Thermal and concentration analysis of Phan-Thien-Tanner fluid flow due to ciliary movement in a peripheral layer

Abstract

This paper presents the analysis of two-layer cilia induced flow of Phan-Thien-Tanner (PTT) fluid with thermal and concentration effect. The Phan-Thien-Tanner fluid model has been used in the analogy of mucus present in the respiratory tract. The two-layer model approach was used due to the Peri Ciliary liquid Layer (PCL) and Airway Ciliary Layer (ACL) present on the epithelium cell in respiratory tract. The mathematical modelling of two-layer flow problem was simplified using long wavelength and small Reynold’s number approximation. The resulting differential equation with moving boundary gives exact solution for velocity, temperature and concentration profiles in two layers. The change in pressure has calculated by the results of velocity profile, also the pressure rise was evaluated by the numerical integration of pressure gradient along the channel wall. The impact of physical parameters on pressure rise, velocity, temperature and concentration profile was explained by the graphs. It can be seen from graphs that velocity and temperature profile are maximum in the inner layer of fluid (PCL) and concentration profile is maximum at outer layers of fluid (ACL).

Keywords

ciliary flow / PTT fluid / two-layer model / thermal analysis / concentration effect

References

[1] ShangY-d, InthavongK, TuJ-yuan. Development of a computational fluid dynamics model for mucociliary clearance in the nasal cavity [J]. Journal of Biomechanics, 2019, 85: 74-83

[2] RubinB K. Secretion properties, clearance, and therapy in airway disease [J]. Translational Respiratory Medicine, 2014, 2: 6

[3] KathemS H, MohieldinA M, NauliS M. The roles of primary cilia in polycystic kidney disease [J]. AIMS Molecular Science, 2014, 1(1): 27-46

[4] TilleyA E, WaltersM S, ShaykhievR, CrystalR G. Cilia dysfunction in lung disease [J]. Annual Review of Physiology, 2015, 77379-406

[5] Vélez-corderoJ R, LaugaE. Waving transport and propulsion in a generalized Newtonian fluid [J]. Journal of Non-Newtonian Fluid Mechanics, 2013, 199: 37-50

[6] HussongJ, LindkenR, FaulhammerP, NoreikatK, SharpK V, KummerW, WesterweelJ. Cilia-driven particle and fluid transport over mucus-free mice tracheae [J]. Journal of Biomechanics, 2013, 46(3): 593-598

[7] GheberL, KorngreenA, PrielZ. Effect of viscosity on metachrony in mucus propelling cilia [J]. Cell Motility and The Cytoskeleton, 1998, 39(1): 9-20

[8] Bustamante-MarinX M, OstrowskiL E. Cilia and mucociliary clearance [J]. Cold Spring Harbor Perspectives in Biology, 2017, 9(4): a028241

[9] SiddiquiA M, HaroonT, RaniM, AnsariA R. An analysis of the flow of a power law fluid due to ciliary motion in an infinite channel [J]. Journal of Biorheology, 2010, 24256-69

[10] SiddiquiA M, FarooqA A, RanaM A. An investigation of non-Newtonian fluid flow due to metachronal beating of cilia in a tube [J]. International Journal of Biomathematics, 2015, 8(2): 1550016

[11] NadeemS, SadafH. Theoretical analysis of Cu-blood nanofluid for metachronal wave of cilia motion in a curved channel [J]. IEEE Transactions on NanoBioscience, 2015, 144447-454

[12] NadeemS, MunimA, ShaheenA, HussainS. Physiological flow of Carreau fluid due to ciliary motion [J]. AIP Advances, 2016, 6(3): 035125

[13] AkbarN S, TripathiD, BégO A, KhanZ H. MHD dissipative flow and heat transfer of Casson fluids due to metachronal wave propulsion of beating cilia with thermal and velocity slip effects under an oblique magnetic field [J]. Acta Astronautica, 2016, 128: 1-12

[14] ManzoorN, MaqboolK, BégO A, ShaheenS. Adomian decomposition solution for propulsion of dissipative magnetic Jeffrey biofluid in a ciliated channel containing a porous medium with forced convection heat transfer [J]. Heat Transfer—Asian Research, 2019, 48(2): 556-581

[15] AkbarN S, TripathiD, KhanZ H, BégO A. Mathematical modelling of pressure-driven micropolar biological flow due to metachronal wave propulsion of beating cilia [J]. Mathematical Biosciences, 2018, 301121-128

[16] SadafH, NadeemS. Fluid flow analysis of cilia beating in a curved channel in the presence of magnetic field and heat transfer [J]. Canadian Journal of Physics, 2020, 98(2): 191-197

[17] BartonC, RaynorS. Analytical investigation of cilia induced mucous flow [J]. The Bulletin of Mathematical Biophysics, 1967, 29(3): 419-428

[18] MillerC E. An investigation of the movement of Newtonian liquids initiated and sustained by the oscillation of mechanical cilia [J]. Aspen Emphysema Conference, 1967, 10: 309-321

[19] RossS M, CorrsinS. Results of an analytical model of mucociliary pumping [J]. Journal of Applied Physiology, 1974, 37(3): 333-340

[20] AgarwalM, ShuklaJ B. Mucus transport in the lung [J]. Mathematical and Computer Modelling, 1988, 11: 797-800

[21] NortonM M, RobinsonR J, WeinsteinS J. Model of ciliary clearance and the role of mucus rheology [J]. Physical Review E, 2011, 83011921

[22] JayathilakeP G, LeD V, TanZ-j, LeeH P, KhooB C. A numerical study of muco-ciliary transport under the condition of diseased cilia [J]. Computer Methods in Biomechanics and Biomedical Engineering, 2015, 18(9): 944-951

[23] ShaheenS, MaqboolK, SiddiquiA M. Micro rheology of Jeffrey nanofluid through cilia beating subject to the surrounding temperature [J]. Rheologica Acta, 2020, 59(8): 565-573

[24] SaeedT, AbbasI, MarinM. A GL model on thermoelastic interaction in a poroelastic material using finite element method [J]. Symmetry, 2020, 12(3): 488

[25] AbrarM N, SagheerM, HussianS. Entropy analysis of SWCNT & MWCNT flow induced by collecting beating of cilia with porous medium [J]. Journal of Central South University, 2019, 2682109-2118

[26] ZhangL-j, ArainM B, BhattiM M, ZeeshanA, Hal-SulamiH. Effects of magnetic Reynolds number on swimming of gyrotactic microorganisms between rotating circular plates filled with nanofluids [J]. Applied Mathematics and Mechanics, 2020, 41(4): 637-654

[27] ShaheenA, HussainS, NadeemS. Physiological flow of Jeffrey six constant fluid model due to ciliary motion [J]. Communications in Theoretical Physics, 2016, 66(6): 701-708

[28] AbdelsalamS I, BhattiM M, ZeeshanA, RiazA, BégO A. Metachronal propulsion of a magnetised particle-fluid suspension in a ciliated channel with heat and mass transfer [J]. Physica Scripta, 2019, 94(11): 115301

[29] ZaherA Z, MoawadA M A, MekheimerK S, BhattiM M. Residual time of sinusoidal metachronal ciliary flow of non-Newtonian fluid through ciliated walls: Fertilization and implantation [J]. Biomechanics and Modeling in Mechanobiology, 2021, 202609-630

[30] Abo-ElkhairR E, BhattiM M, MekheimerK S. Magnetic force effects on peristaltic transport of hybrid bio-nanofluid (AuCu nanoparticles) with moderate Reynolds number: An expanding horizon [J]. International Communications in Heat and Mass Transfer, 2021, 123105228

[31] ZhangL-j, BhattiM M, MarinM, MekheimerK S. Entropy analysis on the blood flow through anisotropically tapered arteries filled with magnetic zincoxide (ZnO) nanoparticles [J]. Entropy, 2020, 22(10): 1070

[32] AbbasiF M, AlsaediA, HayatT. Mixed convective heat and mass transfer analysis for peristaltic transport in an asymmetric channel with Soret and Dufour effects [J]. Journal of Central South University, 2014, 21124585-4591

[33] AbbasiF M, HayatT, AhmadB, ChenB. Peristaltic flow with convective mass condition and thermal radiation [J]. Journal of Central South University, 2015, 22(6): 2369-2375

[34] ChenW-y, WangJ-b, JiangN, ZhaoB, WangZ-dong. Numerical simulation of gas-liquid two-phase jet flow in air-bubble generator [J]. Journal of Central South University of Technology, 2008, 15(1): 140-144

[35] AhmadpourM, SiavashiM, DoranehgardM H. Numerical simulation of two-phase flow in fractured porous media using streamline simulation and IMPES methods and comparing results with a commercial software [J]. Journal of Central South University, 2016, 23(10): 2630-2637

[36] AbdE Y, AbdelsalamS I, MekheimerK S, VafaiK. Electromagnetic flow for two-layer immiscible fluids [J]. Engineering Science and Technology, an International Journal, 2019, 22(1): 237-248

[37] MisraJ C, PandeyS K. Peristaltic flow of a multilayered power-law fluid through a cylindrical tube [J]. International Journal of Engineering Science, 2001, 39(4): 387-402

[38] AwanS E, AwaisM, RajaM A Z, ParveenN, AliH M, KhanW U, HeY-gang. Numerical treatment for dynamics of second law analysis and magnetic induction effects on ciliary induced peristaltic transport of hybrid nanomaterial [J]. Frontiers in Physics, 2021, 9631903

[39] PacherresC O, AhmerkampS, Schmidt-GriebG M, HoltappelsM, RichterC. Ciliary vortex flows and oxygen dynamics in the coral boundary layer [J]. Scientific Reports, 2020, 107541

[40] BhattiM M, ElelamyA F, SaitS M, EllahiR. Hydrodynamics interactions of metachronal waves on particulate-liquid motion through a ciliated annulus: Application of bio-engineering in blood clotting and endoscopy [J]. Symmetry, 2020, 124532

[41] SiddiquiA, ZebM, HaroonT, AzimQ U A. Exact solution for the heat transfer of two immiscible PTT fluids flowing in concentric layers through a pipe [J]. Mathematics, 2019, 7181