Fourier-Homotopy Perturbation Method for Heat and Mass Transfer with 2D Unsteady Squeezing Viscous Flow Problem

Document Type : Research Paper


Department of Mathematics, college of Education for Pure Science, Basrah University, Basrah, Iraq.


In this article, an analytical technique has been proposed for solving the model of heat and mass transfer in the unsteady squeezing flow between parallel plates. The procedure of combining the Fourier transform and the homotopy perturbation method to yield a new technique was successful. The similarity transformation idea has been used to transform the system of governing partial differential equations into the system of ordinary differential equations. The influence of the physical parameters on the velocity, temperature and concentration with different values are discussed. The numerical results of Nusselt and Sherwood numbers, coefficient of skin friction, were compared with previous published works. The convergence of the new method was also discussed theoretically and experimentally. Furthermore, tables and graphs of the new analytical solutions demonstrate possibility, usefulness to use the new algorithm to deal with many nonlinear problems, especially heat transfer problems.


Main Subjects

[1]          M. Mahmood, S. Asghar, M. Hossain, Squeezed flow and heat transfer over a porous surface for viscous fluid, Heat and mass Transfer, Vol. 44, pp. 165-173, 2007.
[2]          M. Mustafa, T. Hayat, S. Obaidat, On heat and mass transfer in the unsteady squeezing flow between parallel plates, Meccanica, Vol. 47, pp. 1581-1589, 2012.
[3]          M. Sheikholeslami, D. Ganji, H. Ashorynejad, Investigation of squeezing unsteady nanofluid flow using ADM, Powder Technology, Vol. 239, pp. 259-265, 2013.
[4]          M. Sheikholeslami, M. Hatami, G. Domairry, Numerical simulation of two phase unsteady nanofluid flow and heat transfer between parallel plates in presence of time dependent magnetic field, Journal of the Taiwan Institute of Chemical Engineers, Vol. 46, pp. 43-50, 2015.
[5]          O. Pourmehran, M. Rahimi-Gorji, M. Gorji-Bandpy, D. Ganji, RETRACTED: analytical investigation of squeezing unsteady nanofluid flow between parallel plates by LSM and CM, Elsevier, 2015.
[6]          K. Singh, S. K. Rawat, M. Kumar, Heat and mass transfer on squeezing unsteady MHD nanofluid flow between parallel plates with slip velocity effect, Journal of Nanoscience, Vol. 2016, 2016.
[7]          G. M. Sobamowo, A. Akinshilo, Double diffusive magnetohydrodynamic squeezing flow of nanofluid between two parallel disks with slip and temperature jump boundary conditions, Applied and Computational Mechanics, Vol. 11, No. 2, 2017.
[8]          N. Balazadeh, M. Sheikholeslami, D. D. Ganji, Z. Li, Semi analytical analysis for transient Eyring-Powell squeezing flow in a stretching channel due to magnetic field using DTM, Journal of Molecular Liquids, Vol. 260, pp. 30-36, 2018.
[9]          M. Atlas, S. Hussain, M. Sagheer, Entropy generation and unsteady Casson fluid flow squeezing between two parallel plates subject to Cattaneo-Christov heat and mass flux, The European Physical Journal Plus, Vol. 134, No. 1, pp. 33, 2019.
[10]        A.-S. Al-Saif, A. Harfash, Perturbation-iteration algorithm for solving heat and mass transfer in the unsteady squeezing flow between parallel plates, Journal of Applied and Computational Mechanics, Vol. 5, No. 4, pp. 804-815, 2019.
[11]        A. Gupta, S. S. Ray, Numerical treatment for investigation of squeezing unsteady nanofluid flow between two parallel plates, Powder Technology, Vol. 279, pp. 282-289, 2015.
[12]        S. H. Seyedi, B. N. Saray, A. Ramazani, On the multiscale simulation of squeezing nanofluid flow by a highprecision scheme, Powder Technology, Vol. 340, pp. 264-273, 2018.
[13]        J.-H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, International Journal of Non-Linear Mechanics, Vol. 35, No. 1, pp. 37-43, 2000/01/01/, 2000.
[14]        J.-H. He, The homotopy perturbation method for nonlinear oscillators with discontinuities, Applied mathematics and computation, Vol. 151, No. 1, pp. 287-292, 2004.
[15]        J.-H. He, Homotopy perturbation technique, Computer methods in applied mechanics and engineering, Vol. 178, No. 3-4, pp. 257-262, 1999.
Volume 54, Issue 2
June 2023
Pages 219-235
  • Receive Date: 20 March 2023
  • Revise Date: 03 April 2023
  • Accept Date: 03 April 2023