Volume-4 , Issue-2 , Apr 2017, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Stochastic Reynolds Equation for Diverse Shaped Slider Bearing when Lubricated with Couplestress Fluid and by Applying MHD

  S.T. Fathima, C.K. Sreekala, B.N. Hanumagouda

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.2 , pp.1-13, Apr-2017

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  Purpose- The objective of this paper is to conduct a theoretical analysis of wide composite slider bearings of diverse film shapes like parabolic, plane, exponential, and secant for the case of couplestress fluid in the existence of magnetic field applied normal to bearing surface and on the basis of roughness of the surface. Design/Methodology – The generalised stochastic Reynolds equation is derived based on Stokes model and Christensen stochastic model. The expressions for the characteristics of bearing are obtained for general lubricant film shape in integral form and are numerically computed for the shapes under consideration. Findings- It is fascinating to note that the impact of magnetic field, couplestress and roughness of surface significantly affect the bearing characteristics. It is concluded from comparison that load supporting capability of parabolic slider is more significant. Originality/value – It is expected that these analyses will help design engineers to choose proper shaped slider bearings with appropriate couplestress, roughness parameters in the occurrence of applied magnetic field, which improves the normal functioning of the bearings.

  Key-Words / Index Term
  Composite slider, Couple-stress fluid, Surface roughness, Magnetic field

  References
  [1] T. Ariman, M.A. Turk, N.D Sylvester., “ Microcontinuim fluid mechanics-a review”, Int. J of Engg Sci., Vol. 11 ,pp.905-930, 1973.
  [2] T. Ariman, M.A Turk, N.D Sylvester., “Application of microcontinuum fluid mechanics”, International journal of Engineering science, Vol. 12, pp 273-293, 1974..
  [3] M.M Khonsari, D. E Brewe, “On the performance of finite journal bearing lubricated with micropolar fluids”, Tribology transaction, Vol. 32, pp.155-160, 1989.
  [4] V. K. Stokes., “ Couplestresses in fluids”, Physics of Fluids, Vol. 9, pp. 1709-1715, 1966.
  [5] G Ramanaiah, P. Sarkar, “Slider bearing lubricated by fluids with couple-stress”, Wear; Vol. 52, pp. 27-36, 1979.
  [6] J.R.Lin, Yu-Ming Lu, “Steady-state performance of wide parabolic shaped slider bearings with a couple stress fluids”, Journal of Marine science and Technology, Vol. 12, pp. 239-246,2004.
  [7] Oladeinde, Mobolaji H Akpobi, A. John., “Performance of Infinitely wide parabolic and inclined slider bearing lubricated with couplestress or magnetic fluids”, Proceedings on world congress on engineering, Vol. 1394, pp. 58-68, 2011.
  [8] J.R Lin, C.R Hung, C.H Hsu, C Lai, “Dynamic stiffness and damping characteristics of one dimensional MHD inclined-plane slider bearing”, Proceedings of the institution of Mechanical engineers-part J Journal of engineering tribology, Vol. 223, pp. 211-219, 2009.
  [9] J.R Lin, R.F Lu. “Dynamic characteristics for magneto-hydrodynamic wide slider bearings with an exponential film profile”, Journal of marine science and technology, Vol.18, Issue.2, pp. 268-276, 2010.
  [10] J. R. Lin, “Dynamic characteristics for wide magneto-hydrodynamic slider bearing with a power-law film profile”, Applied mathematical modelling, Vol. 36, pp. 4521-4528, 2012.
  [11] Lin JR, “MHD steady and dynamic characteristics of wide Tapered-Land Slider Bearings”, Tribology International, Vol. l 43, pp. 2378-2383, 2010.
  [12] J. R Lin, R.F, Lu, T.C,Hung and L.J. Liang , “Effects of magnetic fields on the dynamic characteristics of wide parallel step slider bearing with Electrically conducting Fluids”, Lubrication Science, Vol. 24, pp. 238-250, 2012.
  [13] N.B Naduvinamani, S.T, Fathima, B.N.Hanumagowda., “Magnetohydrodynamic couplestress squeeze film lubrication of circular stepped plates”, JET part J, Vol. 225, pp. 111-119, 2011.
  [14] Biradar Kasinath, B. N Hanumagowda, “MHD effect on composite slider bearing lubricated with couplestress fluids”, International journal of mathematics trends and technology, Vol. 5, pp. 27-49, 2014.
  [15] S. T,Fathima, N. B Naduvinamani, H. M, Shivakumar B. N Hanumagowda, “A Study on the Performance of Hydromagnetic Squeeze Film between Anisotropic Porous Rectangular Plates with Couple Stress Fluids”, Tribology Online, 9, pp. 1–9, 2014.
  [16] S.T Fathima, N. B Naduvinamani, B.N Hanumagowda, J. Santhosh Kumar, “Modified Reynolds Equation for Different Types of Finite Plates with the Combined Effect of MHD and Couple Stresses”, Tribology Transactions, Vol. 12, Issue.58:4, pp. 660-667, 2015.
  [17] H. Christensen. “Stochastic models for hydrodynamic lubrication of rough surfaces”, Proc of the Inst of Mechanical Engineers part I, ,Vol. 184, pp. 1013-1026, 1969.
  [18] N.B. Naduvinamani, A Siddanagouda, “Effect of surface roughness on the hydrodynamic lubrication of porous step-slider bearings with couplestress fluids”, Tribology International, Vol. 40, pp. 780-793, 2007.
  [19] N.B. Naduvinamani, ST, Fathima , P. S. Hiremath, “ On the squeeze effect of lubricants with additives between rough porous rectangular plates”, ZAMM, Vol.84, pp. 825-834, 2004.
  [20] N.B. Naduvinamani, B. N. Hanumagowda, S. T Fathima. “Combined effects of MHD and surface roughness on couple-stresss squeeze film lubrication between porous circular stepped plate”, Tribology International, Vol. 56, pp. 19-29, 2012.
  [21] N.B. Naduvinamani, P.S Hiremath, G Gurubasavaraj, “Effect of surface roughness on the couplestress squeeze film between a sphere and a flat plate,” Tribology International, Vol. 38, pp. 451-458, 2005.
  [22] N.B. Naduvinamani, P. S Hiremath, G. Gurubasavaraj, “ Surface roughness effects in a short porous journal bearing with a couple stress fluid”, Fluid Dynamic Research, Vo.31, Issue.6, pp. 315-316, 2002.
  [23] N.B. Naduvinamani., S.T Fathima, P.S. Hiremath., “Hydrodynamic lubrication of rough slider bearings with couplestress fluids”, Tribology International, Vol. 36, Issue.12, pp. 949-959, 2003.
  

  Citation
  S.T. Fathima, C.K. Sreekala, B.N. Hanumagouda, "Stochastic Reynolds Equation for Diverse Shaped Slider Bearing when Lubricated with Couplestress Fluid and by Applying MHD," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.2, pp.1-13, 2017

• Open Access   Article

  A Fixed Point Theorem for a Contractive Mapping in Dislocated Quasi Metric Space

  V.H. Badshah, V.P. Bairagi, A. Pariya

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.2 , pp.14-17, Apr-2017

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  Aage and Salunke [1] proved the result on fixed point theorem in Dislocated and Dislocated Quasi Metric space. Dass and Gupta [2] have given an extentionsion of Banach Contraction Principal through rational expression. In this paper we establish a common fixed point theorem for continuous contractive mapping in Dislocated Quasi metric space which is the generalized result of Isufati. A [4], Mujeeb Ur Rahman and Muhammad Sarwar [11].

  Key-Words / Index Term
  Dislocated Quasi metric space, common fixed point, continuous contractive mapping

  References
  [1] C.T. Aage, J.N. Salunke, “The Results on Fixed Point Theoremin Dislocated6 and Quasi-Metric Spaces”, Applied Mathematical Science, Vol.2, Issue.59 , pp.2941-2948, 2008.
  [2] B. K. Dass and S. Gupta, “An extension of Banach contraction principle through rational expressions”, Indian Journal of Pure and Applied Mathematics, vol. 6, Issue.12, pp. 1455–1458, 1975.
  [3] P. Hitzler, A.K. Seda, “Dislocated Topologies”, Journal of Electrical Engineering, Vol.51, Issue.12, pp.3-7, 2000.
  [4] A. Isufati, “Fixed Point Theorem in Dislocated Quasi-Metric Space”, Applied Mathematical Sciences, Vol.4, Issue.5, pp.217-223, 2010.
  [5] M. Kohli, R. Sriravastava, M. Sharma, “ Some Results on Fixed Point Theorem in Dislocated Quasi Metric Space”, International Journal of Theoritical&AppliedSciences,Vol.2, Issue.1, pp.27-28, 2010.
  [6] S.S. Pagey, R. Nighojkar, “A Fixed Point Theorem For Expansive Type Mapping in Dislocated Quasi Metric Space ”, International Journal of Theoretical & Applied Sciences,Vol.3, Issue.1, pp.26-27, 2011.
  [7] B.E. Rhoades, “A Comparison of Various Definition of Contractive Mapping”, Transactions of the American Mathematical Society, Vol.226, Issuee.1, pp.257-290, 1977.
  [8]R. Shrivastava, R. Gupta, “A Fixed Point Theorem for Random Operator in Dislocated Quasi Metric Spaces ”, International Journal of Theoretical &Applied Sciences,Vol.3, Issue., pp.47-48 , 2011.
  [9]R. Shrivastava, K. Qureshi, K. Rathore, “A Common Fixed Point Theorem For a Pair of Mapping in Dislocated Metric Space”, Advances in Applied Science Research, Vol.5, Issue.3, pp.417-419, 2014.
  [10] F.M. Zeyada, G.H. Hassan, M.A. Ahmed, “A Generalization of a fixed point theorem due to Hitzler and Seda in dislocated quasi-metric spaces”, The Arabian Journal for Science Engineering., Vol.31, Issue.1, pp.111-114, 2006.
  [11]M.U. Rahman, M. Sarwar, “Fixed Point Results in Dislocated Quasi Metric Spaces”, International Mathematical Forum , Vol.9, Issue.14, pp.677-682, 2014.
  

  Citation
  V.H. Badshah, V.P. Bairagi, A. Pariya, "A Fixed Point Theorem for a Contractive Mapping in Dislocated Quasi Metric Space," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.2, pp.14-17, 2017