M.S. Abdelmeguid^*

Frontiers in Heat and Mass Transfer, Vol.8, pp. 1-8, 2017, DOI:10.5098/hmt.8.28

Abstract In this paper, the effects of suction/blowing and thermal radiation on a hydromagnetic viscous fluid over a non-linear stretching and shrinking sheet are investigated. A similarity transformation is used to reduce the governing equations to a set of nonlinear ordinary differential equations. The system of equations is solved analytically employing homotopy analysis method (HAM). Convergence of the HAM solution is checked. The resulting similarity equations are solved numerically using Matlab bvp4c numerical routine. It is found that dual solutions exist for this particular problem. The comparison of analytical solution and numerical solution for the velocity More >

Nasreen Bano^∗,† , B. B. Singh, S. R. Sayyed

Frontiers in Heat and Mass Transfer, Vol.10, pp. 1-9, 2018, DOI:10.5098/hmt.10.14

Abstract The present study deals with the two dimensional steady laminar forced MHD Hiemenz flow past a flat plate in a porous medium. The effects of thermal radiation and partial slips on the flow field have been investigated under the variable wall temperature condition of the plate. The governing equations have been transformed into a set of coupled non-linear ordinary differential equations (ODEs) by using suitable similarity transformations. These equations have been solved analytically by using homotopy analysis method (HAM). The effects of Prandtl number, suction/blowing parameter, permeability parameter, velocity slip parameter, radiation parameter, magnetic parameter, More >

K.V. Prasad^a, Hanumesh Vaidya^a,*, O. D. Makinde^b , K. Vajravelu^c , A. Wakif^d , Hussain Basha^a

Frontiers in Heat and Mass Transfer, Vol.14, pp. 1-12, 2020, DOI:10.5098/hmt.14.11

Abstract This article explores the three-dimensional (3D) rotating flow of Upper Convected Maxwell (UCM) nanoliquid over an exponentially stretching sheet with a convective boundary condition and zero mass flux for the nanoparticles concentration. The impacts of velocity slip and hall current are being considered. The suitable similarity transformations are employed to reduce the governing partial differential equations into ordinary ones. These systems of equations are highly non-linear, coupled and in turn solved by an efficient semi-analytical scheme known as optimal homotopy analysis method (OHAM). The effects of various physical constraints on velocity, temperature, and concentration fields More >

Girma Tafesse^† , Mitiku Daba, Vedagiri G. Naidu

Frontiers in Heat and Mass Transfer, Vol.20, pp. 1-12, 2023, DOI:10.5098/hmt.20.27

Abstract Innovative technologies necessitate extra energy, which can be captured from environmentally sustainable, renewable solar energy. Here, heat and mass transfer through stirring nanofluids in solar collectors for direct absorption of sunlight are pronounced. The similarity transformation served to turn mathematically regulated partial differential equations into sets of nonlinear higher-order ordinary differential equations. These equations have been resolved by the homotopy analysis method manipulating, BVPh2.0 package in Mathematica 12.1. Validations are justified through comparison. Afterward, stronger magnetic field interactions delay the nanofluids mobility. Temperature increases with thermal radiation and Biot numbers. Entropy formation and nanoparticle concentration More >

Ali. F. Jameel^1,*, N. R. Anakira², A. K. Alomari³, Noraziah H. Man¹

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.3, pp. 875-899, 2021, DOI:10.32604/cmes.2021.014460

Abstract Homotopy Analysis Method (HAM) is semi-analytic method to solve the linear and nonlinear mathematical models which can be used to obtain the approximate solution. The HAM includes an auxiliary parameter, which is an efficient way to examine and analyze the accuracy of linear and nonlinear problems. The main aim of this work is to explore the approximate solutions of fuzzy Volterra integral equations (both linear and nonlinear) with a separable kernel via HAM. This method provides a reliable way to ensure the convergence of the approximation series. A new general form of HAM is presented More >

Mustafa Turkyilmazoglu^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.120, No.1, pp. 63-81, 2019, DOI:10.32604/cmes.2019.06858

Abstract A ratio approach based on the simple ratio test associated with the terms of homotopy series was proposed by the author in the previous publications. It was shown in the latter through various comparative physical models that the ratio approach of identifying the range of the convergence control parameter and also an optimal value for it in the homotopy analysis method is a promising alternative to the classically used h-level curves or to the minimizing the residual (squared) error. A mathematical analysis is targeted here to prove the equivalence of both the ratio approach and the More >

Wei-Chung Tien¹, Yue-Tzu Yang¹, Cha’o-Kuang Chen^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.5, pp. 447-462, 2012, DOI:10.3970/cmes.2012.085.447

Abstract Both buoyancy effects of thermal and mass diffusion in the natural convection flow about a vertical plate are considered in this paper. The non-linear coupled differential governing equations for velocity, temperature and concentration fields are solved by using the homotopy analysis method. Without the need of iteration, the obtained solution is in the form of an infinite power series which indicates those series have high accuracy when comparing it with other-generated by the traditional method. The impact of the Prandtl number, Schmidt number and the buoyancy parameter on the flow are widely discussed in detail. More >

Wei-Chung Tien¹, Yue-Tzu Yang¹, Cha’o-Kuang Chen^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 155-170, 2012, DOI:10.3970/cmes.2012.084.155

Abstract In this paper, the homotopy analysis method is applied to analyze the heat transfer of the oscillating base temperature processes occurring in a convective rectangular fin with variable thermal conductivity. This method is a powerful and easy-to-use tool for non-linear problems and it provides us with a simple way to adjust and control the convergence region of solution series. Without the need of iteration, the obtained solution is in the form of an infinite power series and the results indicated that the series has high accuracy by comparing it with those generated by the complex More >