Abstract
The flow of the Ellis fluid in the renal tubule is investigated in this paper. The fluid absorption at the wall is influenced by the pressure gradient across the wall and by the permeability of the wall. The governing equations are considerably simplified if the tubule radius is assumed to be much smaller than its length. Important quantities of interest are computed numerically. The results are compared with available data and are found to be in good agreement.
Similar content being viewed by others
REFERENCES
“Pressure Flow Patterns in a Cylinder with Reabsorbing Walls," Bull. Math. Biophys. 25 (1), 1–9 (1963).
R. I. Macey, “Hydrodynamics in the Renal Tubule," Bull. Math. Biophys. 27 (2), 117–124 (1965).
A. A. Kozinski, F. P. Schmidt, and E. N. Lightfoot, “Velocity Profiles in Porous-Walled Ducts," Indust. Eng. Chem. Fund.9 (3), 502–505 (1970).
G. Radhakrishnaacharya, P. Chandra, and M. R. Kaimal, “A Hydrodynamical Study of the Flow in Renal Tubules," Bull. Math. Biology 43 (2), 151–163 (1981).
E. A. Marshall and E. A. Trowbridge, “Flow of a Newtonian Fluid Through a Permeable Tube: The Application to the Proximal Renal Tubule," Bull. Math. Biology 36 (5/6), 457–476 (1974).
P. J. Palatt, H. Sackin, and R. I. Tanner, “A Hydrodynamic Model of a Permeable Tubule," J. Theor. Biology 44 (2), 287–303 (1974).
P. Chaturani and T. R. Ranganatha, “Flow of Newtonian Fluid in Non-Uniform Tubes with Variable Wall Permeability with Application to Flow in Renal Tubules," Acta Mech. 88 (1/2), 11–26 (1991).
A. M. Siddique, T. Haroon, and M. Kahshan, “MHD Flow of Newtonian Fluid in a Permeable Tubule," Magnetohydrodynamics51 (4), 655–672 (2015).
M. Kahshan, A. M. Siddique, and T. Haroon, “A Micropolar Fluid Model for Hydrodynamics in the Renal Tubule," Europ. Phys. J. Plus. 133, Art. 546 (2018).
A. Asghar, Q. Hussain, T. Hayat, and A. Alsaedi, “Peristaltic Flow of a Reactive Viscous Fluid Through a Porous Saturated Channel and Convective Cooling Conditions," Appl. Mech. Tech. Phys.56 (4), 580–589 (2015).
N. Ali, M. Sajid, Z. Abbas, and T. Javed, “Non-Newtonian Fluid Flow Induced by Peristaltic Waves in a Curved Channel," Europ. J. Mech. B. Fluids 29 (5), 387–394 (2010).
S. Canic and E. H. Kim, “Mathematical Analysis of Quasilinear Effects in the Hyperbolic Model Blood Flow Through Compliant Axi-Symmetric Vessel," Math. Method Appl. Sci. 26(14), 1161–1186 (2003).
S. Noreen and S. Nadeem, “Carreau Fluid Model for Blood Flow Through a Tapered Artery with a Stenosis," Ain Shams Engng J.5 (4), 1307–1316 (2014).
M. A. Javed, N. Ali, and M. Sajid, “A Theoretical Analysis of the Calendaring of Ellis Fluid," J. Plastic Film Sheet.33 (2), (2016); DOI: 10.1177/8756087916647998.
S. W. Hopke and J. C. Slattery, “Upper and Lower Bounds on the Drag Coefficient of a Sphere in an Ellis Model Fluid," AIChE J.16 (2), 224–229 (1970).
R. P. Chhabra, C. Tiu, and P. H. T. Uhlherr, “Creeping Motion of Spheres Through Ellis Model Fluids," Rheolog. Acta20 (4), 346–351 (1981).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 62, No. 2, pp. 132–140.https://doi.org/10.15372/PMTF20210213.
Rights and permissions
About this article
Cite this article
Sajid, M., Rooman, M., Ali, N. et al. FLOW OF THE ELLIS FLUID IN THE RENAL TUBULE. J Appl Mech Tech Phy 62, 292–299 (2021). https://doi.org/10.1134/S0021894421020139
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894421020139