THE STUDY OF HEAT AND MASS TRANSFER IN A VISCO ELASTIC FLUID DUE TO A CONTINUOUS STRETCHING SURFACE USING HOMOTOPY ANALYSIS METHOD

Rajeswari Seshadri; Shankar Rao Munjam

doi:10.11948/2014022

2014 Volume 4 Issue 4

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2014 > 4(4): 389-403

Next Article Previous Article

Rajeswari Seshadri, Shankar Rao Munjam. THE STUDY OF HEAT AND MASS TRANSFER IN A VISCO ELASTIC FLUID DUE TO A CONTINUOUS STRETCHING SURFACE USING HOMOTOPY ANALYSIS METHOD[J]. Journal of Applied Analysis & Computation, 2014, 4(4): 389-403. doi: 10.11948/2014022

Citation:

Rajeswari Seshadri, Shankar Rao Munjam. THE STUDY OF HEAT AND MASS TRANSFER IN A VISCO ELASTIC FLUID DUE TO A CONTINUOUS STRETCHING SURFACE USING HOMOTOPY ANALYSIS METHOD[J]. Journal of Applied Analysis & Computation, 2014, 4(4): 389-403. doi: 10.11948/2014022

THE STUDY OF HEAT AND MASS TRANSFER IN A VISCO ELASTIC FLUID DUE TO A CONTINUOUS STRETCHING SURFACE USING HOMOTOPY ANALYSIS METHOD

Department of Mathematics, Ramanujan School of Mathematical Sciences, Pondicherry University, Pondicherry-605014, India

Abstract

Abstract

In this paper, an approximate analytical solution is derived for the flow velocity and temperature due to the laminar, two-dimensional flow of nonNewtonian incompressible visco elastic fluid due to a continuous stretching surface. The surface is stretched with a velocity proportional to the distance x along the surface. The surface is assumed to have either power-law heat flux or power-law temperature distribution. The presence of source/sink and the effect of uniform suction and injection on the flow are considered for analysis. An approximate analytical solution has been obtained using Homotopy Analysis Method(HAM) for various values of visco elastic parameter, suction and injection rates. Optimal values of the convergence control parameters are computed for the flow variables. It was found that the computational time required for averaged residual error calculation is very very small compared to the computation time of exact squared residual errors. The effect of mass transfer parameter, visco elastic parameter, source/sink parameter and the power law index on flow variables such as velocity, temperature profiles, shear stress, heat and mass transfer rates are discussed.
- Two-dimensional flow /
- HAM solution /
- viscoelastic /
- stretching surface
MSC: 76M25;76N20;76W05;80A20

FullText(HTML)

References

[1]	S. Abbasbandy, Applications of homotopy analysis method to nonlinear equations arising in heat transfer, Physics Letters A., 360(2006), 109-113. Google Scholar
[2]	M.S. Abel and N. Mahesha, Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation, Applied Mathematical Modeling., 32(2008), 1965-1983. Google Scholar
[3]	M.A.F. Araghi and S. Naghshband, On Convergence of q-homotopy analysis method, Int. J. Contep. Math. Sciences., 8(2013), 481-497. Google Scholar
[4]	M.A.F. Araghi and S. Naghshband On Convergence of homotopy analysis method to solve the schrodinger equation with a power Law nonlinearity, Int. J. Industrial Mathematics., 5(2013), 1-8. Google Scholar
[5]	C.K. Chen and M.I. Char, Heat transfer of a continuous, stretching surface with suction or blowing, Journal of Mathematical Analysis and Applications., 135(1988), 568-580. Google Scholar
[6]	L.J. Crane, Flow past a stretching plate, Z. Angew. Math. Mech., 21(1970), 645-647. Google Scholar
[7]	I.E. Erickson, L.T Fan and V.G. Fox Heat and mass transfer on a moving continuous fast plate with suction or injection, Ind.Engng Chem. Fundm., 5(1966), 19-25. Google Scholar
[8]	R.J. Goldstein, E.R.G Eckert, W. E. Ibele, S.V Patankar, T.W. Simon, T.H Kuehn, P.J. Strykowski, K.K. Tamma, A. Bar Cohen, J.V.R. Heberlein, J.H. Davidson, J. Bischof, F.A. Kulacki, U. Kortshagen and S. Garrick, Heat transfer-a review of 1999 literature, International Journal of Heat and Mass Transfer., 44(2001), 3579-3699. Google Scholar
[9]	R.J. Goldstein, E.R.G Eckert, W.E. Ibele, S.V Patankar, T.W. Simon, T.H Kuehn,P.J. Strykowski, K.K. Tamma, A. Bar Cohen, J.V.R. Heberlein, J.H. Davidson, J. Bischof, F.A. Kulacki, U. Kortshagen, S. Garrick and V. Srinivasan, Heat transfer-a review of 2002 literature, International Journal of Heat and Mass Transfer., 48(2005), 819-927. Google Scholar
[10]	T. Hayat, S.A. Shehzad, and A. Alsaedi, Soret and dufouf effects on MHD flow of casson fluid, Appl. Math. Engl. Ed., 10(2012), 1301-1312. Google Scholar
[11]	S.J. Liao, A kind of approximate solution technique which does not depend upon small parameters(Ⅱ):An application in fluid mechanics, Int J. of Non-linear Mech., 32(1997), 815-822. Google Scholar
[12]	S.J. Liao, Beyond perturbation:Introduction to the homotopy analysis method, CRC Press, Boca Raton:Chapman and Hall., (2003). Google Scholar
[13]	S.J. Liao, On the analytic solution of magnetohydrodynamic flows of nonnewtonian fluids over a stretching sheet, J. Fluid Mech., 488(2003), 189-212. Google Scholar
[14]	S.J. Liao, On the homotopy analysis method for nonlinear problems, Applied Mathematics and Computation., 147(2004), 499-513. Google Scholar
[15]	S.J. Liao, Notes on the homotopy analysis method:Some definitions and theorems, Commun Nonlinear Sci Numer Simulat., 14(2009), 983-997. Google Scholar
[16]	S.J. Liao, An optimal homotopy analysis approach for strongly nonlinear differential equations, Commun Nonlinear Sci Numer Simulat., 15(2010), 2003-2016. Google Scholar
[17]	S.J. Liao, Homotopy analysis method in nonlinear differential equatuions, Higher Education Press, Beijing., (2012). Google Scholar
[18]	V. Marinca and N. Herisanu, Applications of optimal homotopy asymptotic method for solving nonlinear equations arising in heat transfer, Int. Communications in Heat and Mass Transfer., 35(2008), 710-715. Google Scholar
[19]	K. Mallory and R.A. Van Gorder, Control of error in the homotopy analysis of solutions to Zakharov system with dissipation, Numer Algor., 64(2013), 633-657. Google Scholar
[20]	J.C. Misra, G.C Shit and H.J. Rath, Flow and heat transfer of a MHD viscoelastic fluid in a channel with stretching walls:Some applications to hemodynamics, Computers and Fluids., 37(2010), 1-11. Google Scholar
[21]	J.S. Nadjafi, R. Buzhabadi and H.S. Nik, On the homotopy analysis method and optimal value of the convergence control parameter:Solution of Euler Lagrange equations, Applied Mathematics., 3(2012), 873-881. Google Scholar
[22]	K.V. Prasad, D. Pal, V. Umesh and N.S. Prasanna Rao, The effect of variable viscosity on MHD viscoelastic fluid flow and heat transfer over a stretching sheet, Communications in Nonlinear Science and Numerical Simulation., 15(2010), 331-344. Google Scholar
[23]	B. Raftari and K. Vajravelu, Homotopy analysis method for MHD viscoelastic fluid flow and heat transfer in a Channel with a stretching wall, Commun Nonlinear Sci Numer Simulat., 10(2012), 4149-4162. Google Scholar
[24]	S. Rajeswari, S. Nalini and G. Nath, Viscoelastic fluid flow over a continuous stretching surface with mass transfer, Mechanics Research Communications., 22(1995), 627-633. Google Scholar
[25]	S. Rajeswari, S.R. Munjam and J. Sabaskar, An analytical solution of heat transfer on a viscoelastic fluid over a continuous stretching surface, Proceedings of the Indian Society of Theoretical and Applied Mechanics(ISTAM)., 2013. Google Scholar
[26]	M. Sajid, Z. Iqbal, T. Hayat and S. Obaidat, Series solution for rotating flow of an upper convected maxwell fluid over a stretching sheet, Commun. Theor. Phys., 56(2011), 740-744. Google Scholar
[27]	B.C. Sakiadis, Boundary layer behavior on continuous solid surfaces:Ⅱ. Boundary layer on a continuous flat surface, AICHE Journal., 7(1961), 221-225. Google Scholar
[28]	S.A. Shehzad, A. Alsaedi and T. Hayat, Hydromagnetic steady flow of maxwell fluid over a bidirectional stretching surface with prescribed surface temperature and prescribed surface heat flux, PLoS ONE., 8(2013), 1-10. Google Scholar
[29]	S.A. Shehzad, T. Hayat, M. Qasim and S. Asghar, Effects of mass transfer on MHD flow of Casson fluid with chemical reactio and suction, Brazilian Journal of Chemical Engineering., 30(2013), 187-195. Google Scholar
[30]	R.A. Van Gorder and K. Vajravelu, On the selection of auxiliary functions, operators and convergence control parameters in the application of the homotopy analysis method to nonlinear differential equations:a general approach, Commun. Nonlinear Sci. Numer. Simulat., 14(2009), 4078-4089. Google Scholar
[31]	Y. Zhao, Z. Lin and S.J. Liao, A modified homotopy analysis method for solving boundary layer equations, Applied Mathematics., 4(2013), 11-15. Google Scholar