Stratified Flow of Micropolar Nanofluid over Riga Plate: Numerical Analysis

In this article, we present a numerical analysis of the energy and mass transport behavior of microrotational flow via Riga plate, considering suction or injection and mixed convection. The thermal stratified parameters of nanofluid are captured using an interpretation of the well-known Keller box model, which helps us to determine the characteristic properties of the physical parameters. The formulated boundary layer equations (nonlinear partial differential equations) are transformed into coupled ODEs with nonlinearities for the stratified controlled regimes. The impact of embedded flow and all physical quantities of practical interest, such as velocity, temperature, and concentration profile, are inspected and presented through tables and graphs. We found that the heat transfer on the surface decreases for the temperature stratification factor as mass transfer increases. Additionally, the fluid velocity increases as the modified Hartmann number increases.

Numerical simulation of time partial fractional diffusion model by Laplace transform

<abstract><p>In the present work, the authors developed the scheme for time Fractional Partial Diffusion Differential Equation (FPDDE). The considered class of FPDDE describes the flow of fluid from the higher density region to the region of lower density, macroscopically it is associated with the gradient of concentration. FPDDE is used in different branches of science for the modeling and better description of those processes that involve flow of substances. The authors introduced the novel concept of fractional derivatives in term of both time and space independent variables in the proposed FPDDE. We provided the approximate solution for the underlying generalized non-linear time PFDDE in the sense of Caputo differential operator via Laplace transform combined with Adomian decomposition method known as Laplace Adomian Decomposition Method (LADM). Furthermore, we established the general scheme for the considered model in the form of infinite series by aforementioned techniques. The consequent results obtained by the proposed technique ensure that LADM is an effective and accurate technique to handle nonlinear partial differential equations as compared to the other available numerical techniques. At the end of this paper, the obtained numerical solution is visualized graphically by Matlab to describe the dynamics of desired solution.</p></abstract>

The Classical Continuous Mixed Optimal Control of Couple Nonlinear Parabolic Partial Differential Equations with State Constraints

In this work, the classical continuous mixed optimal control vector (CCMOPCV) problem of couple nonlinear partial differential equations of parabolic (CNLPPDEs) type with state constraints (STCO) is studied. The existence and uniqueness theorem (EXUNTh) of the state vector solution (SVES) of the CNLPPDEs for a given CCMCV is demonstrated via the method of Galerkin (MGA). The EXUNTh of the CCMOPCV ruled with the CNLPPDEs is proved. The Frechet derivative (FÉDE) is obtained. Finally, both the necessary and the sufficient theorem conditions for optimality (NOPC and SOPC) of the CCMOPCV with state constraints (STCOs) are proved through using the Kuhn-Tucker-Lagrange (KUTULA) multipliers theorem (KUTULATH).

Solution Non Linear Partial Differential Equations By ZMA Decomposition Method

In this survey, viewed integral transformation (IT) combined with Adomian decomposition method (ADM) as ZMA- transform (ZMAT) coupled with (ADM) in which said ZMA decomposition method has been utilized to solve nonlinear partial differential equations (NPDE's).This work is very useful for finding the exact solution of (NPDE's) and this result is more accurate obtained with compared the exact solution obtained in the literature.

Traveling wave solutions for the extended modified KORTEWEG-DE VRIES equation

In this paper, we study an extended modified Korteweg-de Vries equation, which contains the relevant higher-order nonlinear terms and fifth-order dispersion. This equation is the extension of the modified Korteweg-de Vries equation and described by the Ablowitz-Kaup-Newell-Segur hierarchy. The standard Korteweg-de Vries equation is the pioneer integrable model in solitary waves theory, which gives rise to multiple soliton solutions. The Korteweg-de Vries equation arises naturally from shallow water, plasma physics, and other fields of science. To obtain exact solutions the sine-cosine method is applied. It is shown that the sine-cosine method provides a powerful mathematical tool for solving a great many nonlinear partial differential equations in mathematical physics. Traveling wave solutions are determined for extended modified Korteweg-de Vries equation. The study shows that the sine–cosine method is quite efficient and practically well suited for use in calculating traveling wave solutions for extended modified Korteweg-de Vries equation.

Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations

With the continuous development and progress of machinery and industry equipment, human-machine interface has become an important operation in industry equipment and has been widely used in aviation, monitoring, traffic, special engineering vehicles, and a series of complex fields. Through the human-machine interface information system, information and data are provided for operators s. As the human-machine interface information data of the mechanical equipment system are numerous, complex, and changeable, operators often make operation mistakes, misread and misjudge, and do not give timely feedback, resulting in task failure or, in serious cases, major mechanical faults and accidents. Therefore, the human-machine interface data information is screened, and the information useful for the operator is directly obtained according to the target set by the operator, so as to effectively solve the complex and changeable data information in the information system. Human-machine interface uses electronic communication technology, computer network technology, and database technology to expand and update machinery and industrial equipment. Among them, nonlinear partial differential equations comprise an important branch of equation in mathematics. In this paper, according to the nonlinear partial differential equations, we research and analyze the information system of the human-machine interface design field and solve the system of the cognitive load, which is too large, such as cognitive mismatch problem in the working mode of operating personnel, by satisfying the needs of different users. The human-machine interface of mechanical industrial equipment uses visual optimization design and innovation.

Nonlinear dynamical study to time fractional Dullian–Gottwald–Holm model of shallow water waves

This paper studies the exact traveling wave solutions to the nonlinear Dullin–Gottwald–Holm model which has the application in shallow-water waves in which the fractional derivative is considered in the sense of conformable derivative. Diverse exact solutions in hyperbolic, trigonometric and plane wave forms are obtained using two integration norms. For this purpose [Formula: see text]-expansion method and reccati mapping techniques are used. The 3D plots and their corresponding contour graphs are also depicted. Being concise and straightforward, the calculations demonstrate the effectiveness and convenience of the method for solving other nonlinear partial differential equations.

Numerical Analysis of Cu + Al 2 O 3 / H 2 O Hybrid Nanofluid of Streamwise and Cross Flow with Thermal Radiation Effect: Duality and Stability

The motion of water conveying copper and aluminum nanoparticles on a heated moving sheet when thermal radiation and stretching/shrinking surface is significant and is investigated in this study to announce the increasing effects of volume fractions, thermal radiation, and moving parameters on this transport phenomenon. Furthermore, the flow of a Cu − Al 2 O 3 /water hybrid nanofluid across a heated moving sheet has been studied in both cross and streamwise directions. Thermal radiation effect is also considered, as this effect along with cross flow has not yet been investigated for the hybrid nanofluid in the published literature. Two distinct types of nanoparticles, namely, Al 2 O 3 (alumina) and Cu (copper), have been used to prepare hybrid nanofluid where water is considered as a base fluid. The system of nonlinear partial differential equations (PDEs) has been transferred to ordinary differential equations (ODEs) by compatible transformations before solving them by employing the III-stage Lobatto-IIIa method in bvp4c solver in MATLAB 2017 software. Temporal stability analysis has been carried out in order to verify stable branch between two branches by obtaining the smallest eigenvalue values. The branches obtained are addressed in depth against every applied parameter using figures and tables. The results show that there are three ranges of branches, no solution exists when λ > λ c , dual branches exist when 0.23 ≤ λ ≤ λ c , and a single solution exists when λ > 0.23 . Moreover, thermal layer thickness declines initially and then enhances in the upper and lower solutions for the higher values of the thermal radiation parameter.