Comparative Solution of Heat Transfer Analysis for Squeezing Flow between Parallel Disks

References

[1] E. Babolian, A.R. Vahidi and Z. Azimzadeh, 2012. A Comparison Between Adomian’s Decomposition Method and the Homotopy Perturbation Method for Solving Nonlinear Differential Equations. Journal of Applied Sciences, 12: 793-797. DOI: 10.3923/jas.2012.793.797, URL: https://scialert.net/abstract/?doi=jas.2012.793.797

[2] Abbaoui, K. and Y. Cherruault, 1995. New ideas for proving convergence of decomposition methods. Comput. Math. Appl., 29: 103-108.

[3] Abbasbandy, S., 2006. Numerical solutions of the integral equations: Homotopy perturbation method and Adomian’s decomposition method. Applied Math. Comput., 173: 493-500.

[4] Adomian, G., 1976. Nonlinear stochastic differential equations. J. Math. Anal. Appl., 55: 441-452.

[5] Adomian, G. and R. Rach, 1983. Inversion of nonlinear stochastic operators. J. Math. Anal. Appl., 91: 39-46.

[6] Adomian, G., 1988. A review of decomposition method in applied mathematics. J. Math. Anal. Appl., 135: 501-544.

[7] Adomian, G., 1989. Nonlinear Stochastic Systems Theory and Applications to Physics. Springer, USA., Pages: 224.

[8] Adomian, G., 1994. Solving Frontier problems of Physics: The Decomposition Method. Springer, London, ISBN: 9780792326441, Pages: 372.

[9] Alnasr, M.H. and S. Momani, 2008. Application of homotopy perturbation method to singularly perturbed volterra integral equations. J. Applied Sci., 8: 1073-1078.

[10] Barari, A., A.R. Ghotbi, F. Farrokhzad and D.D. Ganji, 2008. Variational iteration method and homotopy-perturbation method for solving different types of wave equations. J. Applied Sci., 8: 120-126.

[11] Cherruault, Y., 1989. Convergence of Adomian's method. Kybernetes, 8: 31-38.

[12] Cherruault, Y. and G. Adomian, 1993. Decomposition methods: A new proof of convergence. Math. Comput. Modelling, 18: 103-106.

[13] Cherruault, Y. and G. Adomian, K. Abbaoui and R. Rach, 1995. Further remarks on convergence of decomposition method. Int. J. Bio-Med. Comput., 38: 89-93.

[14] Choobbasti, A.J., F. Farrokhzad, A. Barari and D.D. Ganji, 2008. Application of wave equation in pile foundation using homotopy perturbation method and variational iteration method. J. Applied Sci., 8: 2158-2162.

[15] Chowdhury, S.H., 2011. A comparison between the modified homotopy perturbation method and adomian decomposition method for solving nonlinear heat transfer equations. J. Applied Sci., 11: 1416-1420.

[16] Fazeli, M., S.A. Zahedi and N. Tolou, 2008. Explicit solution of non-linear fourth-order parabolic equations via homotopy perturbation method. J. Applied Sci., 8: 2619-2624.

[17] Ganji, D.D., H. Mirgolbabaei, M. Miansari and M. Miansari, 2008. Application of homotopy perturbation method to solve linear and non-linear systems of ordinary differential equations and differential equation of order three. J. Applied Sci., 8: 1256-1261.

[18] Ghotbi, A.R., A. Avaei, A. Barari and M.A. Mohammadzade, 2008. Assessment of He's homotopy perturbation method in burgers and coupled burger's equations. J. Applied Sci., 8: 322-327.

[19] He, J.H., 1999. Homotopy perturbation technique. Comput. Methods Applied Mech. Eng., 178: 257-262.

[20] He, J.H., 2000. A coupling method of a homotopy technique and a perturbation technique for non-linear problems. Int. J. Non-Linear Mech., 351: 37-43.

[21] He, J.H., 2004. Comparison of homotopy perturbation method and homotopy analysis method. Applied Math. Comput., 156: 527-539.

[22] He, J.H., 2006. Perturbation Methods: Basic and Beyond. Elsevier, Amsterdam, Netherlands. Jaradat, O.K., 2008. Adomian decomposition method for solving abelian differential equations. J. Applied Sci., 8: 1962-1966.

[23] Khatami, I., N. Tolou, J. Mahmoudi and M. Rezvani, 2008. Application of homotopy analysis method and variational iteration method for shock wave equation. J. Applied Sci., 8: 848-853.

[24] Li, J.L., 2009. Adomian`s decomposition method and homotopy perturbation method in solving nonlinear equations. Applied Math. Comput., 228: 168-173.

[25] Liao, S., 2004. On the homotopy analysis method for nonlinear problems. Applied Mathe. Comput., 147: 499-513.

[26] Mirgolbabaei, H. and D.D. Ganji, 2009. Application of homotopy perturbation method to solve combined korteweg de vries-modified korteweg de vries equation. J. Applied Sci., 9: 3587-3592.

[27] Noorzad, R., A.T. Poor and M. Omidvar, 2008. Variational iteration method and homotopy-perturbation method for solving burgers equation in fluid dynamics. J. Applied Sci., 8: 369-373.

[28] Ozis, T. and A. Yildirim, 2008. Comparison between Adomian`s decomposition method and He`s homotopy perturbation method. Applied Math. Comput., 56: 1216-1224.

[29] Rach, R., 2008. A new definition of the Adomian polynomials. Kybernetes, 37: 910-955.

[30] Sajid, M. and T. Hayat, 2008. Comparison of HAM and HPM methods in nonlinear heat conduction and convection equations. Nonlinear Anal. Real World Appl., 9: 2296-2301.

[31] Sharma, P.R. and G. Methi, 2011. Applications of homotopy perturbation method to partial differential equations. Asian J. Math. Stat., 4: 140-150.

[32] Vahidi, A.R. and M. Isfahani, 2011. On the homotopy perturbation method and the Adomian decomposition method for solving Abel integral equations of the second kind. Applied Math. Sci., 5: 799-804.

[33] Wazwaz, A.M., 1998. A comparison between Adomian decomposition method and Taylor series method in the series solution. Applied Math. Comput., 97: 37-44.

[34] Wazwaz, A.M., 2000. A new algorithm for calculating Adomian polynomials for non-linear operators. Applied Math. Comput., 111: 33-51.

[35] Rilwan Adewale Mustapha; Ayobami Muhammed Salau.”On the solution of Heat and Mass transfer Analysis in Nanofluids flow using Semi-Analytic Method (HPM) between two parallel Manifolds” Iconic Research And Engineering Journals Volume 4 issue 4 2020 page 78-86.

[36] Mustapha R.A.; Salau A.M. Adomian Decomposition Method for Solving Heat Transfer Analysis for Squeezing Flow of Nanofluid in Parallel Disks. International Journal of Advances in Engineering and Management (IJAEM). Volume 2, Issue 12, pp: 282-288.

[37] MUSTAPHA Rilwan Adewale; SALAU Ayobami Muhammed. (Volume. 6 Issue. 1, January - 2021) “Series Solution of Euler-Bernoulli Beam Subjected to Concentrated Load Using Homotopy Perturbation Method (HPM).", International Journal of Innovative Science and Research Technology (IJISRT), www.ijisrt.com. ISSN - 2456-2165, PP:- 1742-1749.

@article{1702671,
      author = {Salau Ayobami Muhammed, Mustapha Rilwan Adewale},
      title = {Comparative Solution of Heat Transfer Analysis for Squeezing Flow between Parallel Disks},
      journal = {Iconic Research And Engineering Journals},
      year = {2021},
      volume = {4},
      number = {10},
      pages = {136-142},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1702671.pdf},
      abstract = {The main aim of this present work is to compare two methods employed for solving squeezing flow problems namely Homotopy Perturbation Method (HPM) and the Adomian Decomposition Method (ADM). The Comparison between HPM and ADM is bench-marked against a numerical solution Scheme (FDM). The results show that the ADM is more efficient and reliable than HPM from  a computational viewpoint. Although ADM requires tedious computational effort than the HPM, but it yields more accurate and reliable results than the HPM.},
      keywords = {Squeezing flow, magneto-hydro-dynamics (MHD), Homotopy Perturbation Method (HPM), Adomian Decomposition Method (ADM), Parallel manifolds, Finite Difference Method (FDM)},
      month = {April},
  }