# zbMATH — the first resource for mathematics

Numerical study of transient free convective mass transfer in a Walters-B viscoelastic flow with wall suction. (English) Zbl 1221.76028
Summary: A transient model for the free convective, nonlinear, steady, laminar flow and mass transfer in a viscoelastic fluid from a vertical porous plate is presented. The Walters-B liquid model is employed which introduces supplementary terms into the momentum conservation equation. The transformed conservation equations are solved using the finite difference method (FDM). The influence of viscoelasticity parameter $$(\Gamma )$$, species Grashof number $$(Gc)$$, Schmidt number $$(Sc)$$, distance $$(Y)$$ and time $$(t)$$ on the velocity $$(U)$$ and also concentration distribution $$(C)$$ is studied graphically. Velocity is found to increase with a rise in viscoelasticity parameter $$(\Gamma )$$ with both time and distances close to the plate surface. An increase in Schmidt number is observed to significantly decrease both velocity and concentration in time and also with separation from the plate. Increasing species Grashof number boosts the flow velocity through all time and causes a significant rise primarily near the plate surface. The study has applications in polymer materials processing.

##### MSC:
 76A10 Viscoelastic fluids 76R10 Free convection
Full Text:
##### References:
 [1] Joseph, D.D., Fluid dynamics of viscoelastic liquids, (1990), Springer-Verlag New York · Zbl 0698.76002 [2] Metzner, A.B.; White, J.L., Flow behavior of viscoelastic fluids in the inlet region of a channel, Aicheme J, 11, 6, 989-995, (1965) [3] Oldroyd, J.G., On the formulation of rheological equations of state, Proc roy soc (lond) ser, A, 200, 451-523, (1950) · Zbl 1157.76305 [4] Rao, I.J., Flow of a johnson – segalman fluid between rotating coaxial cylinders with and without suction, Int J nonlinear mech, 34, 1, 63-70, (1999) · Zbl 1342.76010 [5] Renardy, M., High weissenberg number boundary layers for the upper convected Maxwell fluid, J non-Newtonian fluid mech, 68, 1125-1132, (1997) [6] Walters, K., Non-Newtonian effects in some elastico-viscous liquids whose behaviour at small rates of shear is characterized by a general linear equation of state, Quart J mech appl math, 15, 63, (1962) · Zbl 0109.43307 [7] Siddappa, B.; Khapate, B.S., Rivlin – ericksen fluid flow past a stretching plate, Rev roum sci techn mech appl, 21, 497, (1975) · Zbl 0377.76032 [8] Rochelle, S.G.; Peddieson, J., Viscoelastic boundary-layer flow past a parabola and a paraboloid, Int J eng sci, 18, 6, 869-874, (1980) · Zbl 0426.76008 [9] Ji, Z.; Rajagopal, K.R.; Szeri, A.Z., Multiplicity of solutions in von karman flows of viscoelastic fluids, J non-Newtonian fluid mech, 36, 1-25, (1990) · Zbl 0708.76009 [10] Rao, Rekha R.; Finlayson, Bruce A., On the quality of viscoelastic flow solutions: an adaptive refinement study of a Newtonian and a Maxwell fluid, Int J numer methods fluids, 11, 5, 571-585, (1990) · Zbl 0711.76005 [11] Ariel, P.D.; Teipel, I., On dual solutions of stagnation point flow of a viscoelastic fluid, Zeitschrift für angewandte Mathematik und mechanik (ZAMM), 74, 8, 341-347, (1994) · Zbl 0814.76008 [12] Baaijens, F.P.T., Application of low-order discontinuous Galerkin methods to the analysis of viscoelastic flows, J non-Newtonian fluid mech, 52, 1, 37-57, (1994) [13] Jitchote, W.; Robertson, A.M., Flow of second order fluids in curved pipes, J non-Newtonian fluid mech, 90, 1, 91-116, (2000) · Zbl 0972.76009 [14] Sadeghy K, Sharifi M. Numerical analysis of viscoelastic boundary layers: the case of plate withdrawal in a Maxwellian fluid. CFD Conference, Windsor, Ontario, June 9-11; 2002. [15] Erdogan, M.E., On the viscoelastic core of a line vortex embedded in a stagnation point flow, Int J appl mech eng, 8, 4, 577-588, (2003) · Zbl 1079.76008 [16] Takhar, H.S.; Bhargava, R.; Rawat, S.; Bég, T.A.; Bég, O.A., Finite element modeling of laminar flow of a third grade fluid in a darcy – forchheimer porous medium with suction effects, Int J appl mech eng, 12, 1, 215-233, (2007) [17] Mansel DaVies, J.; Bhumiratana, Sakarindr; Byron Bird, R., Elastic and inertial effects in pulsatile flow of polymeric liquids in circular tubes, J non-Newtonian fluid mech, 3, 3, 237-259, (1978) · Zbl 0389.76006 [18] Yeow, Y.L., Response of viscoelastic fluids in extensional flow generated by a pulsating sphere, Appl sci res, 40, 2, 121-133, (1983) · Zbl 0532.76008 [19] Phan-Thien, N., Squeezing a viscoelastic liquid from a wedge: an exact solution, J non-Newtonian fluid mech, 16, 3, 329-345, (1984) · Zbl 0569.76014 [20] Bujurke, N.M.; Hiremath, P.S.; Biradar, S.N., Impulsive motion of a non-Newtonian fluid between two oscillating parallel plates, Appl sci res, 45, 3, 211-231, (1988) · Zbl 0667.76005 [21] Northey, P.J.; Armstrong, Robert C.; Brown, Robert A., Finite element calculation of time-dependent two-dimensional viscoelastic flow with the explicitly elliptic momentum equation formulation, J non-Newtonian fluid mech, 36, 109-133, (1990) · Zbl 0708.76010 [22] Xu, S.; Davies, A.R.; Phillips, T.N., Pseudospectral method for transient viscoelastic flow in an axisymmetric channel, Numer methods partial differen eqn, 9, 6, 691-710, (1993) · Zbl 0781.76069 [23] Rasmussen, H.K.; Hassager, O., Simulation of transient viscoelastic flow with second order time integration, J non-Newtonian fluid mech, 56, 1, 65-84, (1995) [24] Wood, W.P., Transient viscoelastic helical flows in pipes of circular and annular cross-section, J non-Newtonian fluid mech, 100, 1-3, 115-126, (2001) · Zbl 1014.76004 [25] Hayat, T., Oscillatory solution in rotating flow of a johnson – segalman fluid, Zamm, 85, 6, 449-456, (2005) · Zbl 1071.76063 [26] Levenspiel, O., Chemical reaction engineering, (1999), John Wiley USA [27] Evans, G.; Skalak, R., Mechanics and thermodynamics of biomembranes, (1982), CRC Press Florida, USA [28] Davis, H.R.; Parkinson, G.V., Mass transfer from small capillaries with wall resistance in the laminar flow regime, Appl sci res, 22, 1, 20-30, (1970) · Zbl 0193.56105 [29] Soundalgekar, V.M., Effects of couple stresses in fluids on the dispersion of a soluble matter in a channel flow with homogeneous and heterogeneous reactions, Int J heat mass transfer, 18, 4, 527-530, (1975) · Zbl 0303.76001 [30] Vidyanidhi, V.; Murty, M.S., The dispersion of a chemically reacting solute in a micropolar fluid, Int J eng sci, 14, 12, 1127-1133, (1976) · Zbl 0344.76056 [31] Soundalgekar, V.M.; Haldavnekar, D.D., On the dispersion of a Dye with a harmonically varying concentration in a channel flow of a micropolar fluid, Int J eng sci, 27, 12, 1527-1530, (1989) · Zbl 0708.76006 [32] Satish, M.G.; Zhu, J., Flow resistance and mass transfer in slow non-Newtonian flow through multiparticle systems, J appl mech, 59, 2, 431-437, (1992) [33] Seshadri, R.; Sreeshylan, Nalini; Nath, G., Viscoelastic fluid flow over a continuous stretching surface with mass transfer, Mech res commun, 22, 6, 627-633, (1995) · Zbl 0843.76004 [34] Siddheshwar, P.G.; Manjunath, S., Unsteady convective diffusion with heterogeneous chemical reaction in a plane-Poiseuille flow of a micropolar fluid, Int J eng sci, 38, 7, 765-783, (2000) [35] Boutoudj, M.S.; Ouibrahim, A.; Deslouis, C., Mass transfer in a laminar elongational flow of a drag reducing surfactant, J non-Newtonian fluid mech, 103, 2-3, 141-148, (2002) [36] Akyildiz, F.T., Dispersion of a solute in a Poiseuille flow of a viscoelastic fluid int, J eng sci, 40, 8, 859-872, (2002) [37] Rashaida, A.A.; Bergstrom, D.J.; Sumner, R.J., Mass transfer from a rotating disk to a Bingham fluid, ASME J appl mech, 73, 1, 108-111, (2006) · Zbl 1111.74608 [38] Rafael, Cortell, Toward an understanding of the motion and mass transfer with chemically reactive species for two classes of viscoelastic fluid over a porous stretching sheet, Chem eng process: process intensification, 46, 10, 982-989, (2007) [39] Hayat, T.; Abbas, Z., Channel flow of a Maxwell fluid with chemical reaction, Zeitschrift angewandte Mathematik physik (ZAMP), 59, 1, 124-144, (2008) · Zbl 1133.76053 [40] Hassanien, I.A., Flow and heat transfer from a continuous surface in a parallel free stream of viscoelastic second-order fluid, Appl sci res, 49, 4, 335-344, (1992) · Zbl 0763.76005 [41] Sharma, R.C.; Kumar, P.; Sharma, S., Rayleigh – taylor instability of walters’ B’ elastico-viscous fluid through porous medium, Int J appl mech eng, 7, 2, 433-444, (2002) · Zbl 1054.76036 [42] Chaudhary, R.C.; Jain, P., Hall effect on MHD mixed convection flow of a viscoelastic fluid past an infinite vertical porous plate with mass transfer and radiation, Theor appl mech, 33, 4, 281-309, (2006) · Zbl 1177.76458 [43] Walters, K., On second-order effect in elasticity, plasticity and fluid dynamics, () [44] Chang, T.B., Effects of capillary force on laminar filmwise condensation on a horizontal disk in a porous medium, Appl therm eng, 26, 2308-2315, (2006)
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.