Three dimensional flow and mass transfer analysis of a second grade fluid in a porous channel with a lower stretching wall

• Autorzy: Khan N. A. , Naz F.

Identyfikatory

DOI

10.1515/ijame-2016-0022

• Języki publikacji: EN

Abstrakty

EN

This investigation analyses a three dimensional flow and mass transfer of a second grade fluid over a porous stretching wall in the presence of suction or injection. The equations governing the flow are attained in terms of partial differential equations. A similarity transformation has been utilized for the transformation of partial differential equations into the ordinary differential equations. The solutions of the nonlinear systems are given by the homotopy analysis method (HAM). A comparative study with the previous results of a viscous fluid has been made. The convergence of the series solution has also been considered explicitly. The influence of admissible parameters on the flows is delineated through graphs and appropriate results are presented. In addition, it is found that instantaneous suction and injection reduce viscous drag on the stretching sheet. It is also shown that suction or injection of a fluid through the surface is an example of mass transfer and it can change the flow field.

Słowa kluczowe

EN

second grade fluid; stretching wall; suction; injection

PL

równania różniczkowe; płyn lepki; pole przepływu

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2016
• Tom: Vol. 21, no. 2
• Strony: 359--376
• Opis fizyczny: Bibliogr. 32 poz., tab., wykr.

Twórcy

autor

Khan N. A.

• Department of Mathematics, University of Karachi Karachi 75270, PAKISTAN

autor

Naz F.

• Department of Mathematics, University of Karachi Karachi 75270, PAKISTAN

Bibliografia

• [1] Dunn J.E. and Fosdick R.L. (1974): Thermodynamics, stability and boundedness of fluids of complexity 2 and fluids of second grade. – Arch. Ration. Mech. Anal., vol.56, pp.191-252.
• [2] Dunn J.E. and Rajagopal K.R. (1995): Fluids of differential type-critical review and thermodynamic analysis. – Int. J. Eng. Sci., vol.33, pp.689-729.
• [3] Ali S.A., Ara A. and Khan N.A. (2007): Martin’s method applied to steady plane flow of a second grade fluid. – Int. J. Appl. Math. Mech., vol.3, pp.71-81.
• [4] Mahmood A., Khan N.A., Fetecau C., Jamil M. and Rubbab Q. (2009): Exact analytic solutions for the flow of second grade fluid between two longitudinally oscillating cylinder. – J. Prime Research in Math., vol.5, pp.192-204.
• [5] Hayat T., Khan M., Ayub M. and Siddiqui A.M. (2005): The unsteady Couette flow of second grade fluid in a layer of porous medium. – Arch. Mech., vol.57, pp.405-416.
• [6] Abdallah I.A. (2009): Analytical solution of heat and mass transfer over a permeable stretching plate affected by a chemical reaction, internal heating, Dufour-Souret effect and Hall effect. – Int. J. Therm. Sci., vol.2, pp.183-197.
• [7] Ariel P.D. (2002): On exact solutions of flow problems of a second grade fluid through two parallel porous walls. – Int. J. Eng. Sci., vol.40, pp.913-941.
• [8] Chen C.I., Chen C.K. and Yang Y.T. (2003): Unsteady unidirectional flow of a second grade fluid between the parallel plates with different given volume flow rate conditions. – Appl. Math. Comput., vol.137, pp.437-450.
• [9] Aksoy Y., Pakdemirli M. and Khalique C.M. (2007): Boundary layer equations and stretching sheet solutions for the modified second grade fluid. – Int. J. Eng. Sci., vol.45, pp.829-841.
• [10] Hayat T. and Sajid M. (2007): Analytical solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet. – Int. J. Heat Mass Transfer, vol.50, pp.75-84.
• [11] Galdi G.P. and Sequeira A. (1994): Further existence results for classical solutions of the equations of second-grade fluid. – Arch. Rat. Mech. Anal., vol.128, pp.297-312.
• [12] Cortell R. (2007): MHD flow and mass transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet with chemically reactive species. – Chem. Eng. Process., vol.46, pp.721-728.
• [13] Ellahi R. (2013): The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: Analytical solutions. – Appl. Math. Model., vol.37, pp.1451-1467.
• [14] Hayat T., Qasim M. and Abbas Z. (2010): Homotopy solution for unsteady three-dimensional MHD flow and mass transfer in a porous space. – Commun. Nonlinear Sci. Numer. Simul., vol.15, pp.2375-2387.
• [15] Hayat T., Mustafa M. and Mesloub S. (2010): Mixed convection boundary layer flow over a stretching surface filled with a Maxwell fluid in presence of Soret and Dufour effects. – Z. Naturforsch., vol.65, pp.401-410.
• [16] Abel M.S., Mahesha N. and Malipatil S.B. (2011): Heat transfer due to MHD slip flow of a second-grade liquid over a stretching sheet through a porous medium with non uniform heat source/sink. – Chem. Eng. Commun., vol.198, pp.191-213.
• [17] Zeeshan A. and Ellahi R. (2013): Series solutions for nonlinear partial differential equations with slip boundary conditions for non-Newtonian MHD fluid in porous space. – J. Appl. Math. Inf. Sci., vol.7, pp.257-265.
• [18] Ellahi R., Wang X. and Hameed M. (2014): Effects of heat transfer and nonlinear slip on the steady flow of Couette fluid by means of Chebyshev spectral method. – Z. Naturforsch. A, vol.69, pp.1-8.
• [19] Sheikholeslami M., Ellahi R., Ashorynejad H.R., Domairry G. and Hayat T. (2014): Effects of heat transfer in flow of nanofluids over a permeable stretching wall in a porous medium. – Comput. Theor. Nanosci., vol.11, pp.486-496.
• [20] Mehmood A. and Ali A. (2011): Across mass transfer phenomenon in a channel of lower stretching wall. – Chem. Eng. Commun., vol.198, pp.678-691.
• [21] Tamayol A., Hooman K. and Bahrami M. (2010): Thermal analysis of flow in a porous medium over a permeable stretching wall. – Transp. Porous Med., vol.85, pp.661-676.
• [22] Raftari B. and Vajravelu K. (2012): Homotopy analysis method for MHD viscoelastic fluid flow and heat transfer in a channel with a stretching wall. – Commun. Nonlinear Sci. Numer. Simulat., vol.17, pp.4149-4162.
• [23] Mehmood A. and Ali A. (2010): Heat transfer analysis of three-dimensional flow in a channel of lower stretching wall. – J. Taiwan Inst. Chem. Eng., vol.41, pp.29-34.
• [24] Munawar S., Mehmood A. and Ali A. (2012): Three-dimensional squeezing flow in a rotating channel of lower stretching porous wall. – Comp. Math. Appl., vol.64, pp.1575-1586.
• [25] Alhuthali M.S., Shehzad S.A., Malaikah H. and Hayat T. (2014): Three dimensional flow of viscoelastic fluid by an exponentially stretching surface with mass transfer. – J. Pet. Sci. Eng., vol.119, pp.221-226.
• [26] Nadeem S., Rizwan Ul Haq, Akbar N.S. and Khan Z.H. (2013): MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet. – Alexandria Engineering Journal, vol.52, pp.577-582.
• [27] Qasim M. (2013): Heat and mass transfer in a Jeffrey fluid over a stretching sheet with heat source/sink. – Alexandria Engineering Journal, vol.52, pp.571-575.
• [28] Abel M.S., Nandeppanavar M.M. and Malipatil S.B. (2010): Heat transfer in a second grade fluid through a porous medium from a permeable stretching sheet with non-uniform heat source/sink. – Int. J. Heat Mass Transfer, vol.53, pp.1788-1795.
• [29] Hayat T., Awais M. and Obaidat S. (2012): Three-dimensional flow of a Jeffery fluid over a linearly stretching sheet. – Commun. Nonlinear Sci. Numer. Simulat., vol.17, pp.699-707.
• [30] Liao S.J. (1992): The proposed homotopy analysis technique for the solution of nonlinear problems. – PhD Thesis, Shanghai Jiao Tong University.
• [31] Khan N.A., Aziz S. and Nadeem. A. Khan (2014): MHD flow of Powell-Eyring fluid over a rotating disk. – J. Taiwan Inst. Chem. E., vol.45, pp.2859-2867.
• [32] Khan N.A. and Riaz F. (2014): Off-centred stagnation point flow of a couple stress fluid towards a rotating disk. – The Scientific World Journal, Article ID 163586.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę