Volume-8 , Issue-5 , Oct 2021, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Reliability of General System Using OM Distribution Function

  Maryam Mohiuddin, R. Kannan

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.5 , pp.1-5, Oct-2021

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  Abstract
  Reliability of the Systems is the main concern of the twenty century. Various authors have been studied the different reliability theories to know the design system safety. Safety of the system is important in the current scenario. In this study, we find the different set of components that provide the maximum system reliability. We analyzed the Parallel-Series and Series-Parallel system in order to know the effect on reliability by adding the components and subsystem to the system. The reliability of the Series-Parallel system is increased by increasing the number of components. The system reliability goes through increasing number of sub-systems to the system. In case of a parallel-series system the system reliability declines with the addition of components to the system and increases with the increase in the number of sub-systems.

  Key-Words / Index Term
  Series-parallel system, Parallel-series system, Reliability analysis

  References
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  [14] A. M. Sarhan, L. Tadj, A. Al-khedhairi, A. Mustafa, “Equivalence factors of a parallel-series system,” Journal of Applied Sciences, 10, pp. 219-230, 2008.
  [15] A. M. Sarhan, “Reliability equivalence factors of a general series-parallel system,” Journal of Reliability Engineering and System Safety, 94(2), pp. 229-236, 2009.
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  [19] A. Mustafa, A. El-Faheem, “Reliability equivalence factors of a system with mixture of n independent and non-identical lifetimes with delay time,” Journal of the Egyptian Mathematical Society, 22, pp. 96-101, 2014.
  [20] M. A. El-Damcese, D. S. Ayoub, “Reliability equivalence factors of a parallel system in two-dimensional distribution,” Journal of Reliability and Statistical Studies, 4(2), pp. 33-42, 2011.
  [21] R. Shanker, K. K. Shukla, “OM distribution with properties and application,” RT&A, 4(51), pp. 13, 2018.
  [22] Maryam Mohiuddin, R. Kannan, Shabir A. Dar, "Improving the Reliability of System by Standby Redundancy Method," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.1, pp.76-82, 2021.

  Citation
  Maryam Mohiuddin, R. Kannan, "Reliability of General System Using OM Distribution Function," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.5, pp.1-5, 2021

• Open Access   Article

  Mixed Convection Boundary Layer Flow with Heat Transfer over a Non-Linear Stretching Wedge-Shaped Surface with the Correlation Coefficient and Multiple Regressions Models

  M. Ali, M.A. Alim

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.5 , pp.6-20, Oct-2021

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  The present paper aims to investigate the MHD two-dimensional mixed convection boundary layer nanofluid flow and heat transfer along with a power-law stretching wedge-shaped surface by using the Buongiorno model. The leading PDEs are modified to ODEs by applying the appropriate similarity transformation. The mathematical model of this problem is solved with the help of SQLM along with MATLAB. Numerical solutions of fluid velocity profile and fluid temperature profile are displayed graphically for different values of controlling flow parameters whereas numerical values of velocity gradient and wall temperature gradient are presented in a tabular form. The numerical results of this paper have been compared with previous working results and found to be almost similar. The correlation coefficient and multiple regression model have been established for the mentioned parameters. The correlation analysis represents that the stretching ratio parameter is negatively correlated with the velocity gradient but the magnetic parameter, porosity parameter, mixed convection parameter and suction parameter are positively correlated. The temperature gradient is positively correlated with the Prandtl number, stretching ratio parameter, porosity parameter, magnetic parameter, and suction parameter whereas negatively correlated with Brownian motion, thermophoresis parameter, and heat generation parameter. The concentration gradient is positively correlated with the Brownian motion, Lewis number, Prandtl number, heat generation, and suction parameter but negatively correlated with the thermophoresis parameter, magnetic parameter and porosity parameter. The results also indicate that within the boundary layer region the fluid velocity is a decreasing function of wedge angle parameter, magnetic parameter, and increasing function of stretching ratio, porosity, wedge angle and mixed convection parameters. Similarly, the temperature is an increasing function of heat generation parameter, Brownian motion, and thermophoresis parameter but a decreasing function of Prandtl number and suction parameter whereas constant in the case of mixed convection parameter. Again, the concentration is a decreasing function of Prandtl number, Lewis number, Brownian motion, heat generation and suction parameter but an increasing function thermophoresis parameter. The observation of this problem may have a bearing in different engineering techniques such as the paper industry, annealing, and tinning of copper wire industry, the process of crystal growing and glass blowing, the continual casting of metals, and spinning of fibbers.

  Key-Words / Index Term
  Boundary layer, wedge flow, correlation, regression, Mixed convection

  References
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  Citation
  M. Ali, M.A. Alim, "Mixed Convection Boundary Layer Flow with Heat Transfer over a Non-Linear Stretching Wedge-Shaped Surface with the Correlation Coefficient and Multiple Regressions Models," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.5, pp.6-20, 2021

• Open Access   Article

  Numerical Solution of Time-Fractional Navier-Stokes Equation in Cylindrical Coordinates

  S.S. Omorodion

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.5 , pp.21-26, Oct-2021

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  This paper presents the numerical solutions of the time-fractional Navier-Stokes equation (N-S equation) in cylindrical coordinates for unsteady one dimensional motion of a viscous fluid via a combination of Tarig transform and projected differential transform method (TPDTM). Two time-fractional N-S equations are solved to validate the effectiveness of the proposed method. The obtained results are presented by 2D plots and table and compared with the results of homotopy analysis method (HAM), fractional modified Laplace decomposition method (FMLDM), homotopy perturbation transform method (HPTM) and q-homotopy analysis transform method (q-HATM). The obtained results show that the TPDTM is an e?ective and straightforward tool for solving nonlinear fractional PDEs and it’s more adaptable than many numerical methods in the literature.

  Key-Words / Index Term
  Time-Fractional Navier-Stokes Equation, Tarig Projected Differential Transform Method, Fractional Order Derivative

  References
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  Citation
  S.S. Omorodion, "Numerical Solution of Time-Fractional Navier-Stokes Equation in Cylindrical Coordinates," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.5, pp.21-26, 2021

• Open Access   Article

  Periodic solutions by Krasnoselskii fixed point theorem of neutral nonlinear system of dynamical equation with Variable Delays

  A.A. Ben Fayed, H.A. Makhzoum, R.A. Elmansouri, A.K. Alshaikhly

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.5 , pp.27-32, Oct-2021

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  Abstract
  The aim of this work to investigate the existence and uniqueness of periodic solutions of the nonlinear neutral system of differential equations by employing Krasnoselskii`s fixed point theorem under slightly more stringent conditions and by applying the solution of the fundamental matrix solution of y`= A(t)y. This is accomplished by transforming the given neutral system differential equation into an equivalent integral equation that allows for the construction of suitable mappings, one of which is a contraction and the other which is compact, both of which allow for the proof of the existence of periodic solutions. Moreover, it was demonstrated that there is a unique periodic solution to the nonlinear neutral system of differential equations by providing some sufficient conditions that can be used to assist in implementing the contraction mapping principle on the nonlinear neutral system of differential equations.

  Key-Words / Index Term
  Krasnoselskii; Neutral differential equation; nonlinear equation; Integral equation; Periodic solution

  References
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  Citation
  A.A. Ben Fayed, H.A. Makhzoum, R.A. Elmansouri, A.K. Alshaikhly, "Periodic solutions by Krasnoselskii fixed point theorem of neutral nonlinear system of dynamical equation with Variable Delays," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.5, pp.27-32, 2021