Solutions of the system of differential equations by differential transform method

Nanofluid flow and heat transfer between parallel plates considering Brownian motion using DTM

The use of variational iteration method, differential transform method and adomian decomposition method for solving different types of nonlinear partial differential equations

Magnetic field effect on unsteady nanofluid flow and heat transfer using Buongiorno model

Recently differential transform method (DTM) has been used to solve various partial differential equations. In this paper, an alternative approach called the reduced differential transform method (RDTM) is presented to overcome the demerit of complex calculation of differential transform method. Comparing the methodology with some known techniques shows that the present approach is effective and powerful. In addition, three test problems of mathematical physics are discussed to illustrate the effectiveness and the performance of the reduced differential transform method.

Reduced Differential Transform Method for Partial Differential Equations

The reasons why mechanical stirring tanks are extensively applied to fermentation, gas absorption, waste water treatment and so on are because of its advantages of easily modified operating conditions, effective liquid separation and many more. Its primary function is to effectively separate liquid so as to boost the liquid flowing efficiency. The paper is mainly focused on analyzing the two-dimensional flow field of mixing blades of different sizes at dissimilar rotational speed. The result shows that the baffles of longer length will easily lead to instability of the flow field. However, we also find out that the longer the tank baffle is, the easier the eddy currents will occur, and the pressure generated by the tank baffle is greater as well. It is easier to mix liquids evenly if the length of a mixing blade is longer.

Flow field analysis of different types of blade and baffle in a fermentor

This paper studies the nonlinear dynamic behavior and bifurcation of a rigid rotor supported by relative short spherical aerodynamic journal bearings. The modified Reynolds equation is solved by a hybrid numerical method combined with the differential transformation method and the finite difference method. The analytical results reveal a complex dynamic behavior including periodic, sub-harmonic, and quasi-periodic responses of the rotor center. Furthermore, the results reveal the changes which take place in the dynamic behavior of the bearing system as the rotor mass and bearing number increase. The current analytical results are found to be in good agreement with those of other numerical methods. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of relative short spherical aerodynamic rotor-bearing systems.

https://iopscience.iop.org/article/10.1088/1742-6596/96/1/012099/pdf

Bifurcation analysis of a relative short spherical aerodynamic journal bearing system

Creative Mechanism Design on Hospital-Bed Rails

Many studies have been shown and focused that variation of the quantity of vasoconstriction and blood pressure will cause the nonlinear chaotic behaviors in the heart blood vessel system and then induce the cardiovascular effect. Due to this kind of non-periodic motion is random and difficult to control, it is important to analyze and understand the status of dynamic system under different parametric conditions. In this paper, the differential transformation method is used to investigate the governing equations of system, and the dynamic behavior is characterized by reference to bifurcation diagrams, phase portraits, power spectra, and Poincare map produced. The results indicate that the system behavior is significantly dependent on the magnitude of the vibrational amplitude. Specifically, the motion changes from T-periodic to 2T-periodic, then from 4T-periodic to 8-periodic, and finally to chaotic motion with windows of periodic motion as the vibrational amplitude is increased from 0.3 to 0.6. The results can be used as the basis for subsequent development of the control system design, and also reduced the possibility of cardiopathy.

Bifurcation and nonlinear dynamic analysis of heart blood vessel system

This paper employs a numerical method combining the differential transformation method and the finite difference method to study the bifurcation behavior of a rigid rotor supported by a micro gas bearing system. The numerical results reveal a complex dynamic behavior comprising periodic, sub-harmonic, and quasi-periodic responses of the rotor center. Furthermore, the results reveal the changes which take place in the dynamic behavior of the bearing system as the bearing number is increased. The current analytical results are found to be in good agreement with those of other numerical methods. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of micro gas film rotor-bearing systems.

Ming-Jyi Jang

Papers

Flow field analysis of different types of blade and baffle in a fermentor

Bifurcation analysis of a relative short spherical aerodynamic journal bearing system

Creative Mechanism Design on Hospital-Bed Rails

Bifurcation and nonlinear dynamic analysis of heart blood vessel system

Influence of the bearing number on micro gas bearing system