Closed Form Solutions of Poiseuille and Couette- Poiseuille Flow of Non-Newtonian Fluid Through Parallel Plates

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2018 by IJMTT Journal
Volume-58 Number-4
Year of Publication : 2018
Authors : S Jana Reddy, D Srinivas Reddy and S P Kishore
  10.14445/22315373/IJMTT-V58P538

MLA

S Jana Reddy, D Srinivas Reddy and S P Kishore "Closed Form Solutions of Poiseuille and Couette- Poiseuille Flow of Non-Newtonian Fluid Through Parallel Plates" , International Journal of Mathematics Trends and Technology (IJMTT). V58(4):286-297 June 2018. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract

The velocity profiles with analytical solutions for the flow rates have been obtained through worked out solutions and are found to be accurate. The solution attributes to poiseuille and couette-poiseuille flow of a third grade fluid between two parallel plates. Such analytical solutions are almost equivalent to the corresponding numerical solutions. They are found to be rich in quality and comparitatively better than the approximate analytical solutions those were brought out in recent times. The impact of several parameters in respect of velocity profile and flow rate has been studied extensively in detail to conform to the process for further Research.

Reference
[1] Bird RB. Stewart WE. Lightfoot EN. Transport phenomena. 2nd ed. New York: John Wiley & Sons: 2002.
[2] Bird RB.Armstrong RC, Hassager O.dynamics of polymeric liuids. In: Fluid mechanics. New York : Wiley-Interscience; 1987 Vol.1.
[3] Rivlin RS ,Ericksen JL.Strees-deformation reactions for isotropic materials.J Ration Mech Anal 1955;3:323-425.
[4] Oldroyd JG. On the formulation of rheological equations of state. Proc R Soc Lond A 1950 ;200:523-41.
[5] Rajagopal KR. On the stability of third grade fluids. Arch Ration Mech Anal 1980;32:867-75.
[6] Fosdick RL, Rajagopal KR. Thermodynamics and stability of fluids of third grade .proc R Soc Lond A 1980;339:351-77.
[7] Passerni A, Patria MC. Existence, uniqueness and stability of steady flows of second and third grade fluids in an unbounded “pipe-like” domain. Int J Nonlinear Mech 2000;35:1081-103.
[8] Bellout H, Necas J. Rajagopal KR. On the existence and uniqueness of flows of multipolar fluids -of grade 3 and their stability. Int J Eng Scie 1999;37:75-96.
[9] Vajravelu K, Cannon JR, Rollins D, Leto J. On Solutions of some nonlinear differential equations arising in third grade fluid flows. Int J Eng Sci 2002;40:1791-805.
[10] Akyildiz FT, Bellout H, Vajravelu K. Exact solutions for thin film flow of a third grade fluid flows. Int J Nonliner Mech 2004;39:1571-8.
[11] Majhi SN ,Nair VR. Puisatile flow of third grade fluids under body acceleration-modeling blood flow.Int J Eng Sci 1994;32:839-46.
[12] Rajagopal KR,Sciubba E. Pulsating Poiseuille flow of a non-Newtonian fluid.Math Comput Simul 1984;26:276-88.
[13] Hayat T, Ellahi R, Mahomed FM. Exact solutions for thin film flow of a third grade fluid down an inclined plane. Chaos solutions Fract 2008;38:1336-41.
[14] Siddiqui AM, Mahmood R, Ghori QK. Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane. Chaos solitons Fract 2008;35:140-7.
[15] Sajid M.Hayat T, The application of homotopy analysis method to thin film flows of a third grade fluid. Chaos solitons Fract 2008;38:506-15.
[16] Siddiqui AM, Zeb A, Ghori QK, Benharbit AM. Homotopy perturbation method for heat transfer flow a third grade fluid between parallel plates. Chaos solitons Fract 2008;36:182-92.
[17] Siddqui AM, Hameed M, Siddiqui BM, Ghori QK,. Use of Adomian decomposition method in the study of parallel plate flow of a third grade fluid Common Nonlinerar Sci Number Simul 2010;15-2388-99
[18] Ayub M. Rasheed A, Hayat T. Exact flow of a third grade fluid past a porous plate using homotopy analysis method. Int J Eng Sci 2003; 41:2091-103.
[19] Rice RG,DO DD.Applied mathematics and modeling for chemical engineers.New York :John Wiley and Sons Inc.;1994.

Keywords
poiseuille, couette-poiseuille flow, third grade fluid, Numerical solution, Closed form solution