Abstract
We investigate the problem of the unsteady mixed convection peristaltic mechanism. The flow includes a temperature-dependent viscosity with thermal diffusion and diffusion-thermo effects. The peristaltic flow is between two vertical walls, one of which is deformed in the shape of traveling transversal waves exactly like peristaltic pumping and the other of which is a parallel flat plate wall. The equations of momentum, energy, and concentration are subject to a set of appropriate boundary conditions by assuming that the solution consists of two parts: a mean part and a perturbed part. The solution of the perturbed part has been obtained by using the long-wave approximation. The mean part has been solved and coincides with the approximation of Ostrach. The mean part (zeroth order), the first order, and the total solution of the problem have been evaluated numerically for several sets of values of the parameters entering the problem. The skin friction, and the rate of heat and mass transfer at the walls are obtained and illustrated graphically.
Similar content being viewed by others
References
Jaluria Y. (1980). Natural Convection Heat and Mass Transfer. Pergamon, Oxford
Gebhart B., Jaluria Y., Mahajan R.L., Sammakia B. (1988). Buoyancy-Induced Flows and Transport. Hemisphere, New York
Aydın O. (1999). Aiding and opposing mechanisms of mixed convection in a shear-and buoyancy-driven cavity. Int. Commun. Heat Mass Transfer 26: 1019–1028
Bejan A. (1995). Convection Heat Transfer. Wiley, New York
Pop I., Ingham D.B. (2001). Convective Heat Transfer. Pergamon, Amsterdam
Jaluria Y. (1987). Basic of natural convection. In: Kakac, S., Shah, R.K., Aung, W. (eds) Handbook of Single-Phase Convective Heat Transfer, pp. Wiley, New York
Chen T.S., Armaly B.F. (1987). Mixed convection in external flow. In: Kakac, S., Shah, R.K., Aung, W. (eds) Handbook of Single-Phase Convective Heat Transfer, pp. Wiley, New York
Kafoussias N.G., Rees D.A.S., Daskalakis J.E. (1998). Numerical study of the combined free-forced convective laminar boundary layer flow past a vertical isothermal flat plate with temperature-dependent viscosity. Acta Mech. 127: 39–50
Hossain M.A., Munir M.S. (2000). Mixed convection flow from a vertical flat plate with temperature dependent viscosity. Int. J. Therm. Sci. 39: 173–183
Abu-Mulaweh H.I. (2003). Measurements of laminar mixed convection flow adjacent to an inclined surface with uniform wall heat flux. Int. J. Therm. Sci. 42: 57–62
Merkin J.H., Pop I. (2002). Mixed convection along a vertical surface:similarity solutions for uniform flow. Fluid Dyn. Res. 30: 233–250
Steinruck H. (2003). About the physical relevance of similarity solutions of the boundary-layer flow equations describing mixed convection flow along a vertical plate. Fluid Dyn. Res. 32: 1–13
Pantokratoras A. (2004). Laminar assisting and mixed convection heat transfer from a vertical isothermal plate to water with variable physical properties. Heat Mass Transfer 40: 581–585
Varol Y., Oztop H.F. (2006). Free convection in a shallow wavy enclosure. Int. Commun. Heat Mass Transfer 33: 764–771
Negny S., Meyer M., Prevost M. (2001). Study of a laminar falling film flowing over a wavy wall column: Part I Numerical investigation of the flow pattern and the coupled heat and mass transfer. J. Heat Mass Transfer 44: 2137–2146
Wang C.C., Chen C.K. (2002). Mixed convection boundary layer flow of non-Newtonian fluids along vertical wavy plates. Int. J. Heat Fluid Flow 23: 831–839
Wang C.C., Chen C.K. (2002). Forced convection in a wavy wall channel. Int. J. Heat Mass Transfer 45: 2587–2595
Bennett C.O., Myers J.E. (1982). Momentum, Heat and Mass Transfer. McGraw-Hill, New York
Pop I., Ingham D.B. (2001). Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media. Pergamon, Oxford
Murthy P.V.S.N. (2000). Effect of double dispersion on mixed convection heat and mass transfer in Non-Darcy porous medium. ASME J. Heat Transfer 122: 476–483
Lekoudis S.G., Nayfeh A.H., Saric W.S. (1976). Compressible boundary layers over wavy walls. Phys. Fluids 19: 514–519
Lessen M., Gangwani S.T. (1976). Effect of small amplitude wall waviness upon the stability of the laminar boundray layer. Phys. Fluids 19: 510–513
Vajravelu K., Sastri K.S. (1978). Free convective heat transfer in a viscous incompressible fluid confined between a long vertical wavy wall and a parallel falt wall. J. Fluid Mech. 86: 365–383
Das U.N., Ahmed N. (1992). Free convective MHD flow and heat transfer in a viscous incompressible fluid confined between a long vertical wavy wall and a parallel flat wall. Indian J. Pure Appl. Math. 23: 295–304
Davalos-Orozco L.A. (1992). Capillary instability due to a shear stress on the free surface of a viscoelastic fluid layer. J. Non-Newtonian Fluid Mech. 45: 171–186
Nakayama M., Sawada T. (1988). Numerical study on the flow of a non-Newtonian fluid through a axisymmetric stenosis. J. Biomech. Eng. 110: 137–143
Eldabe N.T., El-Saka A.G., Fouad A. (2004). Thermal-diffusion and diffusion-thermo effects on mixed free-forced convection and mass transfer boundary layer flow for non-Newtonian fluid with temperature dependent viscosity. Appl. Math. Comput. 152: 867–883
Chin K.E., Nazar R., Arifin N.M., pop I. (2007). Effect of variable viscosity on mixed convection boundary layer flow over a vertical surface embedded in a porous medium. Int. Commun. Heat Mass Transfer 34: 464–473
Ostrach, S.: Laminar natural convection flow and heat transfer of fluids with and without heat sources in channels with constant wall temperature. N. A. C. A. Tech. Note No., vol 2863 (1951)
Raisinghania M.D. (2003). Ordinary and Partial Differential Equations. S. Chand, New Delhi
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Eldabe, N.T.M., El-Sayed, M.F., Ghaly, A.Y. et al. Mixed convective heat and mass transfer in a non-Newtonian fluid at a peristaltic surface with temperature-dependent viscosity. Arch Appl Mech 78, 599–624 (2008). https://doi.org/10.1007/s00419-007-0181-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-007-0181-6