Application of DTM for 2D viscous flow through expanding or contracting gaps with permeable walls

Abstract

In this study, Differential Transformation Method is used to solve the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions. The concept of this method is briefly introduced, and it’s application for this problem is studied. Then, the results are compared with numerical results and the validity of these methods is shown. After this verification, we analyze the effects of some physical applicable parameters to show the efficiency of DTM for this type of problems. Graphical results are presented to investigate the influence of the non-dimensional wall dilation rate () and permeation Reynolds number (Re) on the velocity, normal pressure distribution and wall shear stress. The present problem for slowly expanding or contracting walls with weak permeability is a simple model for the transport of biological fluids through contracting or expanding vessels

Keywords

• Permeation Reynolds number,Non-dimensional wall dilation rate; Differential Transformation Method (DTM)

Application of DTM for 2D viscous flow through expanding or contracting gaps with permeable walls

Öz

Kaynakça

1. Chang ,H.N. and J.S. Ha, J.K. Park, I.H. Kim, H.D. Shin, 1989. Velocity field of pulsatile flow in a porous tube, J. Biomech, 22 :1257_1262.
2. Dauenhauer, E.C. and J. Majdalani, 1999. Unsteady flows in semi-infinite expanding channels with wall injection, in: AIAA paper, 99_3523.
3. Majdalani, J. and C. Zhou, 2003. Moderate-to-large injection and suction driven channel flows with expanding or contracting walls, ZAMM Z. Angew. Math. Mech. 83:181_196.
4. K. Zhou, Differential transformation and its applications for electrical circuits, Huazhong Univ.Press,Wuhan,China, 1986.
5. C.K. Chen, S.H. Ho, Solving partial differential equations by two dimensional differential transform method, Appl. Math. Comput. 106 (1999) 171–179.
6. F. Ayaz, Solutions of the systems of differential equations by differential transform method, Appl. Math. Comput. 147 (2004) 547–567.
7. IH. Abdel-Halim Hassan, Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems, Chaos Solitons and Fractals 36 (2008) 53–65.
8. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, Natural convection heat transfer in a nanofluid filled inclined L-shaped enclosure, IJST, Transactions of Mechanical Engineering, 38 (2014) 217-226.

9. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, P. Rana, Soheil Soleimani, Magnetohydrodynamic free convection of Al2O3-water nanofluid considering Thermophoresis and Brownian motion effects, Computers & Fluids 94 (2014) 147–160.
10. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, Thermal management for free convection of nanofluid using two phase model, Journal of Molecular Liquids 194 (2014) 179–187.
11. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, Heat flux boundary condition for nanofluid filled enclosure in presence of magnetic field, Journal of Molecular Liquids,193 (2014) 174-184.
12. M. Sheikholeslami, D.D. Ganji, M. Gorji-Bandpy, Soheil Soleimani, Magnetic field effect on nanofluid flow and heat transfer using KKL model, Journal of the Taiwan Institute of Chemical Engineers 45 (2014) 795–807
13. M. Sheikholeslami, M. Gorji-Bandpy, Soheil Soleimani, Two phase simulation of nanofluid flow and heat transfer using heatline analysis, International Communications in Heat and Mass Transfer 47 (2013) 73–81
14. M. Sheikholeslami, M. Gorji Bandpy, R. Ellahi, Mohsan Hassan , Soheil Soleimani, Effects of MHD on Cu-water nanofluid flow and heat transfer by means of CVFEM, Journal of Magnetism and Magnetic Materials 349 (2014)188–200.
15. M. Sheikholeslami, M. Gorji-Bandpy, I. Pop, Soheil Soleimani, Numerical study of natural convection between a circular enclosure and a sinusoidal cylinder using control volume based finite element method, International Journal of Thermal Sciences 72 (2013) 147-158.
16. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, Natural convection heat transfer in a cavity with sinusoidal wall filled with CuO-water nanofluid in presence of magnetic field, Journal of the Taiwan Institute of Chemical Engineers 45 (2014) 40–49.
17. M. Sheikholeslami, I. Hashim and Soheil Soleimani, Numerical Investigation of the Effect of Magnetic Field on Natural Convection in a Curved-Shape Enclosure, Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2013, Article ID 831725, 11 pages http://dx.doi.org/10.1155/2013/831725
18. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, Effect of a magnetic field on natural convection in an inclined half-annulus enclosure filled with Cu–water nanofluid using CVFEM, Advanced Powder Technology 24 (2013) 980– 9
19. M. Sheikholeslami, M. Gorji-Bandpy, D. D. Ganji, Soheil Soleimani, MHD natural convection in a nanofluid filled inclined enclosure with sinusoidal wall using CVFEM, Neural Comput & Applic (2014) 24:873–882.
20. M. Sheikholeslami , M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, S.M. Seyyedi, Natural convection of nanofluids in an enclosure between a circular and a sinusoidal cylinder in the presence of magnetic field, International Communications in Heat and Mass Transfer 39 (2012) 1435–1443.
21. Soheil Soleimani, M. Sheikholeslami, D.D. Ganji and M. Gorji-Bandpay, Natural convection heat transfer in a nanofluid filled semi-annulus enclosure, International Communications in Heat and Mass Transfer 39 (2012) 565–574.
22. M. Sheikholeslami, M. Gorji-Bandpay, D.D. Ganji, Investigation of nanofluid flow and heat transfer in presence of magnetic field using KKL model, Arabian Journal for Science and Engineering, 39(6) 2014 5007-5016.
23. Mohsen Sheikholeslami, Mofid Gorji Bandpy, R. Ellahi, A. Zeeshan, Simulation of MHD CuO–water nanofluid flow and convective heat transfer considering Lorentz forces, Journal of Magnetism and Magnetic Materials 369 (2014) 69–80.
24. M. Sheikholeslami, M. Gorji-Bandpay, D.D. Ganji, Magnetic field effects on natural convection around a horizontal circular cylinder inside a square enclosure filled with nanofluid, International Communications in Heat and Mass Transfer 39 (2012) 978– 9
25. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, MHD free convection in an eccentric semi-annulus filled with nanofluid, Journal of the Taiwan Institute of Chemical Engineers 45 (2014) 1204–1216.
26. Mohsen Sheikholeslami, Mofid Gorji-Bandpy, Free convection of ferrofluid in a cavity heated from below in the presence of an external magnetic field, Powder Technology 256 (2014) 490–498
27. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Lattice Boltzmann method for MHD natural convection heat transfer using nanofluid, Powder Technology 254 (2014) 82-93.
28. M. Sheikholeslami, M. Gorji-Bandpy, D. D. Ganji, Numerical investigation of MHD effects on Al2O3-water nanofluid flow and heat transfer in a semi-annulus enclosure using LBM, Energy 60 (2013) 501-510
29. M. Sheikholeslami, M. Gorji-Bandpy, S.M. Seyyedi, D.D. Ganji, Houman B. Rokni, Soheil Soleimani, Application of LBM in simulation of natural convection in a nanofluid filled square cavity with curve boundaries, Powder Technology 247 (2013) 87–
30. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Natural convection in a nanofluid filled concentric annulus between an outer square cylinder and an inner elliptic cylinder, Scientia Iranica, Transaction B: Mechanical Engineering. (2013) 20(4), 1241- 12
31. M. Sheikholeslami, M. Gorji-Bandpy, G. Domairry, Free convection of nanofluid filled enclosure using lattice Boltzmann method (LBM), Appl. Math. Mech. -Engl. Ed., 34(7), (2013) 1–15.
32. Hamid Reza Ashorynejad, Abdulmajeed A. Mohamad, Mohsen Sheikholeslami, Magnetic field effects on natural convection flow of a nanofluid in a horizontal cylindrical annulus using Lattice Boltzmann method, International Journal of Thermal Sciences 64 (2013) 240-250.
33. M. Sheikholeslami, D.D. Ganji, Heated permeable stretching surface in a porous medium using Nanofluids, Journal of Applied Fluid Mechanics, 7(3) (2014) 535-542.
34. M. Sheikholeslami, D.D. Ganji, Three dimensional heat and mass transfer in a rotating system using nanofluid, Powder Technology 253 (2014) 789–796.
35. Mohammad Hatami, Mohsen Sheikholeslami, M. Hosseini, Davood Domiri Ganji, Analytical investigation of MHD nanofluid flow in non-parallel walls, Journal of Molecular Liquids 194 (2014) 251–259.
36. M. Sheikholeslami, D.D. Ganji, Magnetohydrodynamic flow in a permeable channel filled with nanofluid, Scientia Iranica B (2014) 21(1), 203-212 .
37. M. Hatami, M. Sheikholeslami, D.D. Ganji, Nanofluid flow and heat transfer in an asymmetric porous channel with expanding or contracting wall, Journal of Molecular Liquids 195 (2014) 230–239.
38. M. Hatami, M. Sheikholeslami, G. Domairry, High Accuracy Analysis for Motion of a Spherical Particle in Plane Couette Fluid Flow by Multi-step Differential Transformation Method, Powder Technology (2014), doi: 10.1016/j.powtec.2014.02.057
39. M. Sheikholeslami, D.D. Ganji, Numerical investigation for two phase modeling of nanofluid in a rotating system with permeable sheet, Journal of Molecular Liquids 194 (2014) 13-19.
40. M. Sheikholeslami, M. Hatami, D.D.Ganji, Micropolar fluid flow and heat transfer in a permeable channel using analytical method, Journal of Molecular Liquids 194 (2014) 30–36.
41. M. Hatami, M. Sheikholeslami, D.D. Ganji, Laminar flow and heat transfer of nanofluid between contracting and rotating disks by least square method, Powder Technology 253 (2014) 769–779.
42. M. Sheikholeslami, M. Hatami, D.D. Ganji, Nanofluid flow and heat transfer in a rotating system in the presence of a magnetic field, Journal of Molecular Liquids 190 (2014) 112–120.
43. M. Sheikholeslami, F. Bani Sheykholeslami, S. Khoshhal, H. Mola-Abasia, D. D. Ganji, Houman B. Rokni, Effect of magnetic field on Cu–water nanofluid heat transfer using GMDH-type neural network, Neural Comput & Applic, DOI 1007/s00521-013-1459-y.
44. M. Sheikholeslami, R. Ellahi, H. R. Ashorynejad, G. Domairry, and T. Hayat, Effects of Heat Transfer in Flow of Nanofluids Over a Permeable Stretching Wall in a Porous Medium, Journal of Computational and Theoretical Nanoscience, Vol. 11, 1–11, 2014.
45. M. Sheikholeslami, M. Hatami, D. D. Ganji, Analytical investigation of MHD nanofluid flow in a Semi-Porous Channel, Powder Technology 246 (2013) 327–336
46. M. Sheikholeslami, D.D. Ganji, H.R. Ashorynejad, Investigation of squeezing unsteady nanofluid flow using ADM, Powder Technology 239 (2013) 259–265.
47. M. Sheikholeslami, D.D. Ganji, Heat transfer of Cu-water nanofluid flow between parallel plates, Powder Technology 235 (2013) 873–879.
48. H. R. Ashorynejad, M. Sheikholeslami,I. Pop, D. D. Ganji, Nanofluid flow and heat transfer due to a stretching cylinder in the presence of magnetic field, Heat Mass Transfer 49 (2013) 427–436.
49. Davood Domairry, Mohsen Sheikholeslami, Hamid Reza Ashorynejad,Rama Subba Reddy Gorla and Mostafa Khani, Natural convection flow of a non-Newtonian nanofluid between two vertical flat plates, Proc IMechE Part N:J Nanoengineering and Nanosystems225(3) 115–122©IMechE 2012. DOI: 10.1177/1740349911433468.
50. M. Sheikholeslami, D. D. Ganji, H. R. Ashorynejad, Houman B. Rokni, Analytical investigation of Jeffery-Hamel flow with high magnetic field and nano particle by Adomian decomposition method, Appl. Math. Mech.-Engl. Ed., 33(1), 1553–1564 (2012).
51. M. Sheikholeslami,H. R. Ashorynejad, G. Domairry and I. Hashim, Flow and Heat Transfer of Cu-Water Nanofluid between a Stretching Sheet and a Porous Surface in a Rotating System, Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2012, Article ID 421320, 19 pages ,doi:10.1155/2012/421320.
52. M. Sheikholeslami, H. R. Ashorynejad,D. D. Ganji and A. Kolahdooz, Investigation of Rotating MHD Viscous Flow and Heat Transfer between Stretching and Porous Surfaces Using Analytical Method, Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2011, Article ID 258734, 17 pages,doi:10.1155/2011/258734.
53. M. Sheikholeslami, H.R. Ashorynejad, D.D. Ganji, A. Yıldırım, Homotopy perturbation method for three-dimensional problem of condensation film on inclined rotating disk, Scientia Iranica B (2012) 19 (3), 437–442
54. Mohsen Sheikholeslami, Hamid Reza Ashorynejad ,Davood Domairry, Ishak Hashim, Investigation of the Laminar Viscous Flow in a Semi-Porous Channel in the Presence of Uniform Magnetic Field using Optimal Homotopy Asymptotic Method, Sains Malaysiana 41(10)(2012): 1177–1229.
55. M. Sheikholeslami, H.R. Ashorynejad, A. Barari, Soheil Soleimani, Investigation of heat and mass transfer of rotating MHD viscous flow between a stretching sheet and a porous surface. Engineering Computations, 30(3) (2013) 357-3
56. M. Sheikholeslami , D.D. Ganji , Houman B. Rokni ,Nanofluid Flow in a Semi-Porous Channel in the Presence of Uniform Magnetic Field, Ije Transactions C: Aspects Vol. 26, No. 6, (June 2013) 653-662.