Cumulative Impact of Micropolar Fluid and Porosity on MHD Channel Flow: A Numerical Study

The mass and heat transfer magnetohydrodynamic (MHD) flows have a substantial use in heat exchangers, electromagnetic casting, X-rays, the cooling of nuclear reactors, mass transportation, magnetic drug treatment, energy systems, fiber coating, etc. The present work numerically explores the mass and heat transportation flow of MHD micropolar fluid with the consideration of a chemical reaction. The flow is taken between the walls of a permeable channel. The quasi-linearization technique is utilized to solve the complex dynamical coupled and nonlinear differential equations. The consequences of the preeminent parameters are portrayed via graphs and tables. A tabular and graphical comparison evidently reveals a correlation of our results with the existing ones. A strong deceleration is found in the concentration due to the effect of a chemical reaction. Furthermore, the impact of the magnetic field force is to devaluate the mass and heat transfer rates not only at the lower but at the upper channel walls, likewise.

Analytical solution of a class of nonlinear differential equations of the third order in the complex area

В работе приводится доказательство теоремы существования и единственности аналитического решения класса нелинейных дифференциальных уравнений третьего порядка, правая часть которого представлена полиномом шестой степени, в комплексной области. Расширен класс рассматриваемых уравнений за счет новой замены переменных. Получена априорная оценка аналитического приближенного решения. Представлен вариант численного эксперимента оптимизации априорных оценок с помощью апостериорных. The article presents a proof of the theorem of the existence and uniqueness of the analytical solution of the class of nonlinear differential equations of the third order, with a polynomial right-hand side of the sixth degree, in the complex domain. The class of the considered equations has been extended by means of a new change of variables. An a priori estimate of the analytical approximate solution is obtained. A variant of the numerical experiment of optimizing a priori estimates using a posteriori estimates is presented.

FORCE DRIVEN VIBRATIONS OF NONLINEAR PLATES ON A VISCOELASTIC WINKLER FOUNDATION UNDER THE HARMONIC MOVING LOAD

In the present paper, the forced driven nonlinear vibrations of an elastic plate in a viscoelastic medium and resting on a viscoelastic Winkler-type foundation are studied. The damping features of the surrounding medium and foundation are described by the Kelvin-Voigt model and standard linear solid model with fractional derivatives, respectively. The dynamic response of the plate is described by the set of nonlinear differential equations with due account for the fact that the plate is being under the conditions of the internal resonance accompanied by the external resonance. The expressions for the stress function and nonlinear coefficients for different types of boundary conditions are presented.

THE TECHNOLOGY OF WINTER CONCRETING OF MONOLITHIC FRAME STRUCTURES WITH SUBSTANTIATION OF HEAT TREATMENT MODES BY SOLUTIONS OF THE DIFFERENTIAL EQUATION OF THERMAL CONDUCTIVITY OBTAINED BY THE METHOD OF GROUP ANALYSIS

An innovative method for calculating thermal fields inside monolithic structures has been developed, based on the use and analysis of nonlinear differential equations. The innovativeness of the method lies in the approach to the analysis of nonlinear physical processes using nonlinear differential equations. Thanks to the method of group analysis, 13 expressions are obtained from complex mathematical equations, which are easy to use and depend on several empirical coefficients. It is assumed that this calculation method is a priori more accurate than the existing ones, as well as available to people at a construction site without higher mathematical education, which makes it a priority for research. The applicability of this method must be proven by linking empirical coefficients and variables to the conditions of the experiments, while obtaining reliable data that will turn out to be more accurate than the existing calculation methods. This article demonstrates a systematic approach to establishing the suitability of using the method of group analysis of differential equations for problems of winter concreting on the basis of laboratory experiments under stationary conditions. The equations were subject to verification, which, according to the physical description, correspond to the real conditions of the course of thermal processes inside monolithic structures. Based on the obtained processing results, it was decided that it was necessary to further study the innovative method in the conditions of the construction site, but only for some expressions that showed the best results at the stage of laboratory tests.

A Reliable Treatment for Nonlinear Differential Equations

In this paper, we use the concept of homotopy, Laplace transform, and He’s polynomials, to propose the auxiliary Laplace homotopy parameter method (ALHPM). We construct a homotopy equation consisting on two auxiliary parameters for solving nonlinear differential equations, which switch nonlinear terms with He’s polynomials. The existence of two auxiliary parameters in the homotopy equation allows us to guarantee the convergence of the obtained series. Compared with numerical techniques, the method solves nonlinear problems without any discretization and is capable to reduce computational work. We use the method for different types of singular Emden–Fowler equations. The solutions, constructed in the form of a convergent series, are in excellent agreement with the existing solutions.

Inherent Irreversibility of Mixed Convection within Concentric Pipes in a Porous Medium with Thermal Radiation

This work investigated the thermal putrefaction and inherent irreversibility in a steady flow of an incompressible inconstant viscosity radiating fluid within two concentric pipes filled with a porous medium. Following the Brinkmann-Darcy-Forchheimer approach, the nonlinear differential equations governing the model were obtained. The model boundary value problem was addressed numerically via a shooting quadrature with the Runge-Kutta-Fehlberg integration scheme. The effects of diverse emerging parameters on the fluid velocity, temperature, skin friction, Nusselt number, entropy generation rate and the Bejan number are provided in graphs and discussed in this paper.

College Students’ Mental Health Climbing Consumption Model Based on Nonlinear Differential Equations

College students continue to improve their consumption levels due to compassion or vanity, but it not only increases the financial burden of the family, but is also not conducive to their personal health. In order not to affect the mental health of college students, to solve the problem of mutual comparison consumption, this paper establishes differential equation models to describe this phenomenon, from qualitative and quantitative angles to interpret and predict the results of comparison consumption. The results show that the current consumption behaviour of college students also has a reasonable place for being unreasonable, mainly from college students’ own and living environment.