Yu-Ming Chu¹, Sobia Sultana², Shazia Karim³, Saima Rashid^4,*, Mohammed Shaaf Alharthi⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.1, pp. 761-791, 2024, DOI:10.32604/cmes.2023.028600 - 22 September 2023

Abstract The goal of this research is to develop a new, simplified analytical method known as the ARA-residue power series method for obtaining exact-approximate solutions employing Caputo type fractional partial differential equations (PDEs) with variable coefficient. ARA-transform is a robust and highly flexible generalization that unifies several existing transforms. The key concept behind this method is to create approximate series outcomes by implementing the ARA-transform and Taylor’s expansion. The process of finding approximations for dynamical fractional-order PDEs is challenging, but the ARA-residual power series technique magnifies this challenge by articulating the solution in a series pattern… More >

Linjuan Wang^1,*, Jianxiang Wang²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.1, pp. 1-1, 2023, DOI:10.32604/icces.2023.09355

Abstract The prediction of overall dynamics of composite materials has been an intriguing research topic more than a century, and numerous approaches have been developed for this topic. One of the most successful representatives is the classical micromechanical models which assume that the behavior of a composite is the same as its constituents except for the difference in mechanical properties, e.g., effective moduli. With the development of advanced composite materials in recent years, especially metamaterials, it is found that the classical micromechanical models cannot describe complex dynamic responses of composites such as the dispersion and bandgaps… More >

Mohamed Shaimi^* , Rabha Khatyr, Jaafar Khalid Naciri

Frontiers in Heat and Mass Transfer, Vol.20, pp. 1-14, 2023, DOI:10.5098/hmt.20.23

Abstract This paper presents an exact analytical solution to the extended Graetz problem in microchannels and microtubes, including axial heat conduction, viscous dissipation, and rarefaction effects for an imposed constant wall temperature. The flow in the microchannel or microtube is assumed to be hydrodynamically fully developed. At the same time, the first-order slip-velocity and temperature jump models represent the wall boundary conditions. The energy equation is solved analytically, and the solution is obtained in terms of Kummer functions with expansion constants directly determined from explicit expressions. The local and fully developed Nusselt numbers are calculated in… More >

Kue-Hong Chen^{1, *}, Cheng-Tsung Chen^{2, 3}

CMC-Computers, Materials & Continua, Vol.64, No.1, pp. 145-160, 2020, DOI:10.32604/cmc.2020.08864 - 20 May 2020

Abstract In this study, we applied a defined auxiliary problem in a novel error estimation technique to estimate the numerical error in the method of fundamental solutions (MFS) for solving the Helmholtz equation. The defined auxiliary problem is substituted for the real problem, and its analytical solution is generated using the complementary solution set of the governing equation. By solving the auxiliary problem and comparing the solution with the quasianalytical solution, an error curve of the MFS versus the source location parameters can be obtained. Thus, the optimal location parameter can be identified. The convergent numerical More >

Yongping Yu¹, Lihui Chen¹, Shaopeng Zheng¹, Baihui Zeng¹, Weipeng Sun^{2, ∗}

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.1, pp. 185-200, 2020, DOI:10.32604/cmes.2020.07997 - 01 April 2020

Abstract This paper is focused on the post-buckling behavior of the fixed laminated composite beams with effects of axial compression force and the shear deformation. The analytical solutions are established for the original control equations (that is not simplified) by applying the Maclaurin series expansion, Chebyshev polynomials, the harmonic balance method and the Newton’s method. The validity of the present method is verified via comparing the analytical approximate solutions with the numerical ones which are obtained by the shooting method. The present third analytical approximate solutions can give excellent agreement with the numerical solutions for a More >

Partner L. Ndlovu^a,b,∗, Raseelo J. Moitsheki^a,†

Frontiers in Heat and Mass Transfer, Vol.12, pp. 1-8, 2019, DOI:10.5098/hmt.12.7

Abstract In this article, the Differential Transform Method (DTM) is used to perform thermal analysis of natural convective and radiative heat transfer in moving porous fins of rectangular and exponential profiles. This study is performed using Darcy’s model to formulate the governing heat transfer equations. The effects of porosity parameter, irregular profile and other thermo-physical parameters, such as Peclet number and the radiation parameter are also analyzed. The results show that the fin rapidly dissipates heat to the surrounding temperature with an increase in the values of the porosity parameter and the dimensionless time parameter. The More >

Hai Qian^1,*, Sai-Huen Lo², Ding Zhou³, Yang Yang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.121, No.1, pp. 215-247, 2019, DOI:10.32604/cmes.2019.07922

Abstract The temperature and the stress distribution in simply-supported laminated cylindrical shells undergo thermal loads on the surface have been investigated. Exact solutions of physical quantities including temperature, heat flux, thermal displacement and stress are developed for the cylindrical laminated shell. Cylindrical shells are partitioned into more thin layers. In cylindrical coordinate, analytical expressions for physical quantities inside each layer are derived. Taking into account the compatibility of physical quantities at the interfaces, the relations between the outer and the inner layer of the laminated shell can be described with a transfer matrix. The undetermined parameters More >

Hai Qian^1,*, Ding Zhou², Bin Gu¹, Rathnayaka Mudiyanselage D. M. S.³

Structural Durability & Health Monitoring, Vol.12, No.4, pp. 281-298, 2018, DOI:10.32604/sdhm.2018.04618

Abstract The temperature fields in the laminated shells were studied, including open cylindrical shells and cylindrical shells, according to the thermal theory. Analytical solution of the temperature in the shells with the known temperature on the surfaces was present. The thinning layer approach was introduced to simplify the three-dimensional heat conduction equation. Firstly, the layered shell was divided into N thinner layers. The governing equation was simplified by replacing the variable r by r0 in the center line of every thin layer. The general solutions of temperature satisfying the simplified three-dimensional governing equation in single-layered shell… More >

A. Khechiba¹, Y. Benakcha¹, A. Ghezal¹, P. Spetiri²

FDMP-Fluid Dynamics & Materials Processing, Vol.14, No.2, pp. 137-154, 2018, DOI:10.3970/fdmp.2018.04054

Abstract This work investigates the dynamic behavior of a pulsatile flow electrically conducting through porous medium in a cylindrical conduit under the influence of a magnetic field. The imposed magnetic field is assumed to be uniform and constant. An exact solution of the equations governing magneto hydro-dynamics (MHD) flow in a conduit has been obtained in the form of Bessel functions. The analytical study has been used to establish an expression between the Hartmann number, Darcy number and the stress coefficient. The numerical method is based on an implicit finite difference time marching scheme using the More >

Surkay D. Akbarov^1,2, Hatam H. Guliyev³, Yusif M. Sevdimaliyev⁴, Nazmiye Yahnioglu^5,*

CMC-Computers, Materials & Continua, Vol.55, No.2, pp. 359-380, 2018, DOI:10.3970/cmc.2018.00173

Abstract The paper deals with a development of the discrete-analytical method for the solution of the dynamical problems of a hollow sphere with inhomogeneous initial stresses. The examinations are made with respect to the problem on the natural vibration of the hollow sphere the initial stresses in which is caused by internal and external uniformly distributed pressure. The initial stresses in the sphere are determined within the scope of the exact equations of elastostatics. It is assumed that after appearing this static initial stresses the sphere gets a dynamical excitation and mechanical behavior of the sphere… More >