Parametric Analysis of Entropy Generation in Off-centered Stagnation Flow Towards a Rotating Disc

AbstractThe similarity solution for the steady stagnation flow towards an off-centered rotating disc is gives a systemof non-linear partial differential equations. These nonlinear differential equations are numerically solved by applyingwell known Keller-Box Method. After finding the velocity distributions, the important designing subject, entropy generation of this system has been analyzed. Graphical results are presented to investigate effects of the rotation ratio α, off-centering, Reynolds number and axial height on the radial and azimuthal velocities and entropy generation. In order to show the effectiveness of the Keller- Box method, the obtained results are compared with available solutions obtained using DTM. The obtained results demonstrate the reliability of the algorithm and the Keller- Box method is an attractive method in solving the systems of nonlinear partial differential equations, and also the entropy generation is an important parameter depends on design andwork conditions that should be in the attention of designers of these rotating systems.

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THE MODIFIED DIFFERENTIAL TRANSFORM METHOD FOR SOLVING OFF-CENTERED STAGNATION FLOW TOWARD A ROTATING DISC

International Journal of Computational Methods ◽

10.1142/s0219876210002404 ◽

2010 ◽

Vol 07 (04) ◽

pp. 655-670 ◽

Cited By ~ 21

Author(s):

ESMAEEL ERFANI ◽

MOHAMMAD MEHDI RASHIDI ◽

AMIR BASIRI PARSA

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Nonlinear Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Differential Transform Method ◽

Stagnation Flow ◽

Rotating Disc ◽

Partial Differential ◽

Transform Method ◽

Differential Transform

The similarity solution for the steady stagnation flow toward an off-centered rotating disc gives a system of nonlinear partial differential equations. These nonlinear differential equations are analytically solved by applying a newly developed method called DTM–Padé technique (the combination of the differential transform method (DTM) and the Padé approximation). This technique is extended to give solutions for nonlinear differential equations with boundary conditions at infinity. Graphical results are presented to investigate influence of the rotation ratio α on the radial velocity, azimuthal velocity, and the induced velocity. In order to show the effectiveness of the DTM–Padé technique, the results obtained from the DTM–Padé technique are compared with available solutions obtained using shooting method to generate the numerical solution. The obtained results demonstrate the reliability of the algorithm and the DTM–Padé technique is an attractive method in solving the systems of nonlinear partial differential equations.

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Method of Separation of Variables for the Solution of Certain Nonlinear Partial Differential Equations

Journal of Basic Engineering ◽

10.1115/1.3425205 ◽

1971 ◽

Vol 93 (2) ◽

pp. 162-164

Author(s):

V. A. Bapat ◽

P. Srinivasan

Keyword(s):

Differential Equation ◽

Partial Differential Equations ◽

Differential Equations ◽

Nonlinear Differential Equations ◽

Separation Of Variables ◽

Nonlinear Partial Differential Equations ◽

Nonlinear Partial Differential Equation ◽

Exact Methods ◽

Partial Differential ◽

Approximate Methods

A method for the solution of a certain class of nonlinear partial differential equations by the method of separation of variables is presented. The method enables the nonlinear partial differential equation to be reduced to ordinary nonlinear differential equations, which can be solved by exact methods (or by approximate methods if an exact solution is not possible).

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Magnetohydrodynamic bio-nano-convective slip flow with Stefan blowing effects over a rotating disc

Proceedings of the Institution of Mechanical Engineers Part N Journal of Nanomaterials Nanoengineering and Nanosystems ◽

10.1177/2397791419881580 ◽

2019 ◽

Vol 234 (3-4) ◽

pp. 83-97 ◽

Cited By ~ 3

Author(s):

Fatema Tuz Zohra ◽

Mohammed Jashim Uddin ◽

Md Faisal Basir ◽

Ahmad Izani Md Ismail

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Volume Fraction ◽

Nonlinear Partial Differential Equations ◽

Slip Flow ◽

Engineering Application ◽

Rotating Disc ◽

Partial Differential ◽

Similarity Transformations ◽

Wide Range

Microfluidic-related technologies and micro-electromechanical systems–based microfluidic devices have received applications in science and engineering fields. This article is the study of a mathematical model of steady forced convective flow past a rotating disc immersed in water-based nanofluid with microorganisms. The boundary layer flow of a viscous nanofluid is studied with multiple slip conditions and Stefan blowing effects under the magnetic field influence. The microscopic nanoparticles move randomly and have the characteristics of thermophoresis, and it is being considered that the change in volume fraction of the nanofluid does not affect the thermo-physical properties. The governing equations are nonlinear partial differential equations. At first, the nonlinear partial differential equations are converted to system of nonlinear ordinary differential equations using suitable similarity transformations and then solved numerically. The influence of relevant parameters on velocities, temperature, concentration and motile microorganism density is illustrated and explained thoroughly. This investigation indicated that suction provides a better medium to enhance the transfer rate of heat, mass and microorganisms compared to blowing. This analysis has a wide range engineering application such as electromagnetic micro pumps and nanomechanics.

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Nonlinear Partial Differential Equations and Related Problems of Pade Approximations.

10.21236/ada141519 ◽

1983 ◽

Author(s):

D. V. Chudnovsky ◽

G. V. Chudnovsky

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Padé Approximations ◽

Partial Differential ◽

Pade Approximations

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Numerical and Analytical Methods in Nonlinear Partial Differential Equations.

10.21236/ada185210 ◽

1987 ◽

Author(s):

Richard E. Ewing

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Analytical Methods ◽

Nonlinear Partial Differential Equations ◽

Partial Differential ◽

Numerical And Analytical Methods

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Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽

10.2298/fil1809347k ◽

2018 ◽

Vol 32 (9) ◽

pp. 3347-3354 ◽

Cited By ~ 1

Author(s):

Nematollah Kadkhoda ◽

Michal Feckan ◽

Yasser Khalili

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Exact Solutions ◽

Present Article ◽

Analytical Solutions ◽

Nonlinear Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Rational Functions ◽

Expansion Method ◽

Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

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Formation of Shocks for Nonlinear Partial Differential Equations of First Order

Proceedings of the Fourth International Colloquium on Differential Equations, Plovdiv, Bulgaria, 18–22 August 1993 ◽

10.1515/9783112318874-022 ◽

1994 ◽

pp. 199-204

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Partial Differential ◽

First Order

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Lyapunov-type inequalities for partial differential equations with 𝑝-Laplacian

Forum Mathematicum ◽

10.1515/forum-2020-0232 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Robert Stegliński

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Boundary Conditions ◽

Dirichlet Boundary ◽

Nonlinear Partial Differential Equations ◽

Dirichlet Boundary Conditions ◽

Partial Differential ◽

Linear Partial Differential Equations ◽

Lyapunov Inequalities ◽

Funct Anal

Abstract The aim of this paper is to extend results from [A. Cañada, J. A. Montero and S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal. 237 (2006), 1, 176–193] about Lyapunov-type inequalities for linear partial differential equations to nonlinear partial differential equations with 𝑝-Laplacian with zero Neumann or Dirichlet boundary conditions.

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Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water

Open Physics ◽

10.1515/phys-2020-0163 ◽

2020 ◽

Vol 18 (1) ◽

pp. 545-554

Author(s):

Asghar Ali ◽

Aly R. Seadawy ◽

Dumitru Baleanu

Keyword(s):

Wave Propagation ◽

Partial Differential Equations ◽

Differential Equations ◽

Longitudinal Wave ◽

Symbolic Computation ◽

Boussinesq Equation ◽

Nonlinear Partial Differential Equations ◽

Wave Model ◽

Simple Equation ◽

Partial Differential

AbstractThis article scrutinizes the efficacy of analytical mathematical schemes, improved simple equation and exp(-\text{Ψ}(\xi ))-expansion techniques for solving the well-known nonlinear partial differential equations. A longitudinal wave model is used for the description of the dispersion in the circular rod grounded via transverse Poisson’s effect; similarly, the Boussinesq equation is used for extensive wave propagation on the surface of water. Many other such types of equations are also solved with these techniques. Hence, our methods appear easier and faster via symbolic computation.

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