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1 – 10 of over 1000The purpose of this paper is to discuss the homoclinic breathe-wave solutions and the singular periodic solutions for (2 + 1)-dimensional generalized shallow water wave (GSWW…
Abstract
Purpose
The purpose of this paper is to discuss the homoclinic breathe-wave solutions and the singular periodic solutions for (2 + 1)-dimensional generalized shallow water wave (GSWW) equation.
Design/methodology/approach
The Hirota bilinear method, the Lie symmetry method and the non-Lie symmetry method are applied to the (2 + 1)D GSWW equation.
Findings
A reduced (1 + 1)D potential KdV equation can be derived, and its soliton solutions are also presented.
Research limitations/implications
As a typical nonlinear evolution equation, some dynamical behaviors are also discussed.
Originality/value
These results are very useful for investigating some localized geometry structures of dynamical behaviors and enriching dynamical features of solutions for the higher dimensional systems.
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The purpose of this paper is to highlight the effect of combined heat and mass transfer characteristics of magnetohydrodynamic (MHD) free convection flow of an electrically…
Abstract
Purpose
The purpose of this paper is to highlight the effect of combined heat and mass transfer characteristics of magnetohydrodynamic (MHD) free convection flow of an electrically conducting Newtonian fluid on circular cylinder with uniform heat/mass flux, taking into consideration the effects of uniform transverse magnetic field and thermal radiation.
Design/methodology/approach
An analysis is performed to study the momentum, combined heat and mass transfer characteristics of MHD free convection flow past a circular cylinder surface under the effect of thermal radiation with uniform heat and mass flux. By using Lie group method, the infinitesimal generators of governing equations are calculated. Using the resulting generators for the boundary value problem, the equations are transformed into an ordinary differential system. Numerical solutions of the outcoming non‐linear differential equations are found by using a combination of a Runge–Kutta algorithm and shooting technique.
Findings
Application of a magnetic field normal to the flow of an electrically conducting fluid gives rise to a resistive force that acts in the direction opposite to that of the flow. This resistive force tends to slow down the motion of the fluid along the cylinder and causes increases in its temperature and concentration and hence the respective changes in the wall shear stress, local Nusselt and Sherwood numbers as the magnetic parameter, respectively are changed with various values of angle which is measured in degrees from the front stagnation point on the surface. It is noted that these coefficients reduced as the magnetic parameter increases. Also, the effect of thermal radiation works as a heat source and so the quantity of heat added to the fluid increases, therefore the local Nusselt number reduced as the radiation parameter increases.
Research limitations/implications
An analysis is performed to study the momentum, combined heat and mass transfer characteristics of MHD free convection flow of an electrically conducting Newtonian fluid on circular cylinder with uniform heat/mass flux with the effects of uniform transverse magnetic field and thermal radiation.
Practical implications
This paper provides a very useful source of coefficient of heat and mass transfer values for engineers planning to transfer heat and mass by using electrically conducting gases with uniform heat/mass flux.
Originality/value
The combined heat and mass transfer of an electrically conducting gases on free convection flow in the presence of magneto and thermal radiation effects are investigated and can be used by different engineers working on industry, geothermal, geophysical, technological and engineering applications.
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Md. Jashim Uddin, O. Anwar Bég and Izani Md. Ismail
The purpose of this paper is to study two-dimensional nonlinear radiative-convective, steady-state boundary layer flow of non-Newtonian power-law nanofluids along a flat vertical…
Abstract
Purpose
The purpose of this paper is to study two-dimensional nonlinear radiative-convective, steady-state boundary layer flow of non-Newtonian power-law nanofluids along a flat vertical plate in a saturated porous medium taking into account thermal and mass convective boundary conditions numerically.
Design/methodology/approach
The governing equations are reduced to a set of coupled nonlinear ordinary differential equations with relevant boundary conditions. The transformed equations are then solved using the Runge-Kutta-Fehlberg fourth-fifth order numerical method with Maple 17 and Adomian decomposition method (ADM) in Mathematica.
Findings
The transformed equations are controlled by the parameter: power-law exponent, n; temperature ratio, Tr; Rosseland radiation-conduction, R; conduction-convection, Nc; and diffusion-convection, Nd. Temperature and nanoparticle concentration is enhanced with convection-diffusion parameter as are temperatures. Velocities are depressed with greater power-law rheological index whereas temperatures are elevated. Increasing thermal radiation flux accelerate the flow but to strongly heat the boundary layer. Very good correlation of the Maple solutions with previous stationary free stream and ADM solutions for a moving free stream, are obtained.
Practical implications
The study is relevant to high temperature nano-polymer manufacturing systems.
Originality/value
Lie symmetry group is used for the first time to transform the governing equations into a set of coupled nonlinear ordinary differential equations with relevant boundary conditions. The study is relevant to high temperature nano-polymer manufacturing systems.
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Jiaolong Wang, Chengxi Zhang and Jin Wu
This paper aims to propose a general and rigorous study on the propagation property of invariant errors for the model conversion of state estimation problems with discrete group…
Abstract
Purpose
This paper aims to propose a general and rigorous study on the propagation property of invariant errors for the model conversion of state estimation problems with discrete group affine systems.
Design/methodology/approach
The evolution and operation properties of error propagation model of discrete group affine physical systems are investigated in detail. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis which provide a deeper insight and are beneficial to the control and estimation of discrete group affine systems.
Findings
The investigation on the state independency and log-linearity of invariant errors for discrete group affine systems are presented in this work, and it is pivotal for the convergence and stability of estimation and control of physical systems in engineering practice. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis.
Practical implications
An example application to the attitude dynamics of a rigid body together with the attitude estimation problem is used to illustrate the theoretical results.
Originality/value
The mathematical proof and analysis of the state independency and log-linearity property are the unique and original contributions of this work.
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This study aims to introduce a variety of integrable Boussinesq equations with distinct dimensions.
Abstract
Purpose
This study aims to introduce a variety of integrable Boussinesq equations with distinct dimensions.
Design/methodology/approach
The author formally uses the simplified Hirota’s method and lump schemes for exploring lump solutions, which are rationally localized in all directions in space.
Findings
The author confirms the lump solutions for every model illustrated by some graphical representations.
Research limitations/implications
The author examines the features of the obtained lumps solutions.
Practical implications
The author presents a variety of lump solutions via using a variety of numerical values of the included parameters.
Social implications
This study formally furnishes useful algorithms for using symbolic computation with Maple for the determination of lump solutions.
Originality/value
This paper introduces an original work with newly useful findings of lump solutions.
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Naveed Ahmed, Umar Khan and Syed Tauseef Mohyud-din
The aim of this manuscript is to study the flow of a nanofluid through a porous channel under the influence of a transverse magnetic field. Permeability of the walls is…
Abstract
Purpose
The aim of this manuscript is to study the flow of a nanofluid through a porous channel under the influence of a transverse magnetic field. Permeability of the walls is considered to be different, which results in an asymmetric nature of the flow. The height of the channel is variable, and it dilates or squeezes at a uniform rate.
Design/methodology/approach
A numerical solution (Runge–Kutta–Fehlberg) has been obtained after reducing the governing equations to a system of nonlinear ordinary differential equations using some suitable similarity transforms, both in time and space.
Findings
An increase in absolute values of the permeability parameter results in an enhanced mass transfer rate at both the walls, while the rate of heat transfer also increases at the lower wall. Few graphs are also dedicated to see the behavior of Nusselt and Sherwood numbers following the variations in flow parameters.
Originality/value
A pictorial description of the flow and effects of emerging parameters on the temperature and nanoparticle concentration profiles is presented to analyze the flow behavior. It is established that the asymmetry of the channel affects the flow quite significantly.
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The aim of this study is to offer a contemporary approach for getting optical soliton and traveling wave solutions for the Date–Jimbo–Kashiwara–Miwa equation.
Abstract
Purpose
The aim of this study is to offer a contemporary approach for getting optical soliton and traveling wave solutions for the Date–Jimbo–Kashiwara–Miwa equation.
Design/methodology/approach
The approach is based on a recently constructed ansätze strategy. This method is an alternative to the Painleve test analysis, producing results similarly, but in a more practical, straightforward manner.
Findings
The approach proved the existence of both singular and optical soliton solutions. The method and its application show how much better and simpler this new strategy is than current ones. The most significant benefit is that it may be used to solve a wide range of partial differential equations that are encountered in practical applications.
Originality/value
The approach has been developed recently, and this is the first time that this method is applied successfully to extract soliton solutions to the Date–Jimbo–Kashiwara–Miwa equation.
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The purpose of this paper is to study the applications of Lie symmetry method on the boundary value problem (BVP) for nonlinear partial differential equations (PDEs) in fluid…
Abstract
Purpose
The purpose of this paper is to study the applications of Lie symmetry method on the boundary value problem (BVP) for nonlinear partial differential equations (PDEs) in fluid mechanics.
Design/methodology/approach
The authors solved a BVP for nonlinear PDEs in fluid mechanics based on the effective combination of the symmetry, homotopy perturbation and Runge–Kutta methods.
Findings
First, the multi-parameter symmetry of the given BVP for nonlinear PDEs is determined based on differential characteristic set algorithm. Second, BVP for nonlinear PDEs is reduced to an initial value problem of the original differential equation by using the symmetry method. Finally, the approximate and numerical solutions of the initial value problem of the original differential equations are obtained using the homotopy perturbation and Runge–Kutta methods, respectively. By comparing the numerical solutions with the approximate solutions, the study verified that the approximate solutions converge to the numerical solutions.
Originality/value
The application of the Lie symmetry method in the BVP for nonlinear PDEs in fluid mechanics is an excellent and new topic for further research. In this paper, the authors solved BVP for nonlinear PDEs by using the Lie symmetry method. The study considered that the boundary conditions are the arbitrary functions Bi(x)(i = 1,2,3,4), which are determined according to the invariance of the boundary conditions under a multi-parameter Lie group of transformations. It is different from others’ research. In addition, this investigation will also effectively popularize the range of application and advance the efficiency of the Lie symmetry method.
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Fakhar Kamran, Chen Zu‐Chi, Ji Xiaoda and Yi Cheng
Providing a much easier (direct) approach to calculate the Lie point symmetries of (3 + 1) unsteady Navier‐Stokes equations for viscous, incompressible flow in cylindrical polar…
Abstract
Purpose
Providing a much easier (direct) approach to calculate the Lie point symmetries of (3 + 1) unsteady Navier‐Stokes equations for viscous, incompressible flow in cylindrical polar coordinates.
Design/methodology/approach
Lie group theory, is applied to the equations of motion. Symmetries obtained through a direct approach are then used to reduce (3 + 1) Navier‐Stokes system to a system of ordinary differential equations.
Findings
We observed that the approach applied here to calculate the symmetries of the group is entirely straightforward and involves less calculation as compared to the computer programs such as LIE, Symmgrp.max (MACSYMA) or other symbolic manipulation systems. Further, results obtained here will be practical and useful in comprehending the fluid flow behavior.
Research limitations/implications
We only obtained the exact solution through basic transformations (translation and scaling). The similarity reduction through other subalgebras (finite and infinite dimensions) can be used to explore more facts about the Navier‐Stokes equations.
Originality/value
Direct approach provided in this paper can be utilized to achieve symmetries of other physically important PDEs.
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Keywords
Jing‐li Fu, Li‐qun Chen and Xiang‐wei Chen
In this letter, based on the infinitesimal transformations with respect to the generalized coordinates and generalized momentums, we obtain the definition, determining equations…
Abstract
In this letter, based on the infinitesimal transformations with respect to the generalized coordinates and generalized momentums, we obtain the definition, determining equations and structure equation of the momentum‐dependent symmetry for the systems. This study directly leads to the non‐ Noether type conserved quantity for the systems. Further we also give the inverse issue of the momentum‐dependent symmetries of the systems. However, a theory of momentum‐dependent symmetries of the nonconservative Hamiltonian systems is established. Finally, an example is discussed to illustrate the results.
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