Ruijin Huo^1,2,3, Qingxiang Pei^1,2,3, Xiaohui Yuan^1,*, Yanming Xu³

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.2, pp. 2053-2077, 2024, DOI:10.32604/cmes.2024.049185

Abstract In this paper, a generalized th-order perturbation method based on the isogeometric boundary element method is proposed for the uncertainty analysis of broadband structural acoustic scattering problems. The Burton-Miller method is employed to solve the problem of non-unique solutions that may be encountered in the external acoustic field, and the th-order discretization formulation of the boundary integral equation is derived. In addition, the computation of loop subdivision surfaces and the subdivision rules are introduced. In order to confirm the effectiveness of the algorithm, the computed results are contrasted and analyzed with the results under Monte More >

P. Pai Nityanand, B. Devaki, G. Bhat Pareekshith, V. S. Sampath Kumar^*

Frontiers in Heat and Mass Transfer, Vol.22, No.2, pp. 655-673, 2024, DOI:10.32604/fhmt.2024.050237

Abstract The study in this manuscript aims to analyse the impact of thermal radiation on the two-dimensional magnetohydrodynamic flow of upper convected Maxwell (UCM) fluid between parallel plates. The lower plate is porous and stationary, while the top plate is impermeable and moving. The equations that describe the flow are transformed into non-linear ordinary differential equations with boundary conditions by employing similarity transformations. The Homotopy Perturbation Method (HPM) is then employed to approach the obtained non-linear ordinary differential equations and get an approximate analytical solution. The analysis includes plotting the velocity profile for different Reynolds number… More >

T. M. Agbaje^a,b, S. S. Motsa^a,* , S. Mondal^c,† , P. Sibanda^a

Frontiers in Heat and Mass Transfer, Vol.9, pp. 1-13, 2017, DOI:10.5098/hmt.9.36

Abstract In this work, we present a compliment of the spectral perturbation method (SPM) for solving nonlinear partial differential equations (PDEs) with applications in fluid flow problems. The (SPM) is a series expansion based approach that uses the Chebyshev spectral collocation method to solve the governing sequence of differential equation generated by the perturbation series approximation. Previously the SPM had the limitation of being used to solve problems with small parameters only. This current investigation seeks to improve the performance of the SPM by doing the series expansion about a large parameter. The new method namely… More >

V. S. Sampath Kumar, N. P. Pai^†

Frontiers in Heat and Mass Transfer, Vol.12, pp. 1-9, 2019, DOI:10.5098/hmt.12.23

Abstract The present paper encorporates the effet of magnetic field on the incompressible Casson fluid flow between two parallel infinite rectangular plates approaching towards or away from each other with suction or injection at the porous plates. Using similarity transformations the governing Navier-Stokes equations are reduced to a nonlinear ordinary differential equation. Semi-analytical solution is obtained based on the Homotopy perturbation method. Further, the solution is compared with the classical finite difference method separately. The effect of magnetic field on velocity, skin friction and pressure is analysed on flow between two plates with suction or injection, More >

V.S. Sampath Kumar, N.P. Pai^† , B. Devaki

Frontiers in Heat and Mass Transfer, Vol.20, pp. 1-13, 2023, DOI:10.5098/hmt.20.30

Abstract In the present study, we consider Casson fluid flow between two porous plates with permeability criteria in the presence of heat transfer and magnetic effect. A proper set of similarity transformations simplify the Navier-Stokes equations to non-linear ODEs with boundary conditions. The homotopy perturbation method is an efficient and stable method which is used to get solutions. Further, the results obtained are compared with the solution computed through an effective and efficient finite difference approach. The purpose of this analysis is to study the four different cases arise viz: suction, injection, mixed suction and mixed More >

V. S. Sampath Kumar^a , N. P. Pai^a,† , B. Devaki^a

Frontiers in Heat and Mass Transfer, Vol.16, pp. 1-7, 2021, DOI:10.5098/hmt.16.3

Abstract A study is carried out for the two dimensional laminar flow of conducting fluid in presence of magnetic field. The governing non-linear equations of motion are transformed in to dimensionaless form. A solution is obtained by homotopy perturbation method and it is valid for moderately large Reynolds numbers for injection at the wall. Also an efficient algorithm based finite difference scheme is developed to solve the reduced coupled ordinary differential equations with necessary boundary conditions. The effects of Reynolds number, the magnetic parameter and the pradantle number on flow velocity and tempratare distribution is analysed More >

Yusry O. El-Dib, Nasser S. Elgazery^*

Sound & Vibration, Vol.56, No.1, pp. 21-36, 2022, DOI:10.32604/sv.2022.014166

Abstract In this article, the main objective is to employ the homotopy perturbation method (HPM) as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients. As a simple example, the nonlinear damping Mathieu equation has been investigated. In this investigation, two nonlinear solvability conditions are imposed. One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases. The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the More >

Yanni Zhang^1,2, Jing Pang^1,2,*

Sound & Vibration, Vol.55, No.4, pp. 295-303, 2021, DOI:10.32604/sv.2021.014445

Abstract In this article, time fractional Fornberg-Whitham equation of He’s fractional derivative is studied. To transform the fractional model into its equivalent differential equation, the fractional complex transform is used and He’s homotopy perturbation method is implemented to get the approximate analytical solutions of the fractional-order problems. The graphs are plotted to analysis the fractional-order mathematical modeling. More >

A. Shahzad¹, W. A. Khan^2,*, R. Gul¹, B. Dayyan¹, M. Zubair¹

CMC-Computers, Materials & Continua, Vol.68, No.3, pp. 3877-3893, 2021, DOI:10.32604/cmc.2021.012524

Abstract In this work, a steady, incompressible Williamson fluid model is investigated in a porous wavy channel. This situation arises in the reabsorption of useful substances from the glomerular filtrate in the kidney. After 80% reabsorption, urine is left, which behaves like a thinning fluid. The laws of conservation of mass and momentum are used to model the physical problem. The analytical solution of the problem in terms of stream function is obtained by a regular perturbation expansion method. The asymptotic integration method for small wave amplitudes and the RK-Fehlberg method for pressure distribution has been… More >

Khaled A. Gepreel^1,2, Mohamed S. Mohamed^1,3, Hammad Alotaibi¹, Amr M. S. Mahdy^1,2,*

CMC-Computers, Materials & Continua, Vol.67, No.1, pp. 675-686, 2021, DOI:10.32604/cmc.2021.012200

Abstract The development of mathematical modeling of infectious diseases is a key research area in various fields including ecology and epidemiology. One aim of these models is to understand the dynamics of behavior in infectious diseases. For the new strain of coronavirus (COVID-19), there is no vaccine to protect people and to prevent its spread so far. Instead, control strategies associated with health care, such as social distancing, quarantine, travel restrictions, can be adopted to control the pandemic of COVID-19. This article sheds light on the dynamical behaviors of nonlinear COVID-19 models based on two methods: More >