Summary
Using the Oberbeck-Boussinesq (O-B) equations as a mathematical model, asymptotic solutions in closed form and numerical solutions are obtained for the peristaltic transport of a heat-conducting fluid in a three-dimensional flexible tube. The results show that the relation between mass flux and pressure drop remains almost linear and the efficiency of the transport depends mainly on the ratio of the wave amplitudeh and the average radius of the tubed. However, the 3-D flow is much different from the 2-D flow in the following ways: (i) The 3-D flow is much more sensitive to the change of the volume expansion coefficient α r ; (ii) Trapping and backflow are much more common in 3-D case; (iii) The longwave asymptotic approximation in 3-D case is not as good as in 2-D case, especially when α r is not small; (iv) The 3-D flow is more sensitive to Reynolds number change.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Jaffrin, M. Y., Shapiro, A. H.: Peristaltic pumping. Annu. Rev. Fluid Mech.3, 13–36 (1971).
Winet, H.: On the quantitative analysis of liquid flow in physiological tubes. Math. Research Center Technical Summary Report No. 2456, UW-Madison, 1982.
Takabatake, S., Ayukawa, K.: Numerical study of two-dimensional peristaltic flows. J. Fluid Mech.122, 439–465 (1982).
Takabatake, S., Ayukawa, K., Mori, A.: Peristaltic pumping in circular cylindrical tubes: a numerical study of fluid transport and its efficiency. J. Fluid Mech.193, 267–283 (1988).
Hung, T. K., Brown, T. D.: Solid particle motion in two dimensional peristaltic flows. J. Fluid Mech.73, 77–96 (1976).
Kaimal, M. R.: Peristaltic pumping of a Newtonian fluid with particles suspended in it at low Reynolds number under long wavelength approximations. Trans. ASME45, 32–36 (1978).
Fauci, L. J.: Peristaltic pumping of solid particles. Comput. Fluids (to appear).
Bestman, A. R.: Long wavelength peristaltic pumping in a heated tube at low Reynolds number. Dev. Mech.10, 195–199 (1979).
Tang, D., Shen, M. C.: Peristaltic transport of a heat conducting fluid subject to Newton's cooling law at the boundary. Int. J. Eng. Sci.27, 809–825 (1989).
Tang, D., Shen, M. C.: Numerical and asymptotic solutions for the peristaltic transport of a heat-conducting fluid. Acta Mech.83, 93–102 (1990).
Joseph, D.: Stability of fluid motion II. New York: Springer 1976.
Strikwerda, J. G.: Finite difference methods for the Stokes and Navier-Stokes equations. SIAM J. Sci. Statist. Comput.5, 56–58 (1984).
Strikwerda, J. G., Nagel, Y. M.: A numerical method for the incompressible Navier-Stokes equations in three-dimensional cylindrical geometry. J. Comp. Phys.78, 64–78 (1988).
Strikwerda, J. G., Nagel, Y. M.: Finite difference method for polar coordinate systems. ARO Report87-1, 1059–1076 (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tang, D. Three dimensional numerical and asymptotic solutions for the peristaltic transport of a heat-conducting fluid. Acta Mechanica 104, 215–230 (1994). https://doi.org/10.1007/BF01170065
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01170065