Home Comparative study of thermally intense cilia and non-cilia generated motion of Ellis’s fluid by using MATHEMATICA 14.1
Article
Licensed
Unlicensed Requires Authentication

Comparative study of thermally intense cilia and non-cilia generated motion of Ellis’s fluid by using MATHEMATICA 14.1

  • Zareen Zafar , Zulfiqar Ali and Mubbashar Nazeer ORCID logo EMAIL logo
Published/Copyright: May 9, 2025
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 80 Issue 6

Abstract

The flow of non-Newtonian fluids is commonly used in many biological systems such as the transport of foods through the digestive sector, circulations of the blood, and motion of the urine from the bladder to the kidney, etc. Motivated by the applications of non-Newtonian fluids in various biological systems, the objective of this research is to examine the comparative analysis of ciliated and non-ciliated walls in a two-phase flow of Ellis fluid model through a horizontal tube under the impact of the thermal radiation and viscous dissipation by using the WOLFRAM MATHEMATICA 14.1. The fluid and particle suspension models are developed in terms of conservation of mass, momentum, and energy equations with the help of the Ellis fluid model. The dimensionless quantities are utilized to convert the problem into dimensionless form. The assumption of long-wavelength approximation and low-Reynolds number are employed to simplify and generate the exact solution through WOLFRAM MATHEMATICA. The calculated results revealed that the heat transfer rate is increased by 12 % and 25 % against the variation in volume concentration of particle and Brinkman number, respectively, and the thermal radiation parameter drops the heat transfer rate up to 27 %. The wall shear stress is increased by 18 % and 31 % for Ellis’s fluid parameter and amplitude ratio, respectively. The size of the bolus is increased and decreased at the upper and lower wall of the tube respectively against the Ellis fluid parameter. The calculated results of the present study can be useful in understanding the role of ciliated and non-ciliated walls in peristaltic flows and how these are important in flow and heat transfer mechanisms.

Keywords: Ellis’s fluid; cilia and non-cilia driven flow; lubrication approach; uniform tube; MATHEMATICA
Corresponding author: Mubbashar Nazeer, Department of Mathematics, Institute of Arts and Sciences, Government College University Faisalabad, Chiniot Campus 35400, Pakistan, E-mail:

  1. Research ethics: Accepted.

  2. Informed consent: Not applicable.

  3. Author contributions: Dr. Zareen Zafar: Writting and final draft. Dr. Zulfiqar Ali: Formal analysis. Dr. Mubbashar Nazeer: Ideas, Software development, Supervision.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The authors have no conflict of interest related to this manuscript.

  6. Research funding: No funding is received for this research.

  7. Data availability: This article does not contain any studies with human participants performed by any of the authors.

Nomenclature

( r , z )

Cylindrical coordinates (m)

( u 1,2, w 1,2)

Fluid and particle velocity components along radial and transversal directions m s

a

Wave Amplitude (m)

λ

Wavelength of peristaltic Wave (m)

S

Extra stress tensor (Pa)

ρ f

Fluid density (kg.m−3)

k 1

Thermal conductivity W m K

n 1

Radius of particle (m)

W 1

Relation time of particle

W 2

Thermal equilibrium time

n

Power law index

b

Ellis’s fluid material parameter

β

Wave number 1 m

Rd

Thermal radiation paramete

Bi

Biot number

z 0

Particle position

Rd

Thermal radiation parameter

Br

Brinkman number

C

The volume concentration of particles m o l e m 3

μ s

Kinematic viscosity m 2 s

p

Pressure (Pa)

α

Eccentricity of the cilia elliptic path

γ

Particle volume fraction

ϵ

Amplitude ratio (m)

Q

Volumetric flow rate m 3 s

∆P

Pressure rise (Pa)

∂ p ∂ z

Pressure gradient P a m

θ

Temperature (K)

c 1

wave speed m s

t

Time (s)

η 1

convective heat transfer parameter

A 1

First Rivilin-Ericksen tensor

℧

Second invariant tensor

Ψ

Stream function

σ

Stefan-Boltzmann constant

Re

Reynolds number

Pr

Prandtl number

References

[1] N. Ali, A. Abbasi, and I. Ahmad, “Channel flow of Ellis fluid due to peristalsis,” AIP Adv., vol. 5, no. 9, p. 097214, 2015, https://doi.org/10.1063/1.4932042.Search in Google Scholar

[2] W. A. Khan, N. Anjum, I. Hussain, M. Ali, S. Saleem, and R. S. Mohammed, “Thermo-physical properties of non-linear radiative flow of magnetized Ellis fluid comprising analysis of oxytactic microorganisms and nano-enhanced phase materials,” J. Radiat. Res. Appl. Sci., vol. 17, no. 4, p. 101128, 2024, https://doi.org/10.1016/j.jrras.2024.101128.Search in Google Scholar

[3] S. Shaheen, H. Huang, F. A. M. Al-Yarimi, and M. B. Arain, “Theoretical analysis of Ellis fluid flow in two layers due to metachronal propulsion subject to heat and mass transfer: Application in biological function,” Case Stud. Therm. Eng., vol. 59, no. 1, 2024, Art no. 104446. https://doi.org/10.1016/j.csite.2024.104446.Search in Google Scholar

[4] A. Zeeshan, K. Usman, N. Mubbashar, H. S. Rasheed, and A. Kausar, “Computational study of flow and heat transfer analysis of Ellis fluid model in complicated divergent channel,” Mod. Phys. Lett. B, vol. 38, no. 14, p. 2450119, 2024, https://doi.org/10.1142/s0217984924501197.Search in Google Scholar

[5] N. Imran, M. Javed, M. Sohail, M. Qayyum, and R. M. Khan, “Multi-objective study using entropy generation for Ellis fluid with slip conditions in a flexible channel,” Int. J. Mod. Phys. B, vol. 37, no. 27, p. 2350316, 2023, https://doi.org/10.1142/s0217979223503162.Search in Google Scholar

[6] Z. Asghar, R. A. Shah, W. Shatanawi, and N. Ali, “A theoretical approach to mathematical modeling of sperm swimming in viscoelastic Ellis fluid in a passive canal,” Arch. Appl. Mech., vol. 93, no. 4, pp. 1525–1534, 2023, https://doi.org/10.1007/s00419-022-02343-7.Search in Google Scholar

[7] S. Noreen and F. Aslam, “Electro-osmotic mechanism of Ellis fluid with joule heating, viscous dissipation, and magnetic field effects in a pumping microtube,” ASME. J. Biomech. Eng., vol. 147, no. 1, p. 011010, 2024, https://doi.org/10.1115/1.4067083.Search in Google Scholar PubMed

[8] K. V. Prasad, H. Vaidya, C. Rajashekhar, D. Tripathi, R. K. Gulab, and K. S. Nisar, “Influence of slip conditions and applied magnetic field on peristaltic propulsion of Ellis fluid flow in a homogeneous conduit: A parametric analysis,” Int. J. Ambient Energy, vol. 45, no. 1, p. 2409833, 2024, https://doi.org/10.1080/01430750.2024.2409833.Search in Google Scholar

[9] P. K. Yadav and M. Roshan, “Effect of peristaltic endoscope and heat transfer on the magnetohydrodynamic flow of non-Newtonian biviscosity fluid through an inclined annulus: Homotopy perturbation approach,” Mod. Phys. Lett. B, vol. 39, no. 14, 2024, Art no. 2450498. https://doi.org/10.1142/s0217984924504980.Search in Google Scholar

[10] P. K. Yadav and M. Roshan, “Mathematical modeling of blood flow in an annulus porous region between two coaxial deformable tubes: An advancement to peristaltic endoscope,” Chin. J. Phys., vol. 88, no. 1, pp. 89–109, 2024. https://doi.org/10.1016/j.cjph.2024.01.017.Search in Google Scholar

[11] P. K. Yadav and M. Roshan, “Mathematical modeling of creeping electromagnetohydrodynamic peristaltic propulsion in an annular gap between sinusoidally deforming permeable and impermeable curved tubes,” Phys. Fluids, vol. 36, no. 7, 2024, https://doi.org/10.1063/5.0217370.Search in Google Scholar

[12] M. Hatami, K. Hosseinzadeh, G. Domairry, and M. T. Behnamfar, “Numerical study of MHD two-phase Couette flow analysis for fluid-particle suspension between moving parallel plates,” J. Taiwan Inst. Chem. Eng., vol. 45, no. 5, pp. 2238–2245, 2014, https://doi.org/10.1016/j.jtice.2014.05.018.Search in Google Scholar

[13] A. Al-Zubaidi, M. Nazeer, Z. Zafar, A. Zulfiqar, and K. Ramesh, “Comprehensive analysis of thermal radiation and viscous dissipation impacts on fluid-particle suspension of Rabinowitsch fluid through a uniform horizontal tube,” Multiscale Multidiscip. Model., Exp. Des., vol. 7, no. 1, pp. 5933–5945, 2024. https://doi.org/10.1007/s41939-024-00547-8.Search in Google Scholar

[14] M. Nazeer, N. M. Sarhan, Z. Zafar, Z. Ali, M. Norberdiyeva, and M. I. Khan, “Thermal transport characteristics of fluid-particle suspension in a vertical uniform tube: A computational study on Rabinowitsch fluid with uniform heat source,” Numer. Heat Transfer, Part A: Appl., pp. 1–18, 2024, https://doi.org/10.1080/10407782.2024.2373394.Search in Google Scholar

[15] Z. Zafar, et al.., “Analyzing the impact of convective boundary conditions on fluid–particle mixture flow in a ciliated walled horizontal tube filled with Rabinowitsch fluid,” Numer. Heat Transfer, Part A: Appl., pp. 1–17, 2024, https://doi.org/10.1080/10407782.2024.2379618.Search in Google Scholar

[16] F. J. Alguacil and M. Alonso, “The motion of Brownian particles suspended in a non-uniform fluid flow,” J. Aerosol Sci., vol. 179, no. 1, 2024, Art no. 106382. https://doi.org/10.1016/j.jaerosci.2024.106382.Search in Google Scholar

[17] S. A. Khan, et al.., “Study on the novel suppression of heat transfer deterioration of supercritical water flowing in vertical tube through the suspension of alumina nano particles,” Int. Commun. Heat Mass Transfer, vol. 132, no. 1, 2022, Art no. 105893. https://doi.org/10.1016/j.icheatmasstransfer.2022.105893.Search in Google Scholar

[18] B. Ahmed, T. Hayat, F. M. Abbasi, and A. Alsaedi, “Mixed convection and thermal radiation effect on MHD peristaltic motion of Powell-Eyring nanofluid,” Int. Commun. Heat Mass Transfer, vol. 126, no. 1, 2021, Art no. 105320. https://doi.org/10.1016/j.icheatmasstransfer.2021.105320.Search in Google Scholar

[19] A. M. A. Alrashdi, “Mixed convection and thermal radiation effects on non-Newtonian nano fluid flow with peristalsis and ohmic heating,” Front. Mater., vol. 10, no. 1, 2023, Art no. 1178518. https://doi.org/10.3389/fmats.2023.1178518.Search in Google Scholar

[20] M. M. Channakote, C. Siddabasappa, and D. Tripathi, “Peristaltic mechanism of Ellis fluid with viscous dissipation and thermal radiation induced by cilia wave,” Int. J. Comput. Mater. Sci. Eng., p. 2450006, 2024, https://doi.org/10.1142/s2047684124500064.Search in Google Scholar

[21] M. Rooman, M. A. Jan, Z. Shah, and M. R. Alzahrani, “Entropy generation and nonlinear thermal radiation analysis on axisymmetric MHD Ellis nanofluid over a horizontally permeable stretching cylinder,” Waves Random Complex Media, pp. 1–15, 2022, https://doi.org/10.1080/17455030.2021.2020934.Search in Google Scholar

[22] S. Shaheen, M. B. Arain, N. Ijaz, F. Z. Duraihem, and J. Hu, “Insights into metachronal propulsion’s influence on Ellis fluid flow across tri-layers amid dynamic thermal transport; Theoretical study,” ZAMM - J. Appl. Math. Mech., vol. 104, no. 9, p. e202300977, 2024, https://doi.org/10.1002/zamm.202300977.Search in Google Scholar

[23] M. Irfan, I. Siddique, K. A. Gepreel, M. Nazeer, D. Abduvalieva, and M. Ijaz Khan, “Investigation of heat transfer phenomenon in a complex wavy divergent channel under the effects of thermal radiation, joule heating and electroosmosis,” Numer. Heat Transfer, Part A: Appl., pp. 1–20, 2024, https://doi.org/10.1080/10407782.2024.2386033.Search in Google Scholar

[24] H. Sharif, B. Ali, I. Siddique, I. Saman, M. M. Jaradat, and M. Sallah, “Numerical investigation of dusty tri-hybrid Ellis rotating nanofluid flow and thermal transportation over a stretchable Riga plate,” Sci. Rep., vol. 13, no. 1, p. 14272, 2023, https://doi.org/10.1038/s41598-023-41141-1.Search in Google Scholar PubMed PubMed Central

[25] T. J. Lardner and W. J. Shack, “Cilia transport,” Bull. Math. Biophys., vol. 34, no. 1, pp. 325–335, 1972. https://doi.org/10.1007/bf02476445.Search in Google Scholar PubMed

[26] H. L. Agrawal and A. Anawaruddin, “Cilia transport of bio-fluid with variable viscosity,” Indian J. Pure Appl. Math., vol. 15, no. 10, pp. 1128–1139, 1984.Search in Google Scholar

[27] A. M. Siddiqui, A. A. Farooq, and M. A. Rana, “Study of MHD effects on the cilia-induced flow of a Newtonian fluid through a cylindrical tube,” Magnetohydrodynamics, vol. 50, no. 4, pp. 249–261, 2014.10.22364/mhd.50.4.3Search in Google Scholar

[28] A. M. Siddiqui, A. A. Farooq, and M. A. Rana, “Hydromagnetic flow of Newtonian fluid due to ciliary motion in a channel,” Magnetohydrodynamics, vol. 50, no. 3, pp. 109–122, 2014.10.22364/mhd.50.3.4Search in Google Scholar

[29] Z. Min, H. Anwaar, M. B. Arain, S. Shaheen, and F. A. Al-Yarimi, “Numerical investigation of the effects of variable fluid properties on cilia-driven flow of tangent hyperbolic fluid in a channel with heat and mass transfer: A new approach to micro fluidic pumps,” Case Stud. Therm. Eng., vol. 62, no. 1, 2024, Art no. 105120. https://doi.org/10.1016/j.csite.2024.105120.Search in Google Scholar

[30] A. Ali, A. Barman, and S. Das, “EDL aspect in cilia-regulated bloodstream infused with hybridized nano particles via a micro tube under a strong field of magnetic attraction,” Therm. Sci. Eng. Prog., vol. 36, no. 1, 2022, Art no. 101510. https://doi.org/10.1016/j.tsep.2022.101510.Search in Google Scholar

[31] M. Ajmal, R. Mehmood, N. S. Akbar, and T. Muhammad, “Computational study on cilia transport of Prandtl nanofluid (blood-Fe3O4) enhancing convective heat transfer along microorganisms under electroosmotic effects in wavy capillaries,” Int. J. Numer. Methods Heat Fluid Flow, 2024. https://doi.org/10.1108/HFF-07-2024-0503.Search in Google Scholar

[32] K. Javid, et al.., “EMHD ciliated pumping of viscoelastic liquid in a complex convergent/divergent channel,” Waves Random Complex Media, no. 1, pp. 1–23, 2022. https://doi.org/10.1080/17455030.2022.2110622.Search in Google Scholar

[33] N. S. Akbar and A. W. Butt, “Heat transfer analysis of Rabinowitsch fluid flow due to metachronal wave of cilia,” Results Phys., vol. 5, no. 1, pp. 92–98, 2015. https://doi.org/10.1016/j.rinp.2015.03.005.Search in Google Scholar

[34] M. Rafiq, S. Shaheen, M. I. Khan, B. M. Fadhl, S. B. H. Hassine, and S. M. ElDin, “Impact of ciliated walls on peristaltic flow of Rabinowitsch fluid through flexible tube with heat/mass transfer,” Case Stud. Therm. Eng., vol. 45, no. 1, 2023, Art no. 102990. https://doi.org/10.1016/j.csite.2023.102990.Search in Google Scholar

[35] A. M. Siddiqui and W. H. Schwarz, “Peristaltic flow of a second-order fluid in tubes,” J. Non-Newtonian Fluid Mech., vol. 53, no. 1, pp. 257–284, 1994. https://doi.org/10.1016/0377-0257(94)85052-6.Search in Google Scholar

[36] Z. Abbas, A. Shakeel, M. Y. Rafiq, S. Khaliq, J. Hasnain, and A. Nadeem, “Rheology of peristaltic flow in couple stress fluid in an inclined tube: Heat and mass transfer analysis,” Adv. Mech. Eng., vol. 14, no. 11, pp. 1–14, 2022, https://doi.org/10.1177/16878132221139984.Search in Google Scholar

[37] N. S. Akbar, “Entropy generation and energy conversion rate for the peristaltic flow in a tube with magnetic field,” Energy, vol. 82, no. 1, pp. 23–30, 2015. https://doi.org/10.1016/j.energy.2014.12.034.Search in Google Scholar

[38] A. W. Butt, N. S. Akbar, and N. A. Mir, “Heat transfer analysis of peristaltic flow of a Phan-Thien–Tanner fluid model due to metachronal wave of cilia,” Biomech. Model. Mechanobiol., vol. 19, no. 1, pp. 1925–1933, 2020. https://doi.org/10.1007/s10237-020-01317-4.Search in Google Scholar PubMed

[39] S. Saleem, F. Hussain, M. Irfan, I. Siddique, M. Nazeer, and S. M. Eldin, “Theoretical investigation of heat transfer analysis in Ellis nanofluid flow through the divergent channel,” Case Stud. Therm. Eng., vol. 48, no. 1, 2023, Art no. 103140. https://doi.org/10.1016/j.csite.2023.103140.Search in Google Scholar

[40] M. Irfan, I. Siddique, M. Nazeer, S. Saleem, and N. Radwan, “Heat transfer analysis of single-walled carbon nanotubes in Ellis’s fluid model: Comparative study of uniform and non-uniform channels,” Case Stud. Therm. Eng., vol. 54, no. 1, 2024, Art no. 104036. https://doi.org/10.1016/j.csite.2024.104036.Search in Google Scholar

[41] Z. Asghar, M. W. S. Khan, W. Shatanawi, and M. A. Gondal, “Semi-analytical solution of Graetz–Brinkman problem combined with non-Newtonian Ellis fluid flow in a passive channel,” Eur. Phys. J. Plus, vol. 138, no. 11, p. 978, 2023, https://doi.org/10.1140/epjp/s13360-023-04632-8.Search in Google Scholar

[42] R. A. Shah, Z. Asghar, and N. Ali, “Mathematical modeling related to bacterial gliding mechanism at low Reynolds number with Ellis Slime,” Eur. Phys. J. Plus, vol. 137, no. 5, pp. 1–12, 2022, https://doi.org/10.1140/epjp/s13360-022-02796-3.Search in Google Scholar

[43] M. Abbas, B. B. Mohsin, L. Ali, and I. Mahariq, “Significance of activation energy and Stefan blowing on Marangoni convective flow of Ellis tetra hybrid nanofluid with Soret and Dufour effects,” J. Braz. Soc. Mech. Sci. Eng., vol. 47, no. 2, p. 55, 2025, https://doi.org/10.1007/s40430-024-05329-4.Search in Google Scholar

[44] M. M. Bhatti, A. Zeeshan, R. Ellahi, O. A. Bég, and A. Kadir, “Effects of coagulation on the two-phase peristaltic pumping of magnetized Prandtl biofluid through an endoscopic annular geometry containing a porous medium,” Chin. J. Phys., vol. 58, no. 2, pp. 222–234, 2019. https://doi.org/10.1016/j.cjph.2019.02.004.Search in Google Scholar

[45] A. Riaz, A. Zeeshan, S. Ahmad, A. Razaq, and M. Zubair, “Effects of external magnetic field on non-Newtonian two phase fluid in an annulus with peristaltic pumping,” J. Magn., vol. 24, no. 1, pp. 62–69, 2019, https://doi.org/10.4283/jmag.2019.24.1.062.Search in Google Scholar

[46] V. P. Srivastava, “Particle-fluid suspension model of blood flow through stenotic vessels with applications,” Int. J. Bio Med. Comput., vol. 38, no. 2, pp. 141–154, 1995, https://doi.org/10.1016/0020-7101(94)01046-4.Search in Google Scholar PubMed

[47] K. S. Mekheimer and Y. Abd Elmaboud, “Peristaltic transport of a particle–fluid suspension through a uniform and non-uniform annulus,” Appl. Bionics Biomech., vol. 5, no. 2, pp. 47–57, 2008, https://doi.org/10.1155/2008/391687.Search in Google Scholar

[48] M. A. Sleigh, The Biology of Cilia and Flagella, New York, MacMillan, 1962.10.5962/bhl.title.4525Search in Google Scholar

[49] M. Nazeer, S. Saleem, F. Hussain, Z. Zia, K. Khalid, and N. Feroz, “Heat transmission in a magnetohydrodynamic multiphase flow induced by metachronal propulsion through porous media with thermal radiation,” Proc. Inst. Mech. Eng., Part E: J. Process Mech. Eng., p. 09544089221075299, 2022, https://doi.org/10.1177/09544089221075299.Search in Google Scholar

[50] A. Al-Zubaidi, M. Nazeer, K. Khalid, S. Yaseen, S. Saleem, and F. Hussain, “Thermal analysis of blood flow of Newtonian, pseudo-plastic, and dilatant fluids through an inclined wavy channel due to metachronal wave of cilia,” Adv. Mech. Eng., vol. 13, no. 9, p. 16878140211049060, 2021, https://doi.org/10.1177/16878140211049060.Search in Google Scholar

[51] M. Nazeer, et al.., “Mathematical modeling of bio‐magnetic fluid bounded within ciliated walls of wavy channel,” Numer. Methods Part. Differ. Equ., vol. 40, no. 2, p. e22763, 2024, https://doi.org/10.1002/num.22763.Search in Google Scholar

[52] Y. J. Xu, et al.., “Electro-osmotic flow of biological fluid in divergent channel: Drug therapy in compressed capillaries,” Sci. Rep., vol. 11, no. 1, p. 23652, 2021, https://doi.org/10.1038/s41598-021-03087-0.Search in Google Scholar PubMed PubMed Central

[53] P. Y. Xiong, et al.., “Two-phase flow of couple stress fluid thermally effected slip boundary conditions: Numerical analysis with variable liquids properties,” Alex. Eng. J., vol. 61, no. 5, pp. 3821–3830, 2022, https://doi.org/10.1016/j.aej.2021.09.012.Search in Google Scholar

[54] H. A. Ogunseye and P. Sibanda, “A mathematical model for entropy generation in a Powell-Eyring nanofluid flow in a porous channel,” Heliyon, vol. 5, no. 5, p. e01662, 2019, https://doi.org/10.1016/j.heliyon.2019.e01662.Search in Google Scholar PubMed PubMed Central

[55] S. O. Salawu, R. A. Kareem, and S. A. Shonola, “Radiative thermal criticality and entropy generation of hydromagnetic reactive Powell–Eyring fluid in saturated porous media with variable conductivity,” Energy Rep., vol. 5, no. 1, pp. 480–488, 2019. https://doi.org/10.1016/j.egyr.2019.04.014.Search in Google Scholar

[56] J. Vardagala, S. Sreedharamalle, A. Moorthi, S. Gorintla, and L. Pallavarapu, “Hydromagnetic peristaltic flow of convective Casson nanofluid through a vertical porous channel under the influence of Ohmic heating and viscous dissipation effects,” World J. Eng., vol. 22, no. 2, pp. 260–275, 2025, https://doi.org/10.1108/wje-10-2023-0455.Search in Google Scholar

[57] M. Ajithkumar, S. Kuharat, O. A. Bég, G. Sucharitha, and P. Lakshminarayana, “Catalytic effects on peristaltic flow of Jeffrey fluid through a flexible porous duct under oblique magnetic field: Application in biomimetic pumps for hazardous materials,” Therm. Sci. Eng. Prog., vol. 49, no. 1, 2024, Art no. 102476. https://doi.org/10.1016/j.tsep.2024.102476.Search in Google Scholar

[58] M. Ajithkumar, R. Meenakumari, G. Sucharitha, M. Vinodkumar Reddy, K. Javid, and P. Lakshminarayana, “Bioconvective peristaltic transport of hydromagnetic Sutterby nanofluid through a chemically activated porous channel with gyrotactic microorganisms,” J. Appl. Phys., vol. 135, no. 19, 2024, https://doi.org/10.1063/5.0203027.Search in Google Scholar

[59] V. Jagadesh, S. Sreenadh, M. Ajithkumar, G. Sucharitha, and P. Lakshminarayana, “Convective peristaltic pumping of MHD Ree-Eyring nanofluid in a chemically reacting flexible divergent channel with activation energy and radiation,” Radiat. Eff. Defects Solids, vol. 179, nos. 9–10, pp. 1162–1177, 2024, https://doi.org/10.1080/10420150.2024.2332207.Search in Google Scholar
Received: 2025-01-03
Accepted: 2025-04-23
Published Online: 2025-05-09
Published in Print: 2025-06-26

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Dynamical Systems & Nonlinear Phenomena
  3. Controlling the convective heat transfer of shear thinning and shear thickening fluids in parallel plates with magnetic force
  4. Multistability, chaos and hyperchaos in a novel 3D discrete memristive system: microcontroller implementation and cryptography
  5. Comparative study of thermally intense cilia and non-cilia generated motion of Ellis’s fluid by using MATHEMATICA 14.1
  6. Fundamental Concepts of Physical Science
  7. Nonlinear electrodynamics and its possible connection to relativistic superconductivity: instance of a time-dependent system
  8. Galilean decoherence and quantum measurement
  9. Solid State Physics & Materials Science
  10. A dynamically tunable polarization-insensitive broadband vanadium dioxide-assisted absorber for terahertz applications
  11. Thermodynamics & Statistical Physics
  12. Heat transfer analysis for the Cattaneo–Cristov heat flux model using integral transform technique with isothermal and isoflux wall conditions
https://doi.org/10.1515/zna-2025-0006
Keywords for this article
Ellis’s fluid; cilia and non-cilia driven flow; lubrication approach; uniform tube; MATHEMATICA

Articles in the same Issue

  1. Frontmatter
  2. Dynamical Systems & Nonlinear Phenomena
  3. Controlling the convective heat transfer of shear thinning and shear thickening fluids in parallel plates with magnetic force
  4. Multistability, chaos and hyperchaos in a novel 3D discrete memristive system: microcontroller implementation and cryptography
  5. Comparative study of thermally intense cilia and non-cilia generated motion of Ellis’s fluid by using MATHEMATICA 14.1
  6. Fundamental Concepts of Physical Science
  7. Nonlinear electrodynamics and its possible connection to relativistic superconductivity: instance of a time-dependent system
  8. Galilean decoherence and quantum measurement
  9. Solid State Physics & Materials Science
  10. A dynamically tunable polarization-insensitive broadband vanadium dioxide-assisted absorber for terahertz applications
  11. Thermodynamics & Statistical Physics
  12. Heat transfer analysis for the Cattaneo–Cristov heat flux model using integral transform technique with isothermal and isoflux wall conditions
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 5.10.2025 from https://www.degruyterbrill.com/document/doi/10.1515/zna-2025-0006/html
Scroll to top button