Volume-5 , Issue-5 , Oct 2018, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Effects of Hall current and heat absorption on MHD flow with variable wall temperature and mass diffusion.

  U.S. Rajput, Neetu Kanaujia

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.225-230, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.225230

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  Abstract
  The present paper analyses the effects of Hall current and heat absorption on flow model. The flow is along an exponentially accelerated vertical plate with variable heat transfer and mass diffusion. The fluid considered is viscous, incompressible and electrically conducting. The magnetic field is applied perpendicular to the plate. The problems related to rotation, Hall current, heat transfer and mass diffusion are being studied due to their applications in many processes. This is the motivation for the study of this model. Velocity profiles, temperature profiles and concentration profiles are obtained by Laplace transform technique for different parameters like rotation parameter, magnetic field parameter, heat absorption parameter, Hall parameter, acceleration parameter, Prandtl number, the angle of inclination of plate, chemical reaction parameter, acceleration parameter and time. The numerical data obtained are discussed with the help of graphs and tables. The numerical values obtained for skin-friction and Nusselt number have been tabulated.

  Key-Words / Index Term
  MHD flow, Heat absorption fluid, Variable wall temperature, Mass diffusion, Hall current

  References
  [1] Tasawar Hayata, Sabia Asghara, Anum Tanveera, Ahmed Alsaedib, “Chemical reaction in peristaltic motion of MHD couple stress fluid in channel with Soret and Dufour effects’’, Results in Physics,10, 69 – 80 (Elsevier), 2018.
  [2] Emad M. Aboelahad, Elsayel, M. E. Elbarbary, “Hall current effect on magneto hydrodynamic free convection flow past a semi- infinite vertical plate with mass transfer”, international journal of engineering science, 1641–1652, 2001.
  [3] M. A. Seddek, “Finite-element method for the effects of chemical reaction, variable viscosity, thermophoresis and heat generation/absorption on a boundary-layer hydro magnetic flow with heat and mass transfer over a heat surface”. Acta Mech, 177, pp. 1-18, 2005.
  [4] O.D. Makinde, MHD mixed- convection interaction with thermal radiation and nth order chemical reaction past a vertical porous plate embedded in a porous medium, chemical engineering communications, 2010.
  [5] S. A Shehzad, T. Hayat and A. Alsaedi, “Three- dimensional MHD flow of Casson fluid in porous medium with heat generation”, Journal of Applied Fluid Mechanics, Vol. 9, No. 1, pp. 215-223, 2016.
  [6] J. Zueco, and S. Ahmed, “Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source”, Applied. Math. Mech”. 31 (10), 1-14, 2010.
  [7] M G Reddy, P Padma and B Shankar, “Effects of viscous dissipation and heat source on unsteady MHD flow over a stretching sheet”, Ain Shams Engineering Journal, 6, 1195–1201, 2015.
  [8] Seth G. S., Sharma R. and Hussain S. M., “Hall effects on unsteady MHD natural convection flow of a heat absorbing fluid past an accelerated moving vertical plate with ramped temperature”, Emirates Journal for Engineering Research, 19 (2), pp.19-32, 2014.
  [9] M. A. Samad, M. D. Hossain and M. M. Alam “MHD free convection and mass transfer flow through a vertical oscillatory porous plate with Hall ion-slip currents and heat source in a rotating system”, Procedia Engineering (Elsevier) 105, pp. 56 – 63, 2015.
  [10] Hayat, T. Ellahi, R., and Asghar, S. “Hall effect on unsteady flow due to non- coaxicially rotating disk and a fluid at infinity”, chem., eng. Commun. 195 (80), 958-976, 2008.
  [11] K. Manivannan, R. Muthucumarswamy, V. Thangaraj, “Radiation and chemical reaction effects on isothermal vertical oscillating plate with variable mass diffusion”, Thermal science, vol.13, no.2, 2009.
  [12] Rajput and Kanaujia, “MHD flow past a vertical plate with variable temperature and mass diffusion in the presence of Hall current”, International Journal of Applied Science and Engineering, 14, 2, pp. 115-123, 2016.
  [13] S.P. Dahake and A.V Dubewar “Effects of Radiation on Magnetohydrodynamic Convection Flow past an Impulsively Started Vertical Plate Submersed in a Porous Medium with Suction, International Journal of Computer Sciences and Engineering, vol. 2, Issues - 2, 2017.
  

  Citation
  U.S. Rajput, Neetu Kanaujia, "Effects of Hall current and heat absorption on MHD flow with variable wall temperature and mass diffusion.," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.225-230, 2018

• Open Access   Article

  The Poisson-weighted Sujatha Distribution with Properties and Applications

  Rama Shanker, Kamlesh Kumar Shukla

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.231-242, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.231242

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  Abstract
  The Poisson distribution is an important discrete distribution for modeling count data having equi-dispersion. In this paper, a new discrete distribution for modeling count data having over-dispersion, namely, the Poisson-weighted Sujatha distribution which includes Poisson-Sujatha distribution has been proposed by compounding Poisson distribution with a two-parameter weighted Sujatha distribution. Its statistical properties including moments, coefficient of variation, skewness, kurtosis, index of dispersion, unimodality and increasing hazard rate have been discussed. Maximum likelihood estimation has been explained for estimating its parameters. Applications of the distribution have been discussed with some count datasets and its goodness of fit has been compared with other discrete distributions having over-dispersion.

  Key-Words / Index Term
  Poisson- Sujatha distribution, Weighted- Sujatha distribution, Compounding, Moments, Skewness, Kurtosis, Maximum likelihood estimation, Applications

  References
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  [12] H., Zamani and Ismail, “Negative binomial-Lindley distribution and its Applications” , Journal of Mathematics and Statistics, 6(1), 4 – 9, 2010
  [13] M.M.E., Abd El-Monsef and N.M., Sohsah , “ Poisson-Weighted Lindley Distribution”, Jokull Journal, 64(5), 192 – 202, 2014
  [14] M.E., Ghitany ,F., Alqallaf , D.K., Al-Mutairi and H.A., Husain , “A two-parameter weighted Lindley distribution and its applications to survival data”, Mathematics and Computers in simulation, 81, 1190-1201,2011
  [15] R., Shanker (2016 b): The Discrete Poisson-Sujatha Distribution, International Journal of Probability and Statistics, 5(1), 1 – 9.
  [16] R., Shanker (2016 a): Sujatha Distribution and Its Applications, Statistics in Transition-New series, 17(3), 1- 20.
  [17] R., Shanker and K.K.., Shukla (2018): A two-parameter Weighted Sujatha distribution and Its Application to Model Lifetime data, International Journal of Applied Mathematics and Statistics, 57 (3), 106 – 121
  [18] R., Shanker, K.K., Shukla and F., Hagos (2016): On Weighted Lindley distribution and Its Applications to Model Lifetime Data, Jacobs Journal of Biostatistics,1(1), 1- 9
  [19] R., Shanker, K.K., Shukla and A., Mishra, (2017): A Three- parameter weighted Lindley distribution and its applications to model survival time data, Statistics in Transition-New Series, 18 (2), 291 – 300.
  [20] J., Grandell (1997): Mixed Poisson Processes, Chapman& Hall, London.
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  Citation
  Rama Shanker, Kamlesh Kumar Shukla, "The Poisson-weighted Sujatha Distribution with Properties and Applications," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.231-242, 2018

• Open Access   Article

  Stochastic Modeling of Viral Replication and Lysing CD4+TCells in the HIV Infection

  G. Meenakshi and S. Saranya

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.243-252, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.243252

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  Abstract
  The existing models of HIV infection are non-linear system of differential equations. Solving system of differential equations is very difficult task and also drawing inference is not easy. Therefore, an attempt has been made to estimate the HIV replication periodically using Markov processes in the condition of decay of CD_4^+ T cells. The proposed model is illustrated in this paper.

  Key-Words / Index Term
  CD4+ T cell, HIV and Markov processes

  References
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  [6]. Frank S. Heldt, Sascha Y. Kupke, Sebastian Dor Udo Reich & Timo Frensing (2015) Single-cell analysis and stochastic modellingunveil large cell-to-cell variability in influenza A virus infection NATURE COMMUNICATIONS 6:8938 DOI:10.1038/ncomms9938 |www.nature.com/naturecommunications.
  [7]. Hernán Darío, Toro-Zapata, Enmanue Roa, VásquezyMónica, JhoanaMesa, Mazoz, (2017) Stochastic Model or the HIV Infection of Cd4+T Cells in Immune System Rev.Mate.Teor.Aplic. (ISSN print: 1409-2433; online: 2215-3373) Vol. 24(2): 287–313, July 2017
  [8]. Joseph N. Inungu, Daudet InungaTshiswaka, Daryn Papen fuse (2017) Advances in HIV Prevention and Treatment: A Literature Review Inungu ygdz
  [9]. Konstantina Palla, David Knowles, ZoubinGhahramani (2017) A Birth-Death Process for Feature Allocation Proceedings of the 34 th International Conference on Machine Learning, Sydney, Australia, PMLR 70, 2017. Copyright 2017by the author(s).
  [10]. Leonid Shaikhet& Andrei Korobeinikov (2015) Stability of a stochastic model for HIV-1 dynamics with in a host Applicable Analysis, 2016Vol. 95, No. 6, 1228–1238. DOI:10.1080/00036811.2015.1058363
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  [12]. Myron S. Cohen, Nick Hellmann, Jay A. Levy, Kevin DeCock, and Joep Lange5 (2008). The spread, treatment, and prevention of HIV-1: evolution of a global pandemic J. Clin. Invest. 118:1244–1254 (2008). Doi: 10.1172/JCI34706.
  [13]. O. Abu, A.M. Okutachi (2017)Deterministic and Stochastic Models to Simulate the Effects of Antiretroviral Therapy (ART) and Counseling on HIV/AIDS Transmission Dynamics in a Heterosexual Population. Journal of Scientific and Engineering Research, 2017, 4(9):111-121.
  [14]. Susan Cassels, Samuel J. Clark, Martina Morris, (2012) Mathematical Models for HIV Transmission Dynamics: NIH Public Access Author ManuscriptJAcquir Immune DeficSyndr. Author manuscript; available in PMC 2012 July 01.
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  [16]. Waema R. Mbogo, Livingstone S. Luboobi, and John W. Odhiambo (2013) Stochastic Model for In-Host HIV Dynamics with therapeutic Intervention ISRN Biomathematics (2013)
  [17]. Waema R. Mbogo, Livingstone S. Luboobi, and JohnW. Odhiambo (2013) Stochastic Model for In-Host HIV Dynamics with Therapeutic Intervention Hindawi Publishing CorporationISRN Biomathematics Volume 2013, ArticleID103708,11pageshttp://dx.doi.org/10.1155/2013/103708 .
  [18]. Yan Wang and Daqing Jian (2017) Stationary Distribution and Extinction of a Stochastic Viral Infection ModelHindawiDiscrete Dynamics in Nature and SocietyVolume 2017, Article ID 6027509, 13 pages https://doi.org/10.1155/2017/6027509
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  20. Yuan Yuan, Linda J.S. Allen (2011)Stochastic models for virus and immune system dynamics Contents lists available at SciVerse Science DirectMathematical BiosciencesJournal homepage: www.elsevier.com/locate/mbs.
  

  Citation
  G. Meenakshi and S. Saranya, "Stochastic Modeling of Viral Replication and Lysing CD4+TCells in the HIV Infection," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.243-252, 2018

• Open Access   Article

  Effects of Hall current on MHD flow past a rotating inclined plate with heat transfer and mass diffusion.

  U.S. Rajput, Neetu Kanaujia

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.253-258, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.253258

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  Abstract
  In the present paper, effects of Hall current on MHD flow past a rotating inclined plate with heat transfer and mass diffusion on flow model has been study. The fluid flow through porous medium is along an impulsively started exponential accelerated plate with variable heat and mass diffusion. Velocity, temperature and concentration profiles are determined and discussed by Laplace transform technique and presented graphically. The numerical data obtained for skin-friction and Nusslet number have been tabulated. The effects of dimensionless parameter on the flow have been analyzed.

  Key-Words / Index Term
  MHD flow, Heat absorption fluid, variable wall temperature, mass diffusion, Hall current

  References
  [1] M. Kar, s. N. Sahoo, and g. C. Dash, effect of hall current and chemical reaction on MHD flow along an accelerated porous flat plate with internal heat absorption/generation journal of engineering physics and thermophysics, vol. 87, no. 3, may, 2014.
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  [4] Hayat, T., Y. Wang and K. Hutter (2004 c). Hall effects on the unsteady hydromagnetic oscillatory flow of a second-grade fluid. Int. J. Non-linear Mech. 39, 1027-1037.
  [5] Erdogan ME Unsteady flow between two eccentric rotating disks executing non torsional oscillations Int. J. Nonlinear. Mech. 35. 691–9
  [6] Bararnia, H.M Ghotbi, A.R., and Domairry, G. (2009). On the analytical solution for MHD heat generation fluid in porous medium, commun, non linear sci, Numer. Simul., 14, 2689 – 2701.
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  [8] Samad M. A, Hossain M. D and Alam M. M, (2015 ). MHD free convection and mass transfer flow through a vertical oscillatory porous plate with Hall, ion-slip currents and heat source in a rotating system, Procedia Engineering (Elsevier) 105, pp. 56 – 63.
  [9] Zueco, J., and Ahmed, S., (2010). Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source, Applied. Math. Mech. 31 (10), 1-14.
  [10] Agarwal, H.L., Ram, P.C. and Singh, V (1983). Combined influence of dissipation and Hall effect on free convective in a rotating fluid, .Indian J. Pure appl. Math. 14(3):314-32.
  [11] S.P. Dahake and A.V Dubewar “Effects of Radiation on Magnetohydrodynamic Convection Flow past an Impulsively Started Vertical Plate Submersed in a Porous Medium with Suction, International Journal of Computer Sciences and Engineering, vol. 2, Issues - 2, 2017.
  

  Citation
  U.S. Rajput, Neetu Kanaujia, "Effects of Hall current on MHD flow past a rotating inclined plate with heat transfer and mass diffusion.," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.253-258, 2018