TY - JOUR
T1 - Peristaltic transport of a third-order fluid in a circular cylindrical tube
AU - Hayat, T.
AU - Wang, Y.
AU - Siddiqui, A. M.
AU - Hutter, K.
AU - Asghar, S.
N1 - Funding Information:
We gratefully acknowledge the comments of Professor Brian Straughan on this paper. T. H. thanks the Alexander von Humboldt Foundation for nancial support.
PY - 2002/12
Y1 - 2002/12
N2 - The effect of a third-order fluid on the peristaltic transport is analysed in a circular cylindrical tube, such as some organs in the living body. The third-order flow of an incompressible fluid in a circular cylindrical tube, on which an axisymmetric travelling sinusoidal wave is imposed, is considered. The wavelength of the peristaltic waves is assumed to be large compared to the tube average radius, whereas the amplitude of the wave need not be small compared to the average radius. Both analytic (perturbation) and numerical solutions are given. For the perturbation solution, a systematic approach based on an asymptotic expansion of the solution in terms of a small Deborah number is used and solutions up to the first order are presented in closed forms. The numerical solution, valid for any Deborah number, represents a new approach to peristaltic flows, and its features illuminate the physical behaviour much more than the analytical research on this problem. Comparison is made between the analytic (perturbation) and numerical results. Furthermore, the obtained results could also have applications to a range of peristaltic flows for a variety of non-Newtonian fluids such as aqueous solutions of high-molecular weight polyethylene oxide and polyacrylamide.
AB - The effect of a third-order fluid on the peristaltic transport is analysed in a circular cylindrical tube, such as some organs in the living body. The third-order flow of an incompressible fluid in a circular cylindrical tube, on which an axisymmetric travelling sinusoidal wave is imposed, is considered. The wavelength of the peristaltic waves is assumed to be large compared to the tube average radius, whereas the amplitude of the wave need not be small compared to the average radius. Both analytic (perturbation) and numerical solutions are given. For the perturbation solution, a systematic approach based on an asymptotic expansion of the solution in terms of a small Deborah number is used and solutions up to the first order are presented in closed forms. The numerical solution, valid for any Deborah number, represents a new approach to peristaltic flows, and its features illuminate the physical behaviour much more than the analytical research on this problem. Comparison is made between the analytic (perturbation) and numerical results. Furthermore, the obtained results could also have applications to a range of peristaltic flows for a variety of non-Newtonian fluids such as aqueous solutions of high-molecular weight polyethylene oxide and polyacrylamide.
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U2 - 10.1142/S0218202502002288
DO - 10.1142/S0218202502002288
M3 - Article
AN - SCOPUS:0036956766
SN - 0218-2025
VL - 12
SP - 1691
EP - 1706
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
IS - 12
ER -