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To find periodic solutions of nonlinear equations, the Jacobi elliptic function expansion method is used. This strategy is more extensive than expanding the hyperbolic tangent series. This approach can produce periodic shock wave solutions such as solitary wave solutions. [ABSTRACT FROM AUTHOR]

Heat transfer is an important phenomenon in the industrial sector. Thus, the simulation is made to compute the distribution of heat in a rectangular channel in this paper. A heated rod is inserted at the center of the rectangular channel. The fluid flowing in the rectangular channel is considered to be a viscous fluid. Navier–Stokes equations of motion for laminar flow are used. The medium for the fluid motion is considered to be a porous medium. Heat transfer is computed for nonlinear two-dimensional incompressible and unsteady flows. The Fourier's law of heat conduction is used for the transmission of heat in the rectangular channel. The Finite Element Method (FEM) is applied to the solution of the problem. For different values of the permeability parameter, Prandtl number and Rayleigh number, the graphic solution for the velocity and temperature fields is shown. [ABSTRACT FROM AUTHOR]

Partial differential equations may explain anything from planetary movement to tectonic plate, yet it is notoriously difficult to resolve them. Turbulence is present in nearly all fluid flows, and pure laminar flow is extremely unusual in practice. The Large Eddy Simulation (LES) computational model is employed for the simulation of turbulence flow on a spillway having four inlets with a single outlet. Such flows are observed at hydroelectric power dams all over the world. The fluctuated flows produced a large amount of energy in terms of electricity that costs a very low amount compared to the energy obtained in tidal power sectors. In the production of hydropower energy, the flow simulation is of great interest. This paper focuses on the study of turbulence kinetic energy with the help of a LES model. The spillway considered in this paper contains four inlets and a single outlet. The four inlets will allow more flow which will insert more pressure nearer the outlet. The kinetic energy is computed at the inlets and outlet in the turbulent flow. The fluctuated velocity along with the mean velocity at the inlets and outlet is also computed along with the pressure. The C++-based programming is made, which is simulated in Open-source Field Operation and Manipulation (OpenFOAM). The graphs are presented for a better understanding of readers. [ABSTRACT FROM AUTHOR]

Theoretical analysis of heat transfer plays a vital role in updating the quality of heat exchanger products. Experiments cost more compared to computational costs. In this direction, this work is concerned with the unsteady and incompressible fluid flow with a rod inside a square cavity. The disturbance in the flow is induced by the motion of the top and bottom walls of the cavity. The maximum fluid flow will arise, which will help in reducing the temperature of the heated wall or rod in any physical situation. A single wall is considered to be heated, which produces heat in the neighboring fluid layers. A rod is placed to reduce the motion of the heated fluid coming from the heated wall at a high-temperature. The transmission of thermal energy along with fluid flow is carried out using the energy equation and the Navier–Stokes equation of motion, respectively. These equations are transformed to dimensionless form by appropriate parametrization and solved using the finite element method for different parameters such as Rayleigh number and Prandtl number, temperature and velocity fields and are presented graphically [ABSTRACT FROM AUTHOR]

In this study, the impact of Newtonian heating is incorporated into a two-dimensional ferrofluid. The flowing chemically reactive species of ferromagnetic fluid fluids. By virtue of this property, such fluids are necessary for heat transfer in engineering equipment and devices. The main focus of flowing fluids in these devices is to enhance the transfer of heat and decrease friction drag at the surface. Thus, the paper focuses on the analysis of the rate of heat transfer via Fourier's law. The fluid in the problem is taken to be a viscous fluid containing chemically reactive species. Chemically reactive species consist of two or more base fluids. Therefore, the main interest is in watching the heat transfer impacts on the ferromagnetic fluid. This is important in the presence of chemically reactive species. The results obtained are shown to be in excellent agreement in specific cases available in literature. [ABSTRACT FROM AUTHOR]

A heat exchanger is a device that transmits heat energy from one object to another, or within the same object. Examples of heat exchanger include a boiler, an oven and a cooker. Experimental techniques for testing these devices make it more costly and time-consuming. Consequently, computational fluid dynamics (CFD) can manage heat exchanger systems and their performance with ease. The actual impacts of what is being examined may then be predicted computationally which yields a precise output with approximate results. The designed geometry includes a rectangular duct with an inlet, outlet and two obstacles of equal height. The Navier–Stokes equations for the fluid flow are used. During the meshing process, the continuous geometric space of an item is divided into thousands or more forms, which helps to correctly identify the object's physical shape. The desired model is computed numerically. Finite volume method (FVM) is used to study the results at a low Reynolds number (around 2. 3 × 1 0 6). The goal is to theoretically analyze the transmission of heat and fluid resistance to the flow. The CFD findings with experimental data are compared to confirm the model predictions. A CFD model based on the FVM and experimental data from a flow cell is used to study how fluid moves through ducts. This study focuses on the pressure, velocity and temperature fields of a fluid moving through a rectangular duct. As the top wall fluid temperature rises, the temperature distribution changes. Increasing fluid flow declines the temperature distribution. Temperature distribution grows with duct heat flow. As the flow rate rises, so does dispersion. Furthermore, as flow rate and velocity distribution drop, pressure distribution rises. [ABSTRACT FROM AUTHOR]

Practically speaking, fluid flow in round and noncircular nozzle is a very regular occurrence. The cold and hot water used in our homes is delivered to us via pipes. Water is delivered throughout the city via large pipe networks. Large pipelines carry natural gas and oil hundreds of kilometres from one place to another. During the operation of an engine, cooling water is carried by hoses to the radiator's pipes, in which it is cooled as it travels. Experimentally, we detected the results of the model because there is no restriction on the application of experimental research to a certain sector or kind of concept. It may be used for a broad range of events and circumstances. Under parabolic velocity conditions, fluid (Water Pr 6.9) flows from the inlet position. The top and bottom walls of the rectangular nozzle are also moving at the same velocity as they are at the inlet position. Due to the movement of the walls, fluid is compressed in the particular region and also exhibits the same parabolic behavior. The solution of the coupled equations is determined by using the Finite Volume Method (FVM). When partial differential equations are expressed as algebraic equations, the FVM may be used to evaluate them. It can be used to evaluate elliptic, parabolic, and hyperbolic partial differential equations. Using FVM, it is necessary to know the values (and derivatives) of multiple variables at the cell faces, when the values (and derivatives) of these variables are only known at the cell centres. When determining these variables for convective terms, it is common to take the direction of the flow into consideration. The numerical results of the velocity and the pressure could be seen in the rectangular nozzle. [ABSTRACT FROM AUTHOR]

According to new research, methane emissions contribute 25 percent more to global warming than previously assumed. Methane is a crucial precursor gas of tropospheric ozone, a dangerous air pollutant. Methane emissions are responsible for almost half of the reported growth in tropospheric ozone levels on a global scale. But it plays a vital role as an energy source, therefore, the study of methane cut reservoirs is essential. The injection of air can extract additional energy in high methane-cut reservoirs. The analysis is made to compute the theoretical potential of low air flooding in high methane-cut reservoirs. Computational Fluid Dynamics (CFD) is used to study the impact of injecting air on methane. The presence of carbon dioxide and oxygen when injected into the methane cut reservoir produces high-pressure air injection that may cause significant safety damage such as the potential for corrosion or explosion. Past field studies and reported solutions indicate that there are no insurmountable problems in the execution of high-pressure air injection. The results are harmful and need to take useful safety precautions for the engineers who are interested in experiments. The users of CFD use mathematical laws and models that exactly represent the phenomenon they are dealing with. The pressure induced by the air injection is simulated with the help of the Finite Volume Method (FVM). The velocity field near the outlet arises as higher pressure of air from the inlet is observed, whereas, the pressure near the outlet declines. The findings of this study can help for better understanding of outflow of methane from methane reservoirs. [ABSTRACT FROM AUTHOR]

This paper examines nonlinear partial differential equation (PDE) solutions. Scientists and engineers have struggled to solve nonlinear differential equations. Nonlinear equations arrive in nearly all problems in nature. There are no well-established techniques for solving all nonlinear equations, and efforts have been made to enhance approaches for a specific class of problems. Keeping this in mind, we shall investigate the perturbation method's efficiency in solving nonlinear PDEs. Several techniques work well for diverse issues. We recognize that there may be several solutions to a given nonlinear issue. Methods include homotropy analysis, tangent hyperbolic function, factorization and trial function. However, some of these strategies do not cover all nonlinear issue solutions. In this paper, we use the perturbation technique to solve the zeroth-order Airy equation and also find the Bessel function in the first-order nonhomogeneous differential equation by using self-similar solutions that appears in modified Korteweg–de Vries (KdV) equation. This approach will be used for nonlinear equations in physics and applied mathematics. [ABSTRACT FROM AUTHOR]