DTM Simulation of Peristaltic Viscoelastic Biofluid Flow in Asymmetric Porous Media: A Digestive Transport Model
Source abstract
Abstract
A biofluid dynamics mathematical model is developed to study peristaltic flow of non-Newtonian physiological liquid in a two-dimensional asymmetric channel containing porous media as a simulation of obstructed digestive (intestinal) transport. The fractional Oldroyd-B viscoelastic rheological model is utilized. The biophysical flow regime is constructed as a wave-like motion and porous medium is simulated with a modified Darcy-Brinkman model. This model is aimed at describing the digestive transport in intestinal tract containing deposits which induce impedance. A low Reynolds number approximation is employed to eliminate inertial effects and the wavelength to diameter ratio is assumed to be large. The differential transform method (DTM), a semi-computational technique is employed to obtain approximate analytical solutions to the boundary value problem. The influences of fractional (rheological material) parameters, relaxation time, retardation time, amplitude of the wave, and permeability parameter on peristaltic flow characteristics such as volumetric flow rate, pressure difference and wall friction force are computed. The present model is relevant to flow in diseased intestines.
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Research context
OpenAlex topics: Nanofluid Flow and Heat Transfer · Fractional Differential Equations Solutions · Heat and Mass Transfer in Porous Media
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References (40)
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1. Elman R. The danger of sudden deflation of acutely distended bowel in late low intestinal obstruction. The American Journal of Surgery, 1934, 26, 438–446.10.1016/S0002-9610(34)90445-1 ↗
2. Grassi R, Romano S, D’Amario F, Giorgio Rossi A, Romano L, Pinto F, Di Mizio R. The relevance of free fluid between intestinal loops detected by sonography in the clinical assessment of small bowel obstruction in adults. European Journal of Radiology, 2004, 50, 5–14.10.1016/j.ejrad.2003.11.009 ↗
3. Farrell J J. Methods in Disease: Investigating the Gastrointestinal Tract. Gastroenterology, 1999, 116, 1009–1010.10.1016/S0016-5085(99)70106-X ↗
4. Rommel N, Selleslagh M, Rosen R L, L Rodriguez, Kritas S, Scheerens C, Tack J F, Omari T, Nurko S. Esophageal pressure topography (ept) incorporating pressure flow analysis discriminates dysphagia due to weak peristalsis from dysphagia due to abnormal bolus flow resistance in children. Gastroenterology, 2013, 144, S170–S170.10.1016/S0016-5085(13)60608-3 ↗
5. Kishi K, Yamada K. Sugiyama T. Gastric outlet obstruction caused by a large gallstone in the duodenum (Bouveret’s syndrome). Clinical Gastroenterology and Hepatology, 2008, 6, e11.10.1016/j.cgh.2007.12.027 ↗
6. Bég O A, Uddin M J, Khan W A. Bioconvective non-Newtonian nanofluid transport in porous media containing micro-organisms in a moving free stream. Journal of Mechanics Medicine Biology, 2015, 15, 1550071.10.1142/S0219519415500712 ↗
7. Sukop M C, Van Dijk G J, Perfect E, Van Loon W K P. Percolation thresholds in 2-dimensional prefractal models of porous media. Transport in Porous Media, 2002, 48, 187–208.10.1023/A:1015680828317 ↗
8. Frangi, A F, Lassila T, Vardakis J C, Ventikos Y. Multiscale modelling of transport phenomena in biological tissue. 4th International Conference on Computational and Mathematical Biomedical Engineering (CMBE 2015), France, 2015.
9. Zidi M, Tounsi A, Houari M S A, Bedia A A, Bég O A. Bending analysis of FGM plates under hgro-thermo-mechanical loading using a four variable refined plate theory. Aerospace Science and Technology, 2014, 34, 24–34.10.1016/j.ast.2014.02.001 ↗
10. Rohan E. Modeling Large-deformation-induced microflow in soft biological tissues. Theoretical and Computational Fluid Dynamics, 2006, 20, 251–276.10.1007/s00162-006-0020-3 ↗
11. Kothandapani M, Srinivas S. Non-linear peristaltic transport of a Newtonian fluid in an inclined asymmetric channel through a porous medium. Physics Letters A, 2008, 372, 1265–1276.10.1016/j.physleta.2007.09.040 ↗
12. Mekheimer K S, Abd Elmaboud Y. Peristaltic flow through a porous medium in an annulus: Application of an endoscope. Applied Mathematics & Information Sciences, 2008, 2, 103–121.
13. El Shehawey F, Husseny S Z A. Effects of porous boundaries on peristaltic transport through a porous medium. Acta Mechanica, 2000, 143, 165–177.10.1007/BF01170946 ↗
14. Mekheimer K S. Non-linear peristaltic transport through a porous medium in an inclined planar channel. Journal of Porous Media, 2003, 6, 189–201.10.1615/JPorMedia.v6.i3.40 ↗
15. Srinivas S, Gayathri R. Peristaltic transport of a Newtonian fluid in a vertical asymmetric channel with heat transfer and porous medium. Applied Mathematics and Computation, 2009, 215, 185–196.10.1016/j.amc.2009.04.067 ↗
16. Skalak R, Ozkaya N, Skalak T C. Biofluid Mechanics. Annual Review of Fluid Mechanics, 1989, 21, 167–200.10.1146/annurev.fl.21.010189.001123 ↗
17. Radhakrishnamacharya G. Long wave length approximation to peristaltic motion of a power-law fluid. Rheologica Acta, 1982, 21, 30–35.10.1007/BF01520703 ↗
18. Li W G, Luo X Y, Chin S B, Hill N A, Johnson A G, Bird N C. Non-Newtonian bile flow in elastic cystic duct: One- and three-dimensional modeling. Annals of Biomedical Engineering, 2008, 36, 1893–1908.10.1007/s10439-008-9563-3 ↗
19. Akbar N S, Nadeem S. Simulation of peristaltic flow of chyme in small intestine for couple stress fluid. Meccanica, 2013, 49, 325–334.10.1007/s11012-013-9797-5 ↗
20. Muthu P, Ratish Kumar B V, Chandra P. Peristaltic motion of micropolar fluid in circular cylindrical tubes: Effect of wall properties. Applied Mathematical Modelling, 2008, 32, 2019–2033.10.1016/j.apm.2007.06.034 ↗
21. Vicente J D. Viscoelasticity–From Theory to Biological Applications, InTech, Virginia, USA, 2012.10.5772/3188 ↗
22. Norouzi M, Davoodi M, Bég O A, Joneidi A A. Analysis of the effect of normal stress differences on heat transfer in creeping viscoelastic Dean flow. International Journal of Thermal Sciences, 2013, 69, 61–69.10.1016/j.ijthermalsci.2013.02.002 ↗
23. Tripathi D. Numerical and analytical simulation of peristaltic flows of generalized Oldroyd-B fluids. International Journal for Numerical Methods in Fluids, 2011, 67, 1932–1943.10.1002/fld.2466 ↗
24. Yasmin H, Hayat T, Alsaedi A, Alsulami H H. Peristaltic flow of Johnson-Segalman fluid in asymmetric channel with convective boundary conditions. Applied Mathematics and Mechanics, 2014, 35, 697–716.10.1007/s10483-014-1823-6 ↗
25. Tripathi D, Pandey S K, Bég O A. Mathematical modelling of heat transfer effects on swallowing dynamics of viscoe-lastic flood bolus through the human oesophagus. International Journal of Thermal Sciences, 2013, 70, 41–53.10.1016/j.ijthermalsci.2013.03.005 ↗
26. Tripathi D, Bég O A, Curiel-Sosa J L. Homotopy Semi-Numerical Simulation of Peristaltic flow of generalized Oldroyd-B fluids with slip effects. Computer Methods in Biomechanics and Biomedical Engineering, 2014, 17, 433–442.10.1080/10255842.2012.688109 ↗
27. Alemayehu H, Radhakrishnamacharya G. The dispersion in peristaltic flow of micropolar fluid in a porous medium. Journal of Porous Media, 2012, 15, 1067–1077.10.1615/JPorMedia.v15.i11.70 ↗
28. Mekheimer K S. Non-linear peristaltic transport of a second-order fluid through a porous medium. Applied Mathematical Modelling, 2010, 35, 2695–2710.
29. Tripathi D, Bég O A. A numerical study of oscillating peristaltic flow of generalized Maxwell viscoelastic fluids through a porous medium. Transport in Porous Media, 2012, 95, 337–348.10.1007/s11242-012-0046-5 ↗
30. Alemayehu H, Radhakrishnamacharya G. Dispersion of a solute in peristaltic motion of a couple stress fluid through a porous medium. Tamkang Journal of Mathematics, 2012, 43, 541–555.10.5556/j.tkjm.43.2012.811 ↗
31. Tripathi D. Peristaltic hemodynamic flow of couple-stress fluids through a porous medium with slip effect. Transport in Porous Media, 2012, 92, 559–572.10.1007/s11242-011-9920-9 ↗
32. Oldroyd J G. On the formulation of rheological equations of state. Proceedings of the Royal Society of London A, 1950, 200, 523–541.10.1098/rspa.1950.0035 ↗
33. Qi H, Xu M. Some unsteady unidirectional flows of a generalized Oldroyd-B fluid with fractional derivative. Applied Mathematical Modelling, 2009, 33, 4184–4191.10.1016/j.apm.2009.03.002 ↗
34. Nadeem S. General periodic flows of fractional Oldroyd-B fluid for an edge. Physics Letters A, 2007, 368, 181–187.10.1016/j.physleta.2007.04.032 ↗
35. Liu Y, Zheng L, Zhang X. Unsteady MHD Couette flow of a generalized Oldroyd-B fluid with fractional derivative. Computers and Mathematics with Applications, 2011, 61, 443–450.10.1016/j.camwa.2010.11.021 ↗
36. Zhou J K. Differential Transformation and its Application for Electrical Circuits, Huazhong University Press, Wuhan, 1986.
37. Rashidi M M, Parsa A B, Bég O A, Shamekhi L, Sadri S M, Bég T A. Parametric analysis of entropy generation in magneto-hemodynamic flow in a semi-porous channel with OHAM and DTM. Applied Bionics and Biomechanics, 2014, 11, 1–2.10.1155/2014/413213 ↗
38. Tan W C, Masuoka T. Stokes’ first problem for an Oldroyd-B fluid in a porous half space. Physics of Fluids, 2005, 17, 023101.10.1063/1.1850409 ↗
39. Xue C, Nie J. Exact solutions of Rayleigh-Stokes problem for heated generalized Maxwell fluid in a porous half-space. Mathematical Problems in Engineering, 2008, 2008, 641431.10.1155/2008/641431 ↗
40. Khan M, Hayat T, Asghar S. Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy’s law. International Journal of Engineering Sciences, 2006, 44, 333–33910.1016/j.ijengsci.2005.12.004 ↗