Oscillatory Flow of LDL-C and Blood Fluid through a Slanted Channel with Heat within the Sight of Magnetic Field

In this research, we investigated LDL-C and blood movement through a slanted channel with heat within the sight of magnetic field. In the evaluation, mathematical models for the LDL-C and blood stream and energy transfer were developed as partially coupled arrangement of partial differential equation (PDEs), the PDEs were scaled utilizing the dimensionless variables to dimensionless ordinary differential equation, they are further reduced to perturbed differential equations (ODEs) utilizing the perturbation parameters including the oscillatory term, where the non-homogenous equation and conditions are solved straightforwardly utilizing the technique for undetermined coefficient. The velocity and temperature profiles are gotten for certain overseeing boundaries included, and Mathematica codes were created utilizing simulate the impact of entering parameters on the profile. It is seen that the overseeing boundaries impacted that the entering pertinent parameters influences blood flow and it helps it controlling the LDL-C concentration, aiding treatment of atherosclerosis.

Steady Magnetohydrondynamic Natural Convection Coutte Flow With Variable Electrical Conductivity

The steady MAGNETOHYDRODYNAMIC natural convection coutte flow of viscous incompressible and electrically conducting fluid having variable electrical conductivity between two parallel plates when one of the plate is set into motion is studied. The dimensionless differential equations as well as energy equations are solved analytically using the method of undetermined coefficient. The analytical solution are presented numerically inform of line graphs given interms of velocity and skin friction. The result reveal that the effect of the Hartmann number and grashof number are to reduce and increase the velocity respectively. Similarly the skin friction on the moving and stationary plates increase with Grashof number and decreases with increase in Hartmann, a comparetive study review that the effect of Hartmann number and grashof number on velocity and skin friction are same.

ON THE RESPONSE OF VIBRATION ANALYSIS OF BEAM SUBJECTED TO MOVING FORCE AND MOVING MASS

In this paper, vibration of beam subjected to moving force and moving mass is considered. Finite Fourier Sine transform with method of undetermined coefficient is used to solve the governing partial differential equation of order four. It was found that the response amplitude increases as the mass of the load increases for the case of moving mass while the response amplitude for the case of moving mass is not affected by increase in mass of the load. Also analysis shows that the response amplitude for the case of moving force is greater than that of moving mass.

Prediction Model of Minimum Void Ratio for Various Sizes/Shapes of Sandy Binary Mixture

The minimum void ratio is a fundamental physical index for evaluating particle properties in soil mechanics, ceramic processing, and concrete mixes. Previous research found that both particle size distribution and particle shape characteristics would affect minimum void ratio, while the current research generally uses a linear model to estimate the minimum void ratio of a binary mixture, ignoring quantitative effect of particle shape on the minimum void ratio. Based on a study of binary mixtures of natural sand from three different origins and iron particles of two different shapes, this paper analyzes the influence factors of the minimum void ratio, and a quadratic nonlinear model is proposed for estimating the minimum void ratio of binary mixture. The model contains only one undetermined coefficient, a, the value of which is correlated to the particle sphericity, particle size, and particle size ratio. A theoretical calculation formula for the coefficient a is proposed to quantitatively analyze the effects of these three factors on the size of the parameters. In the end, the model is used to estimate the minimum void ratios of sand and substitute particles from different producing areas; the average difference between the estimated values and the fitted values is about 2.03%, suggesting that the estimated values of the model fit well with the measured data.

SOLUSI DARI PERSAMAAN CAUCHY–EULER NONHOMOGEN KASUS LOGARITMIK

Ordinary differential equation is one form of differential equations that are often found in everyday life. One form of ordinary differential equations which has non–constant coefficients is the Cauchy–Euler differential equation. In the nonhomogeneous Cauchy–Euler differential equations, the undetermined coefficient and the parameter variation were the most method that often used to find the particular solution. This paper aimed to show a new solution that was shorter than the previous methods for nonhomogeneous Cauchy–Euler differential equations with the right side was a logarithmic form. The new solution had been proven to produce the same solution as the ordinary solution sought using the undetermined coefficient method.

Comparison of the Probabilistic Ant Colony Optimization Algorithm and Some Iteration Method in Application for Solving the Inverse Problem on Model With the Caputo Type Fractional Derivative

This paper presents the algorithms for solving the inverse problems on models with the fractional derivative. The presented algorithm is based on the Real Ant Colony Optimization algorithm. In this paper, the examples of the algorithm application for the inverse heat conduction problem on the model with the fractional derivative of the Caputo type is also presented. Based on those examples, the authors are comparing the proposed algorithm with the iteration method presented in the paper: Zhang, Z. An undetermined coefficient problem for a fractional diffusion equation. Inverse Probl. 2016, 32.

Exact Combined Solutions for the (2+1)-Dimensional Dispersive Long Water-Wave Equations

The homogeneous balance of undetermined coefficient (HBUC) method is presented to obtain not only the linear, bilinear, or homogeneous forms but also the exact traveling wave solutions of nonlinear partial differential equations. Linear equation is obtained by applying the proposed method to the (2+1)-dimensional dispersive long water-wave equations. Accordingly, the multiple soliton solutions, periodic solutions, singular solutions, rational solutions, and combined solutions of the (2+1)-dimensional dispersive long water-wave equations are obtained directly. The HBUC method, which can be used to handle some nonlinear partial differential equations, is a standard, computable, and powerful method.

Bending and vibration of a discontinuous beam with a curvic coupling under different axial forces

The transverse stiffness and vibration characteristics of discontinuous beams can significantly differ from those of continuous beams given that an abrupt change in stiffness may occur at the interface of the former. In this study, the equations for the deflection curve and vibration frequencies of a simply supported discontinuous beam under axial loads are derived analytically on the basis of boundary, continuity, and deformation compatibility conditions by using equivalent spring models. The equation for the deflection curve is solved using undetermined coefficient methods. The normal function of the transverse vibration equation is obtained by separating variables. The differential equations for the beam that consider moments of inertia, shearing effects, and gyroscopic moments are investigated using the transfer matrix method. The deflection and vibration frequencies of the discontinuous beam are studied under different axial loads and connection spring stiffness. Results show that deflection decreases and vibration frequencies increase exponentially with increasing connection spring stiffness. Moreover, both variables remain steady when connection spring stiffness reaches a considerable value. Lastly, an experimental study is conducted to investigate the vibration characteristics of a discontinuous beam with a curvic coupling, and the results exhibit a good match with the proposed model.

Experimental and Theoretical Study on the Critical Breaking Velocity of Marine Natural Gas Hydrate Sediments Breaking by Water Jet

Water jet technology is a key technology in the marine natural gas hydrate (NGH) solid fluidization mining method. As an important parameter in water jet breaking NGH sediments technology, the critical breaking velocity of NGH sediments is unknown. In the present research, an orthogonal design experiment is carried out to study the critical velocity of NGH breakage by water jet, using frozen soil and sand as experimental samples. First, the time it takes to reach maximum NGH breaking depth is determined. Then, ultimate breaking distance is studied with respect to the NGH saturation, jet pressure, and nozzle diameter. Following that, the variation of critical velocity with NGH saturation is analyzed. Eventually, a formula to calculate the critical velocity for marine NGH breakage by water jet process is established, and the undetermined coefficient (η) in the formula is calibrated with the experiment data. The results show that the ultimate breaking distance is mostly achieved within 63 s. The three experimental factors in order of the effect on the ultimate breaking depth (from high to low) are NGH saturation, jet pressure, and nozzle diameter. The critical velocities for marine NGH breakage corresponding to the NGH saturations of 20%, 40,%, 6%, and 80% are 5.71 m/s, 7.14 m/s, 9.60 m/s, and 10.85 m/s, respectively. The undetermined coefficient η in critical velocity formula is 1.44 m/s.