Developing a new approaching technique of homotopy perturbation method to solve two-group reflected cylindrical reactor

Shqair, Mohammed

doi:10.1016/j.rinp.2019.01.063

Cited by 11 publications

(4 citation statements)

References 18 publications

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“…Couple boundary conditions are considered in such a way diffusion flux vanishes at the critical dimension. As in the same procedure that used in previous works like [20,21], one of the fluxes is normalized (to one) at the core of the reactor, and the other fluxes will be calculated depending on Equation 5as ratios of the normalized flux, for two energy groups of neutrons the ratio between thermal and fast fluxes is given in the data source [2] which convenient with Equation (5) calculations.…”

Section: Practical Numerical Resultsmentioning

confidence: 99%

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Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method

2019

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In this paper, a multi-energy groups of a neutron diffusion equations system is analytically solved by a residual power series method. The solution is generalized to consider three different geometries: slab, cylinder and sphere. Diffusion of two and four energy groups of neutrons is specifically analyzed through numerical calculation at certain boundary conditions. This study revels sufficient analytical description for radial flux distribution of multi-energy groups of neutron diffusion theory as well as determination of each nuclear reactor dimension in criticality case. The generated results are compatible with other different methods data. The generated results are practically efficient for neutron reactors dimension.

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Section: Practical Numerical Resultsmentioning

confidence: 99%

“…An alternative method is used to solve one energy group of a neutron diffusion equation in cylindrical symmetry [16]. There are other efforts to solve different cases of neutron diffusion equations [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method

2019

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“…Various techniques, analytical and numerical, have been employed to solve the neutron diffusion equation throughout the past few decades, such as the homotopy perturbation method, the Laplace transform process, and the Galerkin method with B-splines [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. To the best of our knowledge, the residual power series method (RPSM) [21][22][23][24][25][26][27][28][29], an analytical technique, has never been used to handle issues relating to the neutron diffusion equation.…”

Section: Introductionmentioning

confidence: 99%

A solution for the neutron diffusion equation in the spherical and hemispherical reactors using the residual power series

El-Ajou,

Shqair,

Ghabar

et al. 2023

Front. Phys.

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A novel analytical solution to the neutron diffusion equation is proposed in this study using the residual power series approach for both spherical and hemispherical fissile material reactors. Various boundary conditions are investigated, including zero flux on the boundary, zero flux on the extrapolated boundary distance, and the radiation boundary condition (RBC). The study also shows how two hemispheres with opposing flat faces interact. We give numerical results for the same energy neutrons diffused in pure P239u. By qualitative comparison with the homotopy perturbation method and Bessel function-based solutions, the residual power series method (RPSM) presents accurate series solutions that converge to the exact solutions, as shown in this study. Moreover, numerical results were shown to be improved by the computer implementation of the analytic solutions.

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“…[47][48][49] The HPM has been widely employed as a robust tool for solving similar problems in the studies like Sadeghy et al, 50 Hayat et al, 51 Hayat and Abbas, 52 Mamaloukas et al, 53 Anwar and Makinde, 54 Sajid et al, 55 Abel et al, 56 Karimiasl et al, 57 Jafarimoghaddam, 58 Eldabe and Eldabe, 59 Saradhadevi and Beulah, and 60 and Riaz et al 61 However, to the best of authors' knowledge, it has not been utilized to solve the problem of this study yet. The methods have also been developed in different studies, such as Yu et al, 62 Shqair, 63 Altaie et al, 64 Kharrat and Toma, 65 and De la Luz Sosa et al 66 Having provided explanations for this part, that is, Section 1, the details for modeling are presented in Section 2. Then, the results and discussion are given in Section 3, and finally, the conclusions are introduced in Section 4.…”

mentioning

confidence: 99%

Applying homotopy perturbation method to provide an analytical solution for Newtonian fluid flow on a porous flat plate

Ashrafi

Hoseinzadeh

Sohani

et al. 2021

Math Methods in App Sciences

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This research work is going to apply the homotopy perturbation method to solve the problem of flowing Newtonian fluid on a flat plate. For this purpose, initially, the problem, including the governing equations and boundary conditions, is defined, and after that, the considered assumptions to solve the defined problem are introduced. Next, the working principle of the homotopy perturbation method is described, and then, the way to obtain the analytical solution using the homotopy perturbation method is presented, and finally, the accuracy of the proposed analytical solution in comparison to the numerical approach is compared for validation. Both momentum and energy equations are solved. The maple software program is utilized for carrying out the mathematical calculations, while the validation is done using the profiles for stream function, velocity distribution, stress, and dimensionless temperature as the key indicators related to the solution. The conducted comparison shows that the analytical solution provided by the homotopy perturbation method is able to predict all the important performance criteria for the problem very well, and therefore, the homotopy perturbation method has a strong potential to be employed for providing the analytical solution for such problems.

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Developing a new approaching technique of homotopy perturbation method to solve two-group reflected cylindrical reactor

Cited by 11 publications

References 18 publications

Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method

Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method

A solution for the neutron diffusion equation in the spherical and hemispherical reactors using the residual power series

Applying homotopy perturbation method to provide an analytical solution for Newtonian fluid flow on a porous flat plate

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