integral transform
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Samira Moradi ◽  
Keivan Shayesteh ◽  
Qasem Mohammad

Background: This study aimed to investigate the effect of the hydrodynamic condition on the release rate of urea/acetylated lignin sulfonate (Ac-LS) matrix as slow-release fertilizers (SRFs). Therefore, two models were developed using the mass transfer balance for the finite/infinite volume of fluids, solving finite integral transform/separation of a variable. In these models, the Biot number that verified the hydrodynamic condition appeared. Methods: In the experimental section, the urea/Ac-LS matrix fertilizer was produced. The morphological, thermal, chemical, and mechanical properties of the LS, Ac-LS, urea, and urea/Ac-LS matrix were analyzed using Fe-SEM, TGA, XRD, and SANTAM. Finally, the nitrogen release of the matrix fertilizer was investigated at 25°C for different impeller speeds. Results: The results showed that the thermal and mechanical resistance of urea/Ac-LS, with strong interaction, increased rather than pure urea or Ac-LS. The models were also validated using experimental data. The results further showed that in both states, the external resistance of the mass transfer decreased with increasing impeller speed, and the nitrogen release rate increased with increasing Biot number. Conclusion: It was also observed that, in a given hydrodynamic condition, initially, the release rate in the finite environment was less than the infinite; however, after a while, the type of environment did not affect the release rate

Xing Zhao ◽  
JinXi Liu ◽  
ZhengHua Qian ◽  
CunFa Gao

Magnetoelectric (ME) sandwich structure is a common form in device applications. Poling directions of component materials are essential for the improvement of ME device properties. In this paper, the effects of the electric and magnetic poling directions on the interface fracture of a ME sandwich structure are investigated by integral transform and singular integral equation techniques. The expressions of the normalized stress intensity factors (NSIFs) are derived, and some numerical examples are presented. It is found that the poling direction of active layer can greatly affect the interface cracking mode. And the crack propagation can be promoted or impeded by adjusting the applied field. The structure with a larger volume fraction of active material will be more likely to crack.

Symmetry ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 50
Aliaa Burqan ◽  
Rania Saadeh ◽  
Ahmad Qazza

In this article, a new, attractive method is used to solve fractional neutral pantograph equations (FNPEs). The proposed method, the ARA-Residual Power Series Method (ARA-RPSM), is a combination of the ARA transform and the residual power series method and is implemented to construct series solutions for dispersive fractional differential equations. The convergence analysis of the new method is proven and shown theoretically. To validate the simplicity and applicability of this method, we introduce some examples. For measuring the accuracy of the method, we make a comparison with other methods, such as the Runge–Kutta, Chebyshev polynomial, and variational iterative methods. Finally, the numerical results are demonstrated graphically.

Xuqiong Luo ◽  
Na Yang ◽  
Qingshan Tong

In this paper, a singularly perturbed convection–diffusion equation is studied. At first, the original problem is transformed into a parameterized singularly perturbed Volterra integro-differential equation by using an integral transform. Then, a second-order finite difference method on an arbitrary mesh is given. The stability and local truncation error estimates of the discrete schemes are analyzed. Based on the mesh equidistribution principle and local truncation error estimation, an adaptive grid algorithm is given. In addition, in order to calculate the parameters of the transformation equation, a nonlinear unconstrained optimization problem is constructed. Numerical experiments are given to illustrate the effectiveness of our presented adaptive grid algorithm.

T T Li ◽  
C An ◽  
M L Duan ◽  
H Huang ◽  
W Liang

This paper establishes a fast and accurate solution of the dynamic behaviours of subsea free-spanning pipelines under four different boundary conditions, based on GITT - the generalised integral transform technique. The fluid-structure interaction model is proposed by combining a linear structural equation and a non-linear distributed wake oscillator model, which simulates the effect of external current acting on the pipeline. The eigenvalue problems for the cross-flow vibration of the free-spanning submarine pipeline conveying internal fluid for four different boundary conditions are examined. The solution method of the natural frequency based on GITT is proposed. The explicit analytical formulae for the cross-flow displacement of the pipeline free span are derived, and the mode shapes and dynamic behaviours of the pipeline free span are discussed with different boundary conditions. The methodology and results in this paper can also expand to solving even more complicated boundary-value problems.

C An ◽  
T T Li ◽  
M L Duan ◽  
H B Huang

Due to the complexity of submarine environments, the nature of the dynamic response of free-spanning submarine pipelines, particularly inclined pipelines, is unclear. This paper aims to theoretically analyze the vibration behaviors of inclined fluid-transporting free-spanning submarine pipelines in the deepwater area. The mathematical model for the vibration of inclined fluid-transporting pipelines is established considering the influence of gravity on vibration response, and a non-linear wake oscillator is employed to model the vortex shedding behind the pipeline free span. The partial differential equation system is solved through the generalized integral transform technique (GITT), which is an analytical or semi-analytical method. Parametric analysis are carried out to investigate the effects of the inclination on the dynamic response of fluid-transporting pipelines. It is found that the inclination of the free- spanning pipeline will radically alter the natural frequency of the structure, and consequently the VIV lock-in region. In addition, the slope of the seabed will cause a more significant internal flow effect. The thorough theoretical understanding of inclined fluid-transporting pipelines helps increase the design accuracy for pipelines installed on a seabed with a highly irregular topography.

Mushtaq Ahmad ◽  
Muhammad I Asjad ◽  
Kottakkaran S Nisar ◽  
Ilyas Khan

In this study, an unsteady natural convection flow of second-grade fluid over a vertical plate with Newtonian heating by constant proportional Caputo non-integer order derivative is presented. After developing a dimensionless flow model, the set of governing equations are solved with the help of integral transform, namely the Laplace transform and closed solutions are obtained. Also, some graphs of temperature and velocity field are drawn to see the subjectively of fractional parameter [Formula: see text] and other involved parameters of interest. It also shows dual nature for small and large time behavior due to the power-law kernel. Further, a comparative analysis between the temperature as well as the velocity fields with existing literature has been presented. Further, as a result, it is concluded that constant proportional Caputo derivative shows more decaying nature of the fluid flow properties than classical Caputo and Caputo-Fabrizio fractional derivatives.

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