Nourhan I. Ghoneim^1,*, Ahmed M. Megahed²

FDMP-Fluid Dynamics & Materials Processing, Vol.19, No.2, pp. 407-419, 2023, DOI:10.32604/fdmp.2022.020508 - 29 August 2022

Abstract A mathematical model is elaborated for the laminar flow of an Eyring-Powell fluid over a stretching sheet. The considered non-Newtonian fluid has Prandtl number larger than one. The effects of variable fluid properties and heat generation/absorption are also discussed. The balance equations for fluid flow are reduced to a set of ordinary differential equations through a similarity transformation and solved numerically using a Chebyshev spectral scheme. The effect of various parameters on the rate of heat transfer in the thermal boundary regime is investigated, i.e., thermal conductivity, the heat generation/absorption ratio and the mixed convection More >

Lihua Zhu^1,*, Yu Wang¹, Zhiqiang Wu¹, Cheire Cheng²

Intelligent Automation & Soft Computing, Vol.33, No.1, pp. 291-303, 2022, DOI:10.32604/iasc.2022.024252 - 05 January 2022

Abstract The rapid developments of artificial intelligence in the last decade are influencing aerospace engineering to a great extent and research in this context is proliferating. In this paper, the trajectory optimization of a three-stage launch vehicle in the powering phase subject to the sun-synchronous orbit is considered. To solve the optimal control problem, the Gauss pseudo-spectral method (GPM) is used to transform the optimization model to a nonlinear programming (NLP) problem and sequential quadratic programming is applied to find the optimal solution. However, the sensitivity of the initial guess may cost the solver significant time More >

Amel A. Alaidrous^*

CMC-Computers, Materials & Continua, Vol.67, No.3, pp. 2971-2988, 2021, DOI:10.32604/cmc.2021.015159 - 01 March 2021

Abstract In this paper, we study the water-wave flow under a floating body of an incident wave in a fluid. This model simulates the phenomenon of waves abording a floating ship in a vast ocean. The same model, also simulates the phenomenon of fluid-structure interaction of a large ice sheet in waves. According to this method. We divide the region of the problem into three subregions. Solutions, satisfying the equation in the fluid mass and a part of the boundary conditions in each subregion, are given. We obtain such solutions as infinite series including unknown coefficients.… More >

Shina D. Oloniiju^† , Sicelo P. Goqo, Precious Sibanda

Frontiers in Heat and Mass Transfer, Vol.13, pp. 1-8, 2019, DOI:10.5098/hmt.13.19

Abstract In some recent studies, it has been suggested that non–Newtonian fluid flow can be modeled by a spatially non–local velocity, whose dynamics are described by a fractional derivative. In this study, we use the space fractional constitutive relation to model heat and mass transfer in a nanofluid. We present a numerically accurate algorithm for approximating solutions of the system of fractional ordinary differential equations describing the nanofluid flow. We present numerically stable differentiation matrices for both integer and fractional order derivatives defined by the one–sided Caputo derivative. The differentiation matrices are based on the series More >

W. M. Abd-Elhameed^1,2,*, Y. H. Youssri²

CMES-Computer Modeling in Engineering & Sciences, Vol.121, No.3, pp. 1029-1049, 2019, DOI:10.32604/cmes.2019.08378

Abstract This paper is confined to analyzing and implementing new spectral solutions of the fractional Riccati differential equation based on the application of the spectral tau method. A new explicit formula for approximating the fractional derivatives of shifted Chebyshev polynomials of the second kind in terms of their original polynomials is established. This formula is expressed in terms of a certain terminating hypergeometric function of the type ₄F₃(1). This hypergeometric function is reduced in case of the integer case into a certain terminating hypergeometric function of the type ₃F₂(1) which can be summed with the aid of More >

A.H. Bhrawy^1,2, E.H. Doha³, S.S. Ezz-Eldien⁴, M.A. Abdelkawy²

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.3, pp. 185-209, 2015, DOI:10.3970/cmes.2015.104.185

Abstract In this paper, a high accurate numerical approach is investigated for solving the time-fractional linear and nonlinear Korteweg-de Vries (KdV) equations. These equations are the most appropriate and desirable definition for physical modeling. The spectral collocation method and the operational matrix of fractional derivatives are used together with the help of the Gauss-quadrature formula in order to reduce such problem into a problem consists of solving a system of algebraic equations which greatly simplifying the problem. Our approach is based on the shifted Jacobi polynomials and the fractional derivative is described in the sense of More >

Jianxin Zhu, Zengsi Chen, Zheqi Shen

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.5, pp. 547-560, 2012, DOI:10.3970/cmes.2012.083.547

Abstract An acoustic waveguide with continuously varying sound speed is discussed in this paper. When the waveguide is open along the depth, the perfectly matched layer (PML) is used to terminate the infinite domain. Since the sound speed is gradually varied, the density is assumed as constant in each fluid layer. For this waveguide, it is shown that the mode relation is derived by using the differential transfer matrix method (DTMM). To solve leaky and PML modes, Newton's iteration is applied, and Chebyshev pseudospectral method is used for obtaining initial guesses. The solutions are with high More >

L.Q. Moreira¹, F.P. Mariano², A. Silveira-Neto¹

CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.2, pp. 113-140, 2011, DOI:10.3970/cmes.2011.075.113

Abstract Turbulence in fluid flow is one of the most challenging problems in classical physics. It is a very important research problem because of its numerous implications, such as industrial applications that involve processes using mixtures of components, heat transfer and lubrication and injection of fuel into the combustion chambers and propulsion systems of airplanes. Turbulence in flow presents characteristics that are fully nonlinear and that occur at high Reynolds numbers. Because of the nonlinear nature of turbulent flow, an increase in the Reynolds number implies an increase in the Kolmogorov wave numbers, and the flow… More >

Xie Ming-Liang^1,2, Chan Tat-Leung², Yao Fu-Yuan³

CMES-Computer Modeling in Engineering & Sciences, Vol.67, No.1, pp. 39-54, 2010, DOI:10.3970/cmes.2010.067.039

Abstract A Fourier-Chebyshev Petrov-Galerkin spectral method is described for computation of temporal linear stability in a circular jet. The outer boundary of unbounded domains is truncated by large enough diameter. The mathematical formulation is presented in detail focusing on the analyticity of solenoidal vector field used for the approximation of the flow. The scheme provides spectral accuracy in the present cases studied and the numerical results are in agreement with former works. More >

Hamad F. Al-Harbi¹, Marko Knezevic^1,2, Surya R. Kalidindi^1,3

CMC-Computers, Materials & Continua, Vol.15, No.2, pp. 153-172, 2010, DOI:10.3970/cmc.2010.015.153

Abstract In recent work, we have demonstrated the viability and computational advantages of DFT-based spectral databases for facilitating crystal plasticity solutions in face-centered cubic (fcc) metals subjected to arbitrary deformation paths. In this paper, we extend and validate the application of these novel ideas to body-centered cubic (bcc) metals that exhibit a much larger number of potential slip systems. It was observed that the databases for the bcc metals with a larger number of slip systems were more compact compared to those obtained previously for fcc metals with a smaller number of slip systems. Furthermore, we More >