• The KSFM Journal of Fluid Machinery
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• v.15 no.5
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• pp.11-19
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• 2012

The main function of fuel cell manifold is to render reactants distribution as uniform as possible into a fuel cell stack. The purpose of this study is to numerically investigate the effects of stack manifold design on reactants distribution within a fuel cell stack. Four manifold designs with different manifold entrance shapes (expansion or diffuser) and different values of the extra width between the cell outer channel and manifold side wall are considered and applied to the fuel cell stack consisting of 50 cells. Since the fuel cell stack geometry involves several millions of grid points for numerical calculations, a parallel computing methodology is employed to substantially reduce the computational time and overcome the memory requirement. The numerical simulations are carried out and calculated results clearly demonstrate that both the manifold entrance shape and extra width have a substantial influence on manifold performance, controlling the degree of flow separation and entrance length for fully developed flow in the manifold channel. Finally, we suggest the optimum design of fuel cell manifold based on the simulation results.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.859-870
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• 2008

In the present paper, we investigate the geometric structures of the Dirichlet manifold composed of the Dirichlet distribution. We show that the Dirichlet distribution is an exponential family distribution. We consider its dual structures and give its geometric metrics, and obtain the geometric structures of the lower dimension cases of the Dirichlet manifold. In particularly, the Beta distribution is a 2-dimensional Dirich-let distribution. Also, we construct an affine immersion of the Dirichlet manifold. At last, we give the e-flat hierarchical structures and the orthogonal foliations of the Dirichlet manifold. All these work will enrich the theoretical work of the Dirichlet distribution and will be great help for its further applications.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.137-148
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• 2018

In the present paper we prove that in an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}-nullity$ distribution the three conditions: (i) the Ricci tensor of $M^{2n+1}$ is of Codazzi type, (ii) the manifold $M^{2n+1}$ satisfies div C = 0, (iii) the manifold $M^{2n+1}$ is locally isometric to $H^{n+1}(-4){\times}R^n$, are equivalent. Also we prove that if the manifold satisfies the cyclic parallel Ricci tensor, then the manifold is locally isometric to $H^{n+1}(-4){\times}\mathbb{R}^n$.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1289-1301
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• 2019

In the present paper, we prove that if there exists a second order parallel tensor on an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}$-nullity distribution and $h^{\prime}{\neq}0$, then either the manifold is isometric to $H^{n+1}(-4){\times}{\mathbb{R}}^n$, or, the second order parallel tensor is a constant multiple of the associated metric tensor of $M^{2n+1}$ under certain restriction on k, ${\mu}$. Besides this, we study Ricci soliton on an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}$-nullity distribution. Finally, we characterize such a manifold admitting generalized Ricci soliton.

• 한국신재생에너지학회:학술대회논문집
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• 2007.06a
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• pp.172-175
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• 2007

The Performance of a PEMFC stack is strongly dependent on the uniform reactants distribution on MEA. The uniform distribution can be achieved by flow-field pattern and manifold design optimized to satisfy operating conditions. This paper investigates uniform reactants distribution in channels by changing manifold shape and inlet mass flow rate. Typical U and Z shape and modified U and Z shape manifolds with buffer zone were designed. To check the uniform reactants distribution, standard deviation of mass flow rate was compared. The numerical results show that the inlet mass flow rate, inlet shape, and manifolds shape are critical factor for uniform distribution.

• 한국신재생에너지학회:학술대회논문집
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• 2006.11a
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• pp.320-323
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• 2006

A numerical study is made of a manifold and bipolar plate in polymer electrolyte fuel cells, the aim of the present study is to describe the characteristics of flow pattern In manifold and bipolar plate. The present work shows that the flow pattern in the bipolar plate is affected by the penetration flow through GDL characterized by clamping pressure and GDL intrusion in to a channel area. Manifold geometry also affects the flow distribution. The recirculation flow by bent duct destroy even distribution In manifold, the present work shows that corner rounding can improve the manifold performance.

• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.1-10
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• 2014

In this paper, we study the curvature of locally symmetric or semi-symmetric half lightlike submanifolds M of an indefinite Kenmotsu manifold $\bar{M}$, whose structure vector field is tangent to M. After that, we study the existence of the totally geodesic screen distribution of half lightlike submanifolds of indefinite Kenmotsu manifolds with parallel co-screen distribution subject to the conditions: (1) M is locally symmetric, or (2) the lightlike transversal connection is flat.

• East Asian mathematical journal
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• v.31 no.1
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• pp.33-40
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• 2015

We study the geometry of r-lightlike submanifolds M of a semi-Riemannian manifold $\bar{M}$ with a semi-symmetric non-metric connection subject to the conditions; (a) the screen distribution of M is totally geodesic in M, and (b) at least one among the r-th lightlike second fundamental forms is parallel with respect to the induced connection of M. The main result is a classification theorem for irrotational r-lightlike submanifold of a semi-Riemannian manifold of index r admitting a semi-symmetric non-metric connection.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.401-416
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• 2017

The aim of this paper is to investigate locally ${\phi}-conformally$ symmetric almost Kenmotsu manifolds with its characteristic vector field ${\xi}$ belonging to some nullity distributions. Also, we give an example of a 5-dimensional almost Kenmotsu manifold such that ${\xi}$ belongs to the $(k,\;{\mu})^{\prime}$-nullity distribution and $h^{\prime}{\neq}0$.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.211-228
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• 2012

We study lightlike submanifolds M of a semi-Riemannian manifold $\bar{M}$ with a semi-symmetric non-metric connection subject to the conditions; (a) the characteristic vector field of $\bar{M}$ is tangent to M, (b) the screen distribution on M is totally umbilical in M and (c) the co-screen distribution on M is conformal Killing.