×

zbMATH — the first resource for mathematics

Unsteady flow with heat and mass transfer of a third grade fluid over a stretching surface in the presence of chemical reaction. (English) Zbl 1196.35163
Summary: This paper describes the unsteady flow with heat and mass transfer characteristics in a third grade fluid bounded by a stretching sheet. The resulting problems are solved by means of homotopy analysis method (HAM). Convergence of derived series solutions is explicitly discussed. Graphical results for various interesting parameters are presented and analyzed.

MSC:
35Q35 PDEs in connection with fluid mechanics
35C20 Asymptotic expansions of solutions to PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76A10 Viscoelastic fluids
76V05 Reaction effects in flows
80A20 Heat and mass transfer, heat flow (MSC2010)
80A32 Chemically reacting flows
92E20 Classical flows, reactions, etc. in chemistry
Software:
BVPh
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Fetecau, C.; Athar, M.; Fetecau, C., Unsteady flow of a generalized Maxwell fluid with fractional derivative due to a constantly accelerating plate, Comput. math. appl., 57, 596-603, (2009) · Zbl 1165.76307
[2] Fetecau, C.; Fetecau, C., Starting solutions for the motion of a second grade fluid due to longitudnal and torsional oscillations of a circular cylinder, Internat. J. engrg. sci., 44, 788-796, (2006) · Zbl 1213.76014
[3] Fetecau, C.; Fetecau, C., Starting solutions for some unsteady unidirectional flows of a second grade fluid, Internat. J. engrg. sci., 43, 781-789, (2005) · Zbl 1211.76032
[4] Tan, W.C.; Xiao, P.W.; Yu, X.M., A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model, Internat. J. non-linear mech., 38, 645-650, (2003) · Zbl 1346.76009
[5] Mekheimer, Kh.S.; Abd elmaboud, Y., Peristaltic flow of a couple stress fluid in an annulus: application of an endoscope, Physica A, 387, 2403-2415, (2008) · Zbl 1310.76197
[6] Haroun, M.H., Effect of Deborah number and phase difference on peristaltic transport of a third order fluid in an asymmetric channel, Commun. nonlinear sci. numer. simul., 12, 1464-1480, (2007) · Zbl 1127.76069
[7] Hayat, T.; Abbas, Z.; Sajid, M., Heat and mass transfer analysis on the flows of a second grade fluid in the presence of chemical reaction, Phys. lett. A, 372, 2400-2408, (2008) · Zbl 1220.76009
[8] Abbas, Z.; Wang, Y.; Hayat, T.; Oberlack, M., Hydromagnetic flow in a viscoelastic fluid due to oscillatory stretching surface, Internat. J. non-linear mech., 43, 783-793, (2008) · Zbl 1203.76169
[9] Hayat, T.; Sajid, M.; Ayub, M., On explicit analytic solution for MHD pipe flow of a fourth grade fluid, Commun. nonlinear sci. numer. simul., 13, 745-751, (2008) · Zbl 1221.76221
[10] Hayat, T.; Farooq, M.A.; Javed, T.; Sajid, M., Partial slip effects on the flow and heat transfer characteristics in a third grade fluid, Nonlinear anal. real world appl., 10, 745-755, (2009) · Zbl 1167.76308
[11] Rajagopal, K.R., On boundary conditions for fluid of differential type, () · Zbl 0846.35107
[12] Rajagopal, K.R.; Kaloni, P.N., (), 935-942
[13] Sajid, M.; Ahmed, I.; Hayat, T.; Ayub, M., Unsteady flow and heat transfer of a second grade fluid over a stretching sheet, Commun. nonlinear sci. numer. simul., 14, 96-108, (2009) · Zbl 1221.76022
[14] Hayat, T.; Sajid, M., Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet, Int. J. heat mass transfer, 50, 75-84, (2007) · Zbl 1104.80006
[15] Sajid, M.; Hayat, T., Comparison of HAM and HPM solutions in heat radiation equations, Int. commun. heat mass transfer, 36, 59-62, (2009)
[16] Chen, J.; Liao, S.J., Series solutions of nano-boundary flows by means of the homotopy analysis method, J. math. anal. appl., 343, 233-245, (2008) · Zbl 1135.76016
[17] Hayat, T.; Abbas, Z., Heat transfer analysis on MHD flow of a second grade fluid in a channel with porous medium, Chaos solitons fractals, 38, 556-567, (2008) · Zbl 1146.76670
[18] Hayat, T.; Javed, T.; Sajid, M., Analytic solution for MHD rotating flow of a second grade fluid over a shrinking surface, Phys. lett. A, 372, 3264-3273, (2008) · Zbl 1220.76011
[19] Abbasbandy, S., The application of homotopy analysis method to nonlinear equations arising in the heat transfer, Phys. lett. A, 360, 109-113, (2006) · Zbl 1236.80010
[20] Liao, S.J., Beyond perturbation: introduction to homotopy analysis method, (2003), Chapman and Hall, CRC Press Boca Raton
[21] Abbasbandy, S., Approximate solution of the nonlinear model of diffusion and reaction catalysts by means of homotopy analysis method, Chem. eng. J., 136, 144-150, (2008)
[22] Abbasbandy, S., Homotopy analysis method for generalized benjamin – bona – mahony equation, Zamp, 59, 51-62, (2008) · Zbl 1139.35325
[23] Liao, S.J., Notes on the homotopy analysis method: some definitions and theorems, Commun. nonlinear sci. numer. simul., 14, 983-997, (2009) · Zbl 1221.65126
[24] Abbas, Z.; Hayat, T., Radiation effects on MHD flow in porous space, Int. J. heat mass transfer, 51, 1024-1033, (2008) · Zbl 1141.76069
[25] Hayat, T.; Abbas, Z.; Ali, N., MHD flow and mass transfer of a upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction species, Phys. lett. A, 372, 4698-4704, (2008) · Zbl 1221.76031
[26] Kechil, S.; Hashim, I., Approximate analytical solution for MHD stagnation-point flow in porous media, Commun. nonlinear sci. numer. simul., 14, 1346-1354, (2009)
[27] Hashim, I.; Abdulaziz, O.; Momani, S., Homotopy analysis method for fractional ivps, Commun. nonlinear sci. numer. simul., 14, 674-684, (2009) · Zbl 1221.65277
[28] Bataineh, A.S.; Noorani, M.S.M.; Hashim, I., The homotopy analysis method for Cauchy reaction diffusion problems, Phys. lett. A, 372, 613-618, (2008) · Zbl 1217.35101
[29] Xu, H.; Liao, S.J.; You, X.C., Analysis of nonlinear fractional partial differential equations with homotopy analysis method, Commun. nonlinear sci. numer. simul., 14, 1152-1156, (2009) · Zbl 1221.65286
[30] Sajid, M.; Hayat, T.; Pop, I., Three dimensional flow over a stretching surface in a viscoelastic fluid, Nonlinear anal. real world appl., 9, 1811-1822, (2008) · Zbl 1154.76315
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.