---

Journal of Applied Nonlinear Dynamics 11(3) (2022) 755--765 | DOI:10.5890/JAND.2022.09.014

M Varunkumar

Department of BS\&H, GMR Institute of Technology, Rajam-532127. Andhra Pradesh, India

Download Full Text PDF

 

Abstract

This paper presents the steady flow of viscous incompressible fluid through a permeable channel with the effect of an exponential reabsorption at the walls. The fluid reabsorption across the channel walls is assumed by taking the flux as a function of axial length. The approximate solutions for velocity, mean pressure drop, wall shear stress and streamlines are solved by regular perturbation technique and finite difference method. The effect of reabsorption on the velocity profiles at different locations of axis, wall shear stress, mean pressure drop and streamlines are discussed through graphs. It is observed that the pressure drop and wall shear stress decrease as reabsorption increases. Further the streamlines show that the reabsorption significantly influences the flow pattern.

References

1. [1]	Apelblat, A., Katchasky, A.K., and Silberberg, A. (1974), A mathematical anaylsis of capillary tissue fluid exchange, Biorheology, 11, 1-49.

2. [2]	Berman, A.S. (1953), Laminar flow in channels with porous walls, J. Applied Physics, 24, 1232-1235.

3. [3]	Berman, A.S. (1958), Laminar flow in an annulus with porous walls, J. Applied Physics, 29, 71-75.

4. [4]	Cox, B.J. and Hill, J.M. (2011), Flow through a circular tube with a permeable Navier slip boundary, Nanoscale Research Letters, 6, 389.

5. [5]	Oka, S. and Murata, T. (1970), A theoretical study of the flow of blood in a capillary with permeable wall, Jpn. J. Appl. Phys., 9(4), 345-352.

6. [6]	Saffman, P.G. (1971), On the boundary condition at the surface of a porous medium, Studies in Mathematics, 50(2), 93-101.

7. [7]	Salathe, E.P. and An, K.N. (1976), A mathematical analysis of fluid movement across capillary walls, Microvascular Research, 11, 1-23.

8. [8]	Sutradhar, A., Mondal, J.K., Murthy, P.V.N.S., and Rama, S.R.G. (2016), Influence of Starling's hypothesis and Joule heating on peristaltic flow of an electrically conducting casson fluid in a permeable microvessel, Journal of Fluids Engineering, 138, 111106-1-13.

9. [9]	Yuan, S.W. and Finkelstein, A.B. (1956), Laminar pipe flow with injection and suction through a porous wall, Trans. ASME., 78, 719-724.

10. [10]	Macey, R.I. (1965), Hydrodynamics of renal tubule, Bull. of Mathematical Biophysics, 27, 117-124.

11. [11]	Macey, R.I. (1963), Pressure flow patterns in a cylinder with reabsorbing walls, Bull. of Mathematical Biophysics, 25, 1-9.

12. [12]	Kozinski, A.A., Schmidt, F.P., and Lightfoot, E.N. (1970), Velocity profiles in porous-walled ducts, Industrial and Engineering Chemistry fundamentals, 9(3), 502-505.

13. [13]	Marshall, E.A. and Trowbridge, E.A. (1974), Flow of a Newtonian fluid through a permeable tube: The application to the proximal renal tubule, Bull. of Mathematical Biophysics, 36, 457-476.

14. [14]	Palatt, J.P., Henry S., and Roger I.T. (1974), A hydrodynamical model of a permeable tubule, J. theor. Biol., 44, 287-303.

15. [15]	Acharya, G.R.K., Peeyush, C., and Kaimal, M.R. (1981), A hydrodynamical study of the flow in renal tubules, Bull. of Mathematical Biology, 43, 151-163.

16. [16]	Chaturani, P. and Ranganatha, T.R. (1991), Flow of Newtonian fluid in non-uniform tubes with variable wall permeability with application to flow in renal tubules, Acta Mechanica, 88, 11-26.

17. [17]	Haroon, T., Siddiqui, A.M., and Shahzad, A. (2016), Stokes flow through a slit with periodic reabsorption: An application to renal tubule, Alexandria Engineering Journal, 55, 1799-1810.

18. [18]	Siddiqui, A.M., Haroon, T., and Shahzad, A. (2016), Hydrodynamics of viscous fluid through porous slit with linear absorption, Applied Mathematics and Mechanics, 37(3), 361-378.

19. [19]	Haroon, T., Siddiqui, A.M., Shahzad, A., and Smeltzer, J.H. (2017), Steady creeping slip flow of viscous fluid through a permeable slit with exponential reabsorption, Applied Mathematical Sciences, 11, 2477-2504.

20. [20]	Kelman, R.B. (1962), A theoretical note on exponential flow in the proximal part of the mammalian nephron, Bull. of Mathematical Biophysics, 24, 303-317.