Summary
A fluid of constant density is forced through the porous bottom of a circular slider which is moving laterally on a flat plane. The radius of the slider is assumed to be much larger than gap width between the slider and the plane. The similarity transformations reduce the equations of motion to a set of nonlinear ordinary differential equations which are solved using a semi-analytical numerical technique for small as well as moderately large Reynolds numbers. In this method we develop the series expansion with polynomial coefficients of the solution function. We calculate few terms manually and invoke the series expansion (with polynomial coefficients) for obtaining a large number of terms in the perturbation series using a computer. This series expansion enables us to calculate a sufficiently large number of universal coefficient functions by delegating routine complex algebra to the computer. The region of the validity of the series representing drag and lift are further increased by reverting the corresponding series (by changing the role of dependent and independent variables). Use of Pade' approximants for summing the reverted series is found to accelerate the convergence of the series. Calculation of lift and drag agree favourably with available pure numerical results.
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References
Berman, A. S.: Laminar flow in a channel with porous walls. J. Appl. Phys.24, 1232–1235 (1953).
Proudman, L.: An example of study laminar flow at large Reynolds number. ASME J. Appl. Mech.9, 593–602 (1960).
Terrill, R. M.: Laminar flow in a uniformly porous channel. Aeronaut. Q.15, 299–310 (1964).
Elkouh, A. F.: Laminar flow between rotating porous disks. J. Eng. Mech. Div.94, 919–929 (1968).
Rasmussen, H.: Steady viscous flow between two porous disks. Z. Angew. Math. Phys.21, 187–195 (1970).
Wang, C. Y.: Fluid dynamics of the circular porous slider. ASME J. Appl. Mech.41, 343–347 (1974).
Van Dyke, M.: Analysis and improvement of perturbation series. Q. J. Mech.27, 423–450 (1974).
Bujurke, N. M., Naduvinamani, N. B.: Computer extension and analytic continuation of problems of porous thrust bearing. Z. Angew. Math. Phys. (in press).
Richardson, S.: On Blasius' equation governing in the boundary layer on a plate. Proc. Camb. Phil. Soc.74, 179–184 (1973).
Schwartz, L. W.: Computer extension and analytic continuation of Stokes expansion for gravity waves. J. Fluid Mech.62, 553–578 (1974).
Phan-Thien, N., Bush, M. A.: On the steady flow of a Newtonian fluid between two parallel disks. Z. Angew. Math. Phys.35, 912–919 (1984).
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Bujurke, N.M., Achar, P.K. Computer extended series solution of the circular porous slider. Acta Mechanica 101, 81–92 (1993). https://doi.org/10.1007/BF01175599
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DOI: https://doi.org/10.1007/BF01175599