined through the statistical analysis for the several independent runs.

Approximated Solutions for Axisymmetric Wrinkled Inflated Membranes

2015 ◽  
Vol 82 (11) ◽  
Author(s):  
Riccardo Barsotti
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Finite Element ◽  
Nonlinear Ordinary Differential Equation ◽  
Experimental Results ◽  
Limit Case ◽  
Reasonable Approximation ◽  
Constituent Material ◽  
Actual Solution ◽  
Wrinkled Membrane

The axisymmetric inflation problem for a wrinkled membrane is solved by means of a simple nonlinear ordinary differential equation. The solution is illustrated in full details. Both the free and constrained cases are addressed, in the limit case where the membrane is fully wrinkled. In the constrained inflation problem, no slippage is allowed between the membrane and the constraining surfaces. It is shown that an actual membrane can in no way reach the fully wrinkled configuration during free inflation, regardless of the membrane's initial configuration and constituent material. The fully wrinkled solution is compared to some finite element results obtained by means of an expressly developed iterative–incremental procedure. When the values of the inflating pressure and length of the meridian lie within a suitable applicability range, the fully wrinkled solution may represent a reasonable approximation of the actual solution. A comparison with some numerical and experimental results available in the literature is illustrated.

scholarly journals Mathematical Modeling of Treatment Effect on Tumor Growth and Blood Flow through a Channel with Magnetic Field

2021 ◽  
pp. 66-79
Author(s):  
K. W. Bunonyo ◽  
C. U. Amadi
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Blood Flow ◽  
Tumor Growth ◽  
Blood Velocity ◽  
Frequency Parameter ◽  
Womersley Number ◽  
Permeability Parameter ◽  
Flow Through

In this research, we investigated the effect of tumor growth on blood flow through a micro channel by formulated the governing model with the assumption that blood is an incompressible, eclectrially conducting fluid which flow is caused by the pumping action of the heart and suction. The governing model was scaled using some dimensionless variables and the region of the tumor was obtained from Dominguez [1] which was incorporated in our model. The model is further reduced to an ordinary differential equation using a perturbation condition. However, the ordinary differential equation was solved using method of undermined coefficients, and the constants coefficients obtained via matrix method. Furthermore, the simulation to study the effect of the pertinent parameters was done suing computation software called Mathematica. It is seen in our investigation that the entering parameters such as magnetic field parameter, the Reynolds number, womersley number, oscillatory frequency parameter, and permeability parameter affect the blood velocity profile in decreasing and increasing fashion.

scholarly journals Approximate solution of nonlinear ordinary differential equation using ZZ decomposition method

2020 ◽  
Vol 4 (1) ◽  
pp. 448-455
Author(s):  
Mulugeta Andualem ◽  
◽  
Atinafu Asfaw ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Approximate Solution ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Initial Value ◽  
Transform Method ◽  
Adomian Decomposition

Nonlinear initial value problems are somewhat difficult to solve analytically as well as numerically related to linear initial value problems as their variety of natures. Because of this, so many scientists still searching for new methods to solve such nonlinear initial value problems. However there are many methods to solve it. In this article we have discussed about the approximate solution of nonlinear first order ordinary differential equation using ZZ decomposition method. This method is a combination of the natural transform method and Adomian decomposition method.

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