THERMAL SCIENCE
International Scientific Journal
UNSTEADY FREE CONVECTION HEAT AND MASS TRANSFER IN A WALTERS-B VISCOELASTIC FLOW PAST A SEMI-INFINITE VERTICAL PLATE: A NUMERICAL STUDY
ABSTRACT
A numerical solution for the free convective, unsteady, laminar convective heat and mass transfer in a viscoelastic fluid along a semi-infinite vertical plate is presented. The Walters-B liquid model is employed to simulate medical creams and other rheological liquids encountered in biotechnology and chemical engineering. This rheological model introduces supplementary terms into the momentum conservation equation. The dimensionless unsteady, coupled and non-linear partial differential conservation equations for the boundary layer regime are solved by an efficient, accurate and unconditionally stable finite difference scheme of the Crank-Nicolson type. The velocity, temperature and concentration fields have been studied for the effect of Prandtl number (Pr), viscoelasticity parameter (G), Schmidt number (Sc), Buoyancy ration parameter (N). The local skin-friction, Nusselt number and Sherwood number are also presented and analyzed graphically. It is observed that, when the viscoelasticity parameter (G) increases, the velocity increases close to the plate surface. An increase in Schmidt number is observed to significantly decrease both velocity and concentration.
KEYWORDS
PAPER SUBMITTED: 2010-11-02
PAPER REVISED: 2011-12-21
PAPER ACCEPTED: 2011-12-21
THERMAL SCIENCE YEAR
2011, VOLUME
15, ISSUE
Supplement 2, PAGES [S291 - S305]
- Thibault, F., Tanguy, P. A., Power-Draw Analysis of a Coaxial Mixer with Newtonian and NonNewtonian Fluids in the Laminar Regime, Chemical Engineering Science, 57 (2002), 18, pp. 3861-3872
- Goerke, A. R., Leung, J., Wickramasinghe, S. R., Mass and Momentum Transfer in Blood Oxygenators, Chemical Engineering Science, 57 (2002), 11, pp. 2035-2046
- Wang, W., Chen, G., Heat and Mass Transfer Model of Dielectric-Material-Assisted Microwave Freeze-Drying of Skim Milk with Hygroscopic Effect, Chemical Engineering Science, 60 (2005), 23, pp. 6542-6550
- Vrentas, J. S., Vrentas, C. M., Axial Moment Analyses of Convective Heat and Mass Transfer Processes, Chemical Engineering Science, 51 (1996), 6, pp. 921-929
- Ayazi Shamlou, P., Edwards, M. F., Heat Transfer to Viscous Newtonian and Non-Newtonian Fluids for Helical Ribbon Mixers, Chemical Engineering Science, 41 (1986), 8, pp. 1957-1967
- Jarzebski, A. B., Malinowski, J. J., Transient Mass and Heat Transfer from Drops or Bubbles in Slow Non-Newtonian Flows, Chemical Engineering Science, 41 (1986), 10, pp. 2575-2578
- Elperin, T., Fominykh, A., Effect of Solute Concentration Level on the Rate of Coupled Mass and Heat Transfer During Solid Sphere Dissolution in a Uniform Fluid Flow, Chemical Engineering Science, 56 (2001), 10, pp. 3065-3074
- Waslo, S., Gal-or, B., Boundary Layer Theory for Mass and Heat Transfer in Clouds of Moving Drops, Bubbles or Solid Particles, Chemical Engineering Science, 26 (1971), 6, pp. 829-838
- Prakash Bharti, R., Chhabra, R. P., Eswaran, V., Effect of Blockage on Heat Transfer from a Cylinder to Power Law Liquids, Chemical Engineering Science, 62 (2007), 17, pp. 4729-4741
- Mahalingam, R., Chan, S. F., Coulson, J. M., Laminar Pseudoplastic Flow Heat Transfer with Prescribed Wall Heat Flux, Chemical Engineering J., 9 (1975), 2, pp. 161-166
- Kleinstreuer, C., Wang, T.-Y., Mixed Convection Heat and Surface Mass Transfer between Power-Law Fluids and Rotating Permeable Bodies, Chemical Engineering Science, 44 (1989), 12, pp. 2987-2994
- White, J. L., Metzner, A. B., Thermodynamic and Heat Transport Considerations for Viscoelastic Fluids, Chemical Engineering Science, 20 (1965), 12, pp. 1055-1062
- Shenoy, A. V., Mashelkar, R. A., Laminar Natural Convection Heat Transfer to a Viscoelastic Fluid, Chemical Engineering Science, 33 (1978), 6, pp. 769-776
- Syrjala, S., Laminar Flow of Viscoelastic Fluids in Rectangular Ducts with Heat Transfer: A Finite Element Analysis, Int. Comm. Heat and Mass Transfer, 25 (1998), 2, pp. 191-204
- Hayat, T., et al., Heat Transfer in Pipe Flow of a Johnson-Segalman Fluid, Int. Comm. Heat and Mass Transfer, 35 (2008), 10, pp. 1297-1301
- Hammad, K. J., Vradis, G. C., Viscous Dissipation and Heat Transfer in Pulsatile Flows of a YieldStress Fluid, Int. Comm. Heat and Mass Transfer, 23 (1996), 5, pp. 599-612
- Beg, O. A., et al., Computational Fluid Dynamics Modelling of Buoyancy Induced Viscoelastic Flow in a Porous Medium with Magnetic Field, Int. J. Applied Mechanics Engineering, 6 (2001), 1, pp. 187-210
- Bhargava, R., et al., Numerical Study of Heat Transfer of a Third Grade Viscoelastic Fluid in NonDarcy Porous Media with Thermophysical Effects, Physica Scripta: Proc. Royal Swedish Academy of Sciences, 77 (2008), pp. 1-11
- Beg, O. A., et al., Computational Modeling of Biomagnetic Micropolar Blood Flow and Heat Transfer in a Two-Dimensional Non-Darcian Porous Medium, Meccanica, 43 (2008), 4, pp. 391-410
- Zueco, J., Beg, O. A., Network Numerical Simulation Applied to Pulsatile Non-Newtonian Flow through a Channel with Couple Stress and Wall Mass Flux Effects, Int. J. Applied Mathematics and Mechanics, 5 (2009), 2, pp. 1-16
- 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. Applied. Math., 15 (1962), 1, pp. 63-76
- Soundalgekar, V. M., Puri, P., On Fluctuating Flow of an Elastico-Viscous Fluid Past an Infinite Plate with Variable Suction, J. Fluid Mechanics, 35 (1969), 3, pp. 561-573
- Rath, R. S., Bastia, S. N., Steady Flow and Heat Transfer in a Visco-Elastic Fluid between Two Coaxial Rotating Disks, Proc. Mathematical Sciences, 87 (1978), 8, pp. 227-236
- Roy, J. S., Chaudhury, N. K., Heat Transfer by Laminar Flow of an Elastico-Viscous Liquid along a Plane Wall with Periodic Suction, Czech. J. Physics, 30 (1980), 11, pp. 1199-1209
- Raptis, A. A., Takhar, H. S., Heat Transfer from Flow of an Elastico-Viscous Fluid, Int. Comm. Heat and Mass Transfer, 16 (1989), 2, pp. 193-197
- Chang, T. B., et al., Numerical Study of Transient Free Convective Mass Transfer in a Walters-B Viscoelastic Flow with Wall Suction, J. Theoretical Applied Mechanics, under review (2009)
- Nanousis, N., Unsteady Magnetohydrodynamic Flows in a Rotating Elasto-Viscous Fluid, Astrophysics and Space Science, 199 (1993), 2, pp. 317-321
- Sharma, V., Rana, G. C., Thermosolutal Instability of Walters' (model B') Visco-Elastic Rotating Fluid Permeated with Suspended Particles and Variable Gravity Field in Porous Medium, Int. J. Applied Mechanics Engineering, 6 (2001), 4, pp. 843-860
- Sharma, R. C., Kumar, P., Sharma., S., Rayleigh-Taylor Instability of Walter’ B’ Elastico-Viscous Fluid through Porous Medium, Int. J. Applied Mechanics Engineering, 7 (2002), 2, pp. 433-444
- 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, Theoretical and Applied Mechanics, 33 (2006), 4, pp. 281-309
- Ray Mahapatra, T., Dholey, S., Gupta, A. S., Momentum and Heat Transfer in the Magnetohydrodynamic Stagnation-Point Flow of a Viscoelastic Fluid toward a Stretching Surface, Meccanica, 42 (2007), 3, pp. 263-272
- Veena, P. H.,, Pravin, V. K., Padashetty, S. C., Non-Similar Solutions in Viscoelastic MHD Flow and Heat Transfer over a Porous Stretching Sheet with Internal Heat Generation and Stress Work, Int. J. Modern Mathematics, 2 (2007), 2, pp. 267-281
- Rajagopal, K., Veena, P. H., Pravin, V. K., Nonsimilar Solutions for Heat and Mass Transfer Flow in an Electrically Conducting Viscoelastic Fluid over a Stretching Sheet Saturated in a Porous Medium with Suction/Blowing, J. Porous Media, 11 (2008), 2, pp. 219-230
- Pohlhausen, E., Heat Transfer between Solid Body and Fluid Flow with Small Friction Forces and Small Heat Flux (in German), ZAMM, 1 (1921), pp. 115-121
- Somers, E. V., Theoretical Considerations of Combined Thermal and Mass Transfer from Vertical Flat Plate, Journal of Appl. Mech., 23 (1956), 295-301
- Mathers, W. G., Madden, A. J., Piret, E. L., Simultaneous Heat and Mass Transfer in Free Convection, Ind Engg. Chem., 49 (1956), 961-968
- Gebhart, B., Pera, L., The Nature of Vertical Natural Convection Flows Resulting from the Combined Buoyancy Effects of Thermal and Mass Diffusion, International Journal of Heat and Mass Transfer, 14 (1971), 12, pp. 2025-2050
- Soundalgekar, V. M., Ganesan, P., Finite Difference Analysis of Transient Free Convection with Mass Transfer on an Isothermal Vertical Flat Plate, International Journal of Engineering Science, 19 (1981), 6, pp. 757-770
- Prasad., V. R., Bhaskar Reddy, N., Muthucumaraswamy, R., Radiation Effects on MHD unsteady Free Convection Flow with Mass Transfer Past a Vertical Plate with Variable Surface Temperature and Concentration, Journal of Energy, Heat and Mass Transfer, 31 (2009), pp. 239-260
- Incropera, F. P., Dewitt, D. P., Fundamentals of Heat and Mass Transfer, 5th ed., John Wiley and Sons, New York, USA, 2007
- Crank, J., Nicolson, P., A Practical Method for Numerical Evaluation of Solutions of Partial Differential Equations of the Heat Conduction Type, Proc. Camb. Phil. Society, 43 (1947), pp. 50-67
- Prasad, V. R., Bhaskar Reddy, N., Muthucumaraswamy, R., Radiation and Mass Transfer Effects on Two-Dimensional Flow Past an Impulsively Started Infinite Vertical Plate, Int. J. Thermal Sciences, 46 (2007), 12, pp. 1251-1258
- Gebhart, B., et al., Buoyancy-Induced Flows and Transport, Hemisphere, Washington, USA, 1988