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Significance of Micro-Rotation on Buoyancy Driven Oscillatory Flow of Micropolar-Casson Fluid Through Tapered Wavy Channels: A Numerical Approach

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Abstract

The present study introduces a novel investigation into the heat and mass transfer in oscillatory micropolar-Casson fluid flow through a tapered wavy channel, considering both small and large values of plastic dynamic viscosity. The micropolar-Casson fluid models offer a novel perspective for understanding the complex dynamics of blood flow in restricted blood vessels. Incorporating micro-rotational effects and yield stress characteristics into these models provides a more comprehensive understanding of hemodynamic patterns and the potential for thrombosis. The objective of the study is to explore the novelty in the analysis of plastic dynamic viscosity through an asymmetric tapered wavy channel by examining its effect on the time-dependent oscillatory flow of a micropolar-Casson fluid in the presence of buoyancy forces and chemical reaction. The Plank's approximation is adopted to model the radiation component of heat transfer. An implicit finite difference numerical scheme called the Crank-Nicolson method is applied to solve the governing equations. Graphical analysis is employed to explore the influence of different physical parameters, including micropolar parameter, Peclet number, Hartmann number and transient. The numerical results of couple stress coefficient, heat and mass transfer rate are tabulated to highlight the significant effects of various fluid flow parameters. Higher values of the micropolar parameter, Lorentz force and micropolar-Casson parameter result in decreased velocity fields. For high values of Peclet number, there is a significant change in the fluid temperature between the centre of the channel and the right wall. The micropolar parameter plays a critical role in sha** fluid behavior by affecting microstructural interactions and fluid rotation. By scrutinizing the data points using slope regression analysis, it is noted that for both buoyancy and Lorentz force, the rates of couple stress coefficient are higher for larger plastic dynamic viscosity (PDV) values than smaller PDV values.

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Data availability

All data generated or analyzed during this study are included in this published article.

Abbreviations

u :

Fluid velocity [ms−1]

p :

Fluid pressure [kgm−1 s−2]

j :

Micro-inertia density [m2]

x, y :

Spatial coordinates [m]

\(T_{0} {,}T_{1}\) :

Reference fluid temperatures [K]

\(N^{\prime}\) :

Angular velocity [rad s−1]

\(a_{1} ,a_{2}\) :

Amplitudes of the wavy walls [m]

\(H_{1} ,H_{2}\) :

Channel walls [m],

\(h_{1} ,h_{2}\) :

Dimensionless channel walls -

\(C_{0} ,C_{1}\) :

Reference fluid concentration [M]

a, b :

Amplitude ratios -

m :

Taperedness parameter -

d :

Average channel width [m]

U :

Non Dimensional velocity -

N :

Dimensionless angular velocity -

g :

Acceleration due to gravity [ms−2]

\(p_{y}\) :

Yield stress of the fluid [kgm−1 s−2]

\(q_{r}\) :

Radiative heat flux -

\(B_{0}\) :

Magnetic field intensity [m−1A]

k :

Thermal conductivity of the fluid [Wm−1 K−1]

\(C_{p}\) :

Specific heat at constant pressure [Jkg−1 K−1]

Gr :

Grashof number -

P :

Dimensionless fluid pressure -

\(K^{\prime}\) :

Rotational viscosity coefficient [kgs−1 m−1]

Gc :

Modified Grashof number -

R :

Thermal radiation parameter -

t :

Time [s]

Sh :

Sherwood number -

T :

Temperature of fluid [K]

C :

Fluid concentration [M]

Nu :

Nusselt number -

K :

Micropolar parameter -

\(k^{*}\) :

Porous permeability [m2]

Sc :

Schmidt Number -

Ha :

Hartmann number -

Re :

Reynolds number -

S :

Suction/injection parameter -

Pe :

Peclet number -

D :

Diffusivity [m2 s−1]

Da :

Darcy number -

Kr :

Chemical reaction parameter [Mol l−1 s−1]

\(S_{f}\) :

Skin friction coefficient -

\(\tau_{m}\) :

Couple stress coefficient

\(\lambda \) :

Dimensionless pressure gradient -

\({\nu }_{0}\) :

Constant horizontal velocity [ms−1]

\(\psi \) :

Phase angle Degrees

\({\lambda}^{\prime}\) :

Wavelength m

\(\beta \) :

Casson fluid parameter -

\(\alpha \) :

Mean radiation absorption coefficient [Wm−1]

\(\mu \) :

Viscosity of fluid [N s m−2]

\(\phi \) :

Dimensionless concentration -

\(\omega \) :

Frequency of oscillation [s−1]

\({\mu }_{s}\) :

Microrotational coupling coefficient N s

\(\sigma \) :

Fluid conductivity [S m−1]

\(\rho \) :

Density of fluid [kg m−3]

\({\beta }_{T}\) :

Thermal expansion coefficient [K−1]

\(\theta \) :

Dimensionless temperature -

\({\beta }_{c}\) :

Mass expansion coefficient

References

  1. Eringen, A.C.: Theory of micropolar fluids. J. Math. Mech. 16(1), 1–18 (1966)

    MathSciNet  Google Scholar 

  2. Lukaszewicz, G.: Micropolar fluids: theory and applications. Springer Science & Business Media, Boston (1999)

    Book  Google Scholar 

  3. Misra, J.C., Chandra, S., Shit, G.C., Kundu, P.K.: Electroosmotic oscillatory flow of micropolar fluid in microchannels: application to dynamics of blood flow in microfluidic devices. Appl. Math. Mech. 35, 749–766 (2014). https://doi.org/10.1007/s10483-014-1827-6

    Article  MathSciNet  Google Scholar 

  4. Ali, A., Umar, M., Bukhari, Z., Abbas, Z.: Pulsating flow of a micropolar-Casson fluid through a constricted channel influenced by a magnetic field and Darcian porous medium: a numerical study. Res. Phys. 19, 103544 (2020). https://doi.org/10.1016/j.rinp.2020.103544

    Article  Google Scholar 

  5. Abbas, Z., Rafiq, M.Y.: Numerical simulation of thermal transportation with viscous dissipation for a peristaltic mechanism of micropolar-Casson fluid. Arab. J. Sci. Eng. 47(7), 8709–8720 (2022). https://doi.org/10.1007/s13369-021-06354-4

    Article  Google Scholar 

  6. Iqbal, Z., Mehmood, R., Azhar, E., Mehmood, Z.: Impact of inclined magnetic field on micropolar Casson fluid using Keller box algorithm. Eur. Phys. J. Plus 132, 1–13 (2017). https://doi.org/10.1140/epjp/i2017-11443-7

    Article  Google Scholar 

  7. Alkasasbeh, H.T.: Numerical solution of micropolar Casson fluid behaviour on steady MHD natural convective flow about a solid sphere. J. Adv. Res. Fluid Mech. Therm. Sci. 50(1), 55–66 (2018)

    Google Scholar 

  8. Prakash, D., Muthtamilselvan, M.: Effect of radiation on transient MHD flow of micropolar fluid between porous vertical channel with boundary conditions of the third kind. Ain Shams Eng. J. 5(4), 1277–1286 (2014). https://doi.org/10.1016/j.asej.2014.05.004

    Article  Google Scholar 

  9. Sheikholeslami, M., Hatami, M., Ganji, D.D.: Micropolar fluid flow and heat transfer in a permeable channel using analytical method. J. Mol. Liq. 194, 30–36 (2014). https://doi.org/10.1016/j.molliq.2014.01.005

    Article  Google Scholar 

  10. Kataria, H.R., Patel, H.R., Singh, R.: Effect of magnetic field on unsteady natural convective flow of a micropolar fluid between two vertical walls. Ain Shams Eng. J. 8(1), 87–102 (2017). https://doi.org/10.1016/j.asej.2015.08.013

    Article  Google Scholar 

  11. Sasikumar, J., Senthamarai, R.: Chemical reaction and viscous dissipation effect on MHD oscillatory blood flow in tapered asymmetric channel. Math. Model. Comput. 9(4), 999–1010 (2022). https://doi.org/10.23939/mmc2022.04.999

    Article  Google Scholar 

  12. Chun, O., Raja, M.A.Z., Naz, S., Ahmad, I., Akhtar, R., Ali, Y., Shoaib, M.: Dynamics of inclined magnetic field effects on micropolar Casson fluid with Lobatto IIIA numerical solver. AIP Adv. (2020). https://doi.org/10.1063/5.0004386

    Article  Google Scholar 

  13. Chamkha, A.J., Groşan, T., Pop, I.: Fully developed free convection of a micropolar fluid in a vertical channel. Int. Commun. Heat Mass Transf. 29(8), 1119–1127 (2002). https://doi.org/10.1016/S0735-1933(02)00440-2

    Article  Google Scholar 

  14. Prakash, D., Saraswathy, M., Kumar, S.: Transient Convective Heating Transport of the Micropolar Fluid Flow Between Asymmetric Channel with Activation Energy. In IOP Conference Series: Materials Science and Engineering (Vol. 1130, No. 1, p. 012049). IOP Publishing. (2021). https://doi.org/10.1088/1757-899X/1130/1/012049

  15. Mirgolbabaee, H., Ledari, S.T., Ganji, D.D.: Semi-analytical investigation on micropolar fluid flow and heat transfer in a permeable channel using AGM. J. Assoc. Arab Univ. Basic Appl. Sci. 24, 213–222 (2017). https://doi.org/10.1016/j.jaubas.2017.01.002

    Article  Google Scholar 

  16. Srinivasacharya, D., Bindu, K.H.: Entropy generation in a micropolar fluid flow through an inclined channel. Alex. Eng. J. 55(2), 973–982 (2016). https://doi.org/10.1016/j.aej.2016.02.027

    Article  Google Scholar 

  17. Krishna, M.V., Ahamad, N.A., Aljohani, A.F.: Thermal radiation, chemical reaction, Hall and ion slip effects on MHD oscillatory rotating flow of micro-polar liquid. Alex. Eng. J. 60(3), 3467–3484 (2021). https://doi.org/10.1016/j.aej.2021.02.013

    Article  Google Scholar 

  18. Khan, M.N., Nadeem, S., Muhammad, N.: Micropolar fluid flow with temperature-dependent transport properties. Heat Transf. 49(4), 2375–2389 (2020). https://doi.org/10.1002/htj.21726

    Article  Google Scholar 

  19. Jaiswal, S., Yadav, P.K.: A micropolar-Newtonian blood flow model through a porous layered artery in the presence of a magnetic field. Phys. Fluids (2019). https://doi.org/10.1063/1.5100802

    Article  Google Scholar 

  20. Barkilean, J., Jagadeesan, S.: Heat transfer characteristics on MHD oscillatory radiative nanofluid with H2O/C2H6O2 (Basefluid): a comparative study of different nanoparticles of various shapes. Int. J. Heat Technol. 41(3), 529–540 (2023)

    Article  Google Scholar 

  21. Karvelas, E., Sofiadis, G., Papathanasiou, T., Sarris, I.: Effect of micropolar fluid properties on the blood flow in a human carotid model. Fluids 5(3), 125 (2020). https://doi.org/10.3390/fluids5030125

    Article  Google Scholar 

  22. Sasikumar, J., Govindarjan, A.: Effect of heat and mass transfer on MHD oscillatory flow with chemical reaction and slip conditions in asymmetric wavy channel. J. Eng. Appl. Sci. 11(2), 1164–1170 (2016)

    Google Scholar 

  23. Vaidehi, P., Sasikumar, J.: Darcy flow of unsteady Casson fluid subject to thermal radiation and Lorentz force on wavy walls: Case of slip flow for small and large values of plastic dynamic viscosity. Therm. Sci Eng. Prog. 42, 101885 (2023). https://doi.org/10.1016/j.tsep.2023.101885

    Article  Google Scholar 

  24. Sasikumar, J., Bhati, D., Bhaskar, V.: Effect of heat and mass transfer on MHD oscillatory flow through asymmetric wavy channel in a porous medium with suction and injection. In AIP Conference Proceedings (Vol. 2277, No. 1). AIP Publishing. (2020). https://doi.org/10.1063/5.0025530

  25. Vaidehi, P., Sasikumar, J.: Thermo diffusion and chemical reaction effect on MHD oscillatory flow of viscoelastic fluid in an asymmetric wavy channel under the influence of magnetic field. Math. Eng. Sci. Aerosp. 14(2), 373 (2023)

    Google Scholar 

  26. Sasikumar, J., Bhuvaneshwari, S., Govindarajan, A.: Diffusion of chemically reactive species in MHD oscillatory flow with thermal radiation in the presence of constant suction and injection. In Journal of Physics: Conference Series (Vol. 1000, No. 1, p. 012033). IOP Publishing. (2018). https://doi.org/10.1088/1742-6596/1000/1/012033

  27. Ogulu, A., Bestman, A.R.: Deep heat muscle treatment a mathematical model - I. Acta Physica Hungarica 73, 3–16 (1993)

    Article  Google Scholar 

  28. Animasaun, I.L., Ibraheem, R.O., Mahanthesh, B., Babatunde, H.A.: A meta-analysis on the effects of haphazard motion of tiny/nano-sized particles on the dynamics and other physical properties of some fluids. Chin. J. Phys. 60, 676–687 (2019). https://doi.org/10.1016/j.cjph.2019.06.007

    Article  MathSciNet  Google Scholar 

  29. Boussinesq, J.: Théorie de l'écoulement tourbillonnant et tumultueux des liquides dans les lits rectilignes à grande section. (Vol. 1). Gauthier-Villars. (1897)

  30. Wakif, A., Animasaun, I.L., Narayana, P.S., Sarojamma, A.G.: Meta-analysis on thermo-migration of tiny/nano-sized particles in the motion of various fluids. Chin. J. Phys. 68, 293–307 (2020). https://doi.org/10.1016/j.cjph.2019.12.002

    Article  Google Scholar 

  31. Alkasasbeh, H.: Numerical solution on heat transfer magnetohydrodynamic flow of micropolar Casson fluid over a horizontal circular cylinder with thermal radiation. Front. Heat Mass Transf. (FHMT) (2018). https://doi.org/10.5098/hmt.10.32

    Article  Google Scholar 

  32. Shah, N.A., Animasaun, I.L., Ibraheem, R.O., Babatunde, H.A., Sandeep, N., Pop, I.: Scrutinization of the effects of Grashof number on the flow of different fluids driven by convection over various surfaces. J. Mol. Liq. 249, 980–990 (2018). https://doi.org/10.1016/j.molliq.2017.11.042

    Article  Google Scholar 

  33. Narayana, P.S., Venkateswarlu, B., Devika, B.: Chemical reaction and heat source effects on MHD oscillatory flow in an irregular channel. Ain Shams Eng. J. 7(4), 1079–1088 (2016). https://doi.org/10.1016/j.asej.2015.07.012

    Article  Google Scholar 

  34. Salahuddin, T., Siddique, N., Arshad, M.: Insight into the dynamics of the non-Newtonian Casson fluid on a horizontal object with variable thickness. Math. Comput. Simul. 177, 211–231 (2020). https://doi.org/10.1016/j.matcom.2020.04.032

    Article  MathSciNet  Google Scholar 

  35. Idowu, A.S., Falodun, B.O.: Variable thermal conductivity and viscosity effects on non-Newtonian fluids flow through a vertical porous plate under Soret-Dufour influence. Math. Comput. Simul. 177, 358–384 (2020). https://doi.org/10.1016/j.matcom.2020.05.001

    Article  MathSciNet  Google Scholar 

  36. Khader, M.M., Sharma, R.P.: Evaluating the unsteady MHD micropolar fluid flow past stretching/shirking sheet with heat source and thermal radiation: Implementing fourth order predictor–corrector FDM. Math. Comput. Simul. 181, 333–350 (2021). https://doi.org/10.1016/j.matcom.2020.09.014

    Article  MathSciNet  Google Scholar 

  37. Mabood, F., Shamshuddin, M.D., Mishra, S.R.: Characteristics of thermophoresis and Brownian motion on radiative reactive micropolar fluid flow towards continuously moving flat plate: HAM solution. Math. Comput. Simul. 191, 187–202 (2022). https://doi.org/10.1016/j.matcom.2021.08.004

    Article  MathSciNet  Google Scholar 

  38. Roy, N.C., Ghosh, A., Pop, I.: Magnetohydrodynamic micropolar nanofluid flow in a shrinking channel with second-order velocity slip and thermal radiation. Arab. J. Sci. Eng. 49(2), 1–13 (2023). https://doi.org/10.1007/s13369-023-08011-4

    Article  Google Scholar 

  39. Padhi, S., Nayak, I.: Numerical study of unsteady MHD second grade fluid flow and heat transfer within porous channel. Int. J. Appl. Comput. Math. 7(6), 255 (2021). https://doi.org/10.1007/s40819-021-01196-y

    Article  MathSciNet  Google Scholar 

  40. Khound, A.S., Dey, D., Borah, R.: Analysis of entropy generation of casson fluid flow over a stretching surface with second-order velocity slip in presence of radiation and chemical reaction. Int. J. Appl. Comput. Math. 8(2), 46 (2022). https://doi.org/10.1007/s40819-022-01243-2

    Article  MathSciNet  Google Scholar 

  41. Jaismitha, B., Sasikumar, J.: Chemically reactive oscillatory Casson hybrid nanofluid flow with heat generation/absorption phenomenon through radiating wavy channel. IAENG Int. J. Appl. Math. 53(4), 1–14 (2023)

    Google Scholar 

  42. Nithya, N., Vennila, B.: The flow past a non-isothermal shrinking sheet with the effects of thermal radiation and heat source/sink. IAENG Int. J. Appl. Math. 53(4), 1–12 (2023)

    Google Scholar 

  43. Nithya, N., Vennila, B.: MHD Nanofluid boundary layer flow over a stretching sheet with viscous, ohmic dissipation. Math. Model. Comput. 10(1), 195–203 (2023)

    Article  Google Scholar 

  44. Tarakaramu, N., Reddappa, B., Radha, G., Abduvalieva, D., Sivakumar, N., Awwad, F.A., Ismail, E.A.A., Reddy, K.A.: Thermal radiation and heat generation on three-dimensional Casson fluid motion via porous stretching surface with variable thermal conductivity. Open Phys. 21(1), 20230137 (2023). https://doi.org/10.1515/phys-2023-0137

    Article  Google Scholar 

  45. Kumar, P.V., Sivakumar, N., Shukla, P., Prakash, P., Durgaprasad, P., Krishna, C.M., Raju, C.S.K., Reddy, G.V.: Dynamics of Brownian motion and flux conditions on naturally unsteady thermophoretic flow with variable fluid properties. Heat Transf. 52(6), 4137–4157 (2023). https://doi.org/10.1002/htj.22872

    Article  Google Scholar 

  46. Abbas, Z., Rafiq, M.Y., Asghar, H., Khaliq, S.: Exploration of the dynamics of non-Newtonian Casson fluid subject to viscous dissipation and Joule heating between parallel walls due to buoyancy forces and pressure. Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng. (2023). https://doi.org/10.1177/09544089221148294

    Article  Google Scholar 

  47. Rafiq, M.Y., Abbas, Z., Ullah, M.Z.: Peristaltic mechanism of couple stress nanomaterial in a tapered channel. Ain Shams Eng. J. 13(6), 101779 (2022). https://doi.org/10.1016/j.asej.2022.101779

    Article  Google Scholar 

  48. Rafiq, M.Y., Abbas, Z.: Analysis of entropy optimization for sinusoidal wall motion of fourth-grade fluid with temperature-dependent viscosity. Waves Random Complex Media (2021). https://doi.org/10.1080/17455030.2021.2008048

    Article  Google Scholar 

  49. Abbas, Z., Rafiq, M.Y.: Peristaltic transportation of thermally radiative Sutterby fluid in a tapered microfluidic vessel with convective conditions. Waves Random Complex Media (2023). https://doi.org/10.1080/17455030.2023.2226766

    Article  Google Scholar 

  50. Abbas, Z., Rafiq, M.Y., Khaliq, S., Ali, A.: Dynamics of the thermally radiative and chemically reactive flow of Sisko fluid in a tapered channel. Adv. Mech. Eng. 14(10), 16878132221129736 (2022). https://doi.org/10.1177/16878132221129735

    Article  Google Scholar 

  51. Rafiq, M.Y., Abbas, Z., Hasnain, J.: Theoretical exploration of thermal transportation with Lorentz force for fourth-grade fluid model obeying peristaltic mechanism. Arab. J. Sci. Eng. 46(12), 12391–12404 (2021). https://doi.org/10.1007/s13369-021-05877-0

    Article  Google Scholar 

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Acknowledgements

The authors are very much thankful to the management and Department of Mathematics of SRM Institute of Science and Technology for their continuous support and encouragement.

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  1. Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, 603203, India

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P.V : Conceptualization, Methodology, Software, Data curation, Writing – original draft, Visualization, Formal analysis. J.S : Supervision, Software, Validation, Formal analysis, Writing –review & editing.

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Vaidehi, P., Sasikumar, J. Significance of Micro-Rotation on Buoyancy Driven Oscillatory Flow of Micropolar-Casson Fluid Through Tapered Wavy Channels: A Numerical Approach. Int. J. Appl. Comput. Math 10, 103 (2024). https://doi.org/10.1007/s40819-024-01740-6

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