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Heat transfer analysis on micropolar alumina–silica–water nanofluid flow in an inclined square cavity with inclined magnetic field and radiation effect

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Abstract

In engineering and industrial process, the primary focus is on heat transfer developments. Numerous techniques are adopted to enhance the heat transfer by suspending nano-size materials in traditional liquids which  are received significant attention. Motivated by this, the present study aims to demonstrate the Lorentz force impact on the radiative aluminum oxide–silicon dioxide–water hybrid nanoliquid flow inside an enclosure. A two-phase flow model is used to discuss the base fluid and nanoparticle characteristics inside a cavity. The energy and momentum equations subject to the limiting conditions are dimensionalized by applying suitable non-dimensional quantities. The marker and cell finite-difference approach is applied to solve the transformed dimensionless constitutive equations of the present analysis. The present results find good accordance with the earlier literature results, which confirms that the adopted scheme is precise. Results indicate that the rate of heat transfer minutely magnifies when the volume fraction is magnified. The magnifications in the heat source parameter have the tendency to amplify the heat transfer rate. Higher values of the nanoparticle volume fraction result in a larger Nusselt number proportional to the heat transfer. More so, as the values of the heat generation parameter increase, the rate of heat transfer increases. Higher thermal radiation intensities cause higher energy transmission.

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Abbreviations

B :

Dimensionless heat sink position’s length

cp:

Specific heat at constant pressure (J Kg−1 K−1)

D :

Dimensionless heat source position’s length

B0 :

External magnetic field (Tesla)

Ha:

Hartmann number

Ra:

Rayleigh number

N :

Dimensional microrotation angular velocity

Da:

Darcy number

Ha:

Hartmann number

F * :

Non-Darcy parameter

j :

Micro-inertia per unit mass (m2)

H :

Length of the square cavity (m)

v :

Velocity component along y-direction (m s−1)

V :

Dimensionless velocity component along the y-direction

XY:

Dimensionless Cartesian coordinates

u :

Velocity component along x-direction (ms−1)

T :

Dimensional fluid temperature

Pr:

Prandtl number

k :

Thermal conductivity

p :

Pressure (Nm−2)

g :

Gravitational acceleration (m s−2)

U :

Dimensionless velocity component along x-direction

K :

Porous permeability parameter

xy:

Cartesian coordinates

n :

Micro‐gyration parameter

Q :

Heat sink/source parameter

Rd:

Thermal radiation

E :

Micropolar parameter

P :

Dimensionless pressure

Α :

Thermal diffusivity (m2 s−1)

ρ :

Density (kg m−3)

κ :

Vortex viscosity parameter

μ :

Dynamic viscosity (kg m−1 s−1)

σ :

Electrical conductivity (s m−1)

Φ :

Cavity’s inclination angle

ν :

Kinematic viscosity (m2s−1)

f :

Fluid

nf:

Nanofluid

bf:

Base fluid

hnf:

Hybrid nanofluid

c-:

Cold

References

  1. Animasaun IL, Shah NA, Wakif A, Mahanthesh B, Sivaraj R, Koriko OK. Ratio of momentum diffusivity to thermal diffusivity: introduction, Meta-analysis, and scrutinization. Boca Raton: Chapman and Hall/CRC; 2022. https://doi.org/10.1201/9781003217374.

    Book  Google Scholar 

  2. Eringen AC. Simple microfluids. Int J Eng Sci Pergamon. 1964;2:205–17.

    Article  Google Scholar 

  3. Wang CC, Chen CK. Forced convection in a wavy-wall channel. Int J Heat Mass Transf Pergamon. 2002;45:2587–95.

    Article  Google Scholar 

  4. Muthtamilselvan M, Periyadurai K, Doh DH. Impact of nonuniform heated plate on double-diffusive natural convection of micropolar fluid in a square cavity with soret and dufour effects. Adv Powder Technol. 2018. https://doi.org/10.1016/j.apt.2017.10.012.

    Article  Google Scholar 

  5. Loukopoulos VC, Bourantas GC, Miller K. Study of the thermo-magneto-hydrodynamic flow of micropolar-nanofluid in square enclosure using dynamic mode decomposition and proper orthogonal decomposition. Eur J Mech B/Fluids. 2020. https://doi.org/10.1016/j.euromechflu.2020.06.012.

    Article  Google Scholar 

  6. Mansour MA, Ahmed SE, Aly AM, Raizah ZAS, Morsy Z. Triple convective flow of micropolar nanofluids in double lid-driven enclosures partially filled with LTNE porous layer under effects of an inclined magnetic field. Chin J Phys. 2020. https://doi.org/10.1016/j.cjph.2020.10.001.

    Article  Google Scholar 

  7. Hatami M, Safari H. Effect of inside heated cylinder on the natural convection heat transfer of nanofluids in a wavy-wall enclosure. Int J Heat Mass Transf Pergamon. 2016;103:1053–7.

    Article  CAS  Google Scholar 

  8. Hashem Zadeh SM, Sabour M, Sazgara S, Ghalambaz M. Free convection flow and heat transfer of nanofluids in a cavity with conjugate solid triangular blocks: employing buongiorno’s mathematical model. Phys A Stat Mech its Appl. 2020. https://doi.org/10.1016/j.physa.2019.122826.

    Article  Google Scholar 

  9. Nong H, Fatah AM, Shehzad SA, Ambreen T, Selim MM, Albadarin AB. Numerical modeling for steady-state nanofluid free convection involving radiation through a wavy cavity with lorentz forces. J Mol Liq. 2021;336:116324.

    Article  CAS  Google Scholar 

  10. Hatami M, Sheikholeslami M, Domairry G. High accuracy analysis for motion of a spherical particle in plane couette fluid flow by Multi-step differential transformation method. Powder Technol. 2014;260:59–67.

    Article  CAS  Google Scholar 

  11. Choi SUS, Eastman JA. Enhancing thermal conductivity of fluids with nanoparticles. Am Soc Mech Eng Fluids Eng Div FED. 1995;231:99–105.

    CAS  Google Scholar 

  12. Ghasemi SE, Vatani M, Hatami M, Ganji DD. Analytical and numerical investigation of nanoparticle effect on peristaltic fluid flow in drug delivery systems. J Mol Liq. 2016;215:88–97.

    Article  CAS  Google Scholar 

  13. Song D, Hatami M, Wang Y, Jing D, Yang Y. Prediction of hydrodynamic and optical properties of TiO2/water suspension considering particle size distribution. Int J Heat Mass Transf Pergamon. 2016;92:864–76.

    Article  CAS  Google Scholar 

  14. Salleh SNA, Bachok N, Arifin NM, Ali FM. Influence of Soret and Dufour on forced convection flow towards a moving thin needle considering buongiorno’s nanofluid model. Alexandria Eng J. 2020. https://doi.org/10.1016/j.aej.2020.06.045.

    Article  Google Scholar 

  15. Alkanhal TA, Sheikholeslami M, Usman M, Haq R, et al. Thermal management of MHD nanofluid within the porous medium enclosed in a wavy shaped cavity with square obstacle in the presence of radiation heat source. Int J Heat Mass Transf. 2019;139:87–94. https://doi.org/10.1016/j.ijheatmasstransfer.2019.05.006.

    Article  CAS  Google Scholar 

  16. Alsabery AI, Tayebi T, Kadhim HT, Ghalambaz M, Hashim I, Chamkha AJ. Impact of two-phase hybrid nanofluid approach on mixed convection inside wavy lid-driven cavity having localized solid block. J Adv Res. 2021;30:63–74. https://doi.org/10.1016/j.jare.2020.09.008.

    Article  CAS  Google Scholar 

  17. Goswami KD, Chattopadhyay A, Pandit SK, Sheremet MA. Transient thermogravitational convection for magneto hybrid nanofluid in a deep cavity with multiple isothermal source-sink pairs. Int J Therm Sci. 2022;173:107376. https://doi.org/10.1016/j.ijthermalsci.2021.107376.

    Article  CAS  Google Scholar 

  18. Babazadeh H, Shah Z, Ullah I, Kumam P, Shafee A. Analysis of hybrid nanofluid behavior within a porous cavity including Lorentz forces and radiation impacts. J Therm Anal Calorim. 2021;143(2):1129–37.

    Article  CAS  Google Scholar 

  19. Revnic C, Groşan T, Sheremet M, Pop I. Numerical simulation of MHD natural convection flow in a wavy cavity filled by a hybrid Cu-Al2O3-water nanofluid with discrete heating. Appl Math Mech. 2020;41(9):1345–58.

    Article  Google Scholar 

  20. Basha HT, Sivaraj R. Exploring the heat transfer and entropy generation of Ag/Fe3O4 -blood nanofluid flow in a porous tube: a collocation solution. Eur Phys J E. 2021. https://doi.org/10.1140/epje/s10189-021-00024-x.

    Article  CAS  Google Scholar 

  21. Shaik J, Polu BAR, Mohamed Ahmed M, Ahmed MR. Characteristics of moving hot block and non-Fourier heat flux model on sinusoidal wavy cavity filled with hybrid nanofluid. Eur Phys J Plus. 2022. https://doi.org/10.1140/epjp/s13360-022-02361-y.

    Article  Google Scholar 

  22. Mosayebidorcheh S, Hatami M. Analytical investigation of peristaltic nanofluid flow and heat transfer in an asymmetric wavy wall channel (Part I: Straight channel). Int J Heat Mass Transf Pergamon. 2018;126:790–9.

    Article  CAS  Google Scholar 

  23. Sivaraj R, Rushi KB. Unsteady MHD dusty viscoelastic fluid couette flow in an irregular channel with varying mass diffusion. Int J Heat Mass Transfer. 2012;55:3076–89. https://doi.org/10.1016/j.ijheatmasstransfer.2012.01.049.

    Article  CAS  Google Scholar 

  24. Jagadeesha RD, Prasanna BMR, Sankar M. Double diffusive convection in an inclined parallelogrammic porous enclosure. Procedia Eng. 2015;127:1346–53.

    Article  Google Scholar 

  25. Mythili D, Sivaraj R. Influence of higher order chemical reaction and non-uniform heat source/sink on casson fluid flow over a vertical cone and flat plate. J Mol Liq. 2016;216:466–75. https://doi.org/10.1016/j.molliq.2016.01.072.

    Article  CAS  Google Scholar 

  26. Jakeer S, Anki RB. Competence of magnetic dipole and radiation on permeable surface using prescribed heat flux / prescribed surface temperature and homogeneousheterogeneous reactions. Spec Top Rev Porous Media An Int J. 2021;12:91–107.

    Article  Google Scholar 

  27. Nguyen Q, Beni MH, Parsian A, Malekahmadi O, Karimipour A. Discrete ordinates thermal radiation with mixed convection to involve nanoparticles absorption, scattering and dispersion along radiation beams through the nanofluid. J Therm Anal Calorim. 2020. https://doi.org/10.1007/s10973-020-10005-5.

    Article  Google Scholar 

  28. Balla CS, Ramesh A, Kishan N, Rashad AM, Abdelrahman ZMA. Bioconvection in oxytactic microorganism-saturated porous square enclosure with thermal radiation impact. J Therm Anal Calorim. 2020;140:2387–95.

    Article  CAS  Google Scholar 

  29. Reddy PS, Sreedevi P. Buongiorno’s model nanofluid natural convection inside a square cavity with thermal radiation. Chinese J Phys. 2021;72:327–44. https://doi.org/10.1016/j.cjph.2020.08.016.

    Article  CAS  Google Scholar 

  30. Afrand M, Pordanjani AH, Aghakhani S, Oztop HF, Abu-Hamdeh N. Free convection and entropy generation of a nanofluid in a tilted triangular cavity exposed to a magnetic field with sinusoidal wall temperature distribution considering radiation effects. Int Commun Heat Mass Transf. 2020;112:1045. https://doi.org/10.1016/j.icheatmasstransfer.2020.104507.

    Article  CAS  Google Scholar 

  31. Sankar M, Pushpa BV, Prasanna BMR, Do Y. Influence of size and location of a thin baffle on natural convection in a vertical annular enclosure. J Appl Fluid Mech. 2016;9:2671–84.

    Article  Google Scholar 

  32. Pushpa BV, Sankar M, Prasanna BMR, Siri Z. Influence of thin baffle and magnetic field on buoyant convection in a vertical annulus. Lect Notes Mech Eng. 2021. https://doi.org/10.1007/978-981-15-4308-1_8.

    Article  Google Scholar 

  33. Kiran S, Sankar M, Swamy HAK, Makinde OD. Unsteady buoyant convective flow and thermal transport analysis in a nonuniformly heated annular geometry. Comput Therm Sci [Internet]. Begel House Inc.; 2022 [cited 2022 Sep 8];14. Available from: https://www.dl.begellhouse.com/journals/648192910890cd0e,56fc6bdc1fb8d5de,6957a7e47fd86b51.html

  34. Kemparaju S, Kumara Swamy HA, Sankar M, Mebarek-Oudina F. Impact of thermal and solute source-sink combination on thermosolutal convection in a partially active porous annulus. Phys Scr. 2022. https://doi.org/10.1088/1402-4896/ac6383.

    Article  Google Scholar 

  35. Hatami M. Numerical study of nanofluids natural convection in a rectangular cavity including heated fins. J Mol Liq Elsevier. 2017;233:1–8.

    Article  CAS  Google Scholar 

  36. Batool S, Nawaz M. Investigation of thermal enhancement in non-Newtonian fluid with hybrid micro-structures in an enclosure. Int Commun Heat Mass Transf. 2020;117:104777. https://doi.org/10.1016/j.icheatmasstransfer.2020.104777.

    Article  CAS  Google Scholar 

  37. Sreedevi P, Sudarsana RP. Effect of magnetic field and thermal radiation on natural convection in a square cavity filled with TiO2 nanoparticles using Tiwari-Das nanofluid model. Alexandria Eng J. 2021;61(2):1529–41. https://doi.org/10.1016/j.aej.2021.06.055.

    Article  Google Scholar 

  38. Aly AM, El-Sapa S. Effects of Soret and Dufour numbers on MHD thermosolutal convection of a nanofluid in a finned cavity including rotating circular cylinder and cross shapes. Int Commun Heat Mass Transf. 2022;130:105819. https://doi.org/10.1016/j.icheatmasstransfer.2021.105819.

    Article  CAS  Google Scholar 

  39. Hassanien IA, Mansour MA, Gorla RSR. Combined convection on a vertical slender cylinder in a micropolar fluid. Wärme-und Stoffübertra. 1994;29:355–9. https://doi.org/10.1007/BF01878345.

    Article  CAS  Google Scholar 

  40. Siddiqui MA, Riaz A, Khan I, Sooppy Nisar K. Augmentation of mixed convection heat transfer in a lid-assisted square enclosure utilizing micropolar fluid under magnetic environment: a numerical approach. Resu Phys. 2020;18:103245. https://doi.org/10.1016/j.rinp.2020.103245.

    Article  Google Scholar 

  41. Raizah ZAS, Ahmed SE, Alrowaili D, Mansour MA, Morsy Z. Magnetic micropolar nanofluids flow in double lid-driven enclosures using two-energy equation model. Heat Transfer. 2020. https://doi.org/10.1002/htj.22003.

    Article  Google Scholar 

  42. Shah NA, Animasaun IL, Wakif A, Koriko OK, Sivaraj R, Adegbie KS, et al. Significance of suction and dual stretching on the dynamics of various hybrid nanofluids: Comparative analysis between type i and type II models. Phys Scr. 2020. https://doi.org/10.1088/1402-4896/aba8c6.

    Article  Google Scholar 

  43. Khan MR, Pan K, Khan AU, Nadeem S. Dual solutions for mixed convection flow of SiO2−Al2O3/water hybrid nanofluid near the stagnation point over a curved surface. Phys A Stat Mech its Appl. 2020;547:123959.

    Article  CAS  Google Scholar 

  44. Hidayathulla Khan BMD, Ramachandra Prasad V, Bhuvana VR. Thermal radiation on mixed convective flow in a porous cavity: numerical simulation. Nonlinear Eng. 2018;7:253–61.

    Article  Google Scholar 

  45. Anwar Bég O, Venkatadri K, Ramachandra Prasad V, Bég TA, Kadir A, Leonard HJ. Numerical simulation of hydromagnetic Marangoni convection flow in a Darcian porous semiconductor melt enclosure with buoyancy and heat generation effects. Mater Sci Eng B Solid-State Mater Adv Technol. 2020;261:114722. https://doi.org/10.1016/j.mseb.2020.114722.

    Article  CAS  Google Scholar 

  46. Venkatadri K, Shobha A, Lakshmi V, Prasad VR, Khan BMH. Influence of magnetic wire positions on free convection of Fe3O4-water nanofluid in a square enclosure utilizing with MAC algorithm. J Comput Appl Mech. 2020;51:323–31.

    Google Scholar 

  47. Sivarami Reddy C, Ramachandra Prasad V, Jayalakshmi K. Numerical simulation of natural convection heat transfer from a heated square cylinder in a square cavity filled with micropolar fluid. Heat Transf. 2021;50:5267–85.

    Article  Google Scholar 

  48. Hidayathulla Khan BM, Venkatadri K, Anwar Bég O, Ramachandra Prasad V, Mallikarjuna B. Natural convection in a square cavity with uniformly heated and/or insulated walls using marker-and-cell method. Int J Appl Comput Math. 2018. https://doi.org/10.1007/s40819-018-0492-z.

    Article  Google Scholar 

  49. Hidayathulla Khan BMD, Ramachandra Prasad V, Bhuvana VR. Thermal radiation on mixed convective flow in a porous cavity: numerical simulation. Nonlinear Eng. 2018;7(4):253–61. https://doi.org/10.1515/nleng-2017-0053/html.

    Article  Google Scholar 

  50. Xia WF, Animasaun IL, Wakif A, Shah NA, Yook SJ. Gear-generalized differential quadrature analysis of oscillatory convective Taylor-couette flows of second-grade fluids subject to lorentz and darcy-forchheimer quadratic drag forces. Int Commun Heat Mass Transf Pergamon. 2021;126:105395.

    Article  Google Scholar 

  51. Cao W, Animasaun IL, Yook SJ, Oladipupo VA, Ji X. Simulation of the dynamics of colloidal mixture of water with various nanoparticles at different levels of partial slip: Ternary-hybrid nanofluid. Int Commun Heat Mass Transf Pergamon. 2022;135:106069.

    Article  CAS  Google Scholar 

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Acknowledgements

The second author (R. Sivaraj) is thankful to the Ministry of Education, United Arab Emirates, for the financial assistance to complete this research work through the Collaborative Research Program Grant 2019 (CRPG 2019) with the fund number 21S107.

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Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, VIT, Vellore, 632014, India

    P. Vijayalakshmi & R. Sivaraj

  2. Department of Mathematical Sciences, United Arab Emirates University, Al Ain, United Arab Emirates

    R. Sivaraj

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  1. P. Vijayalakshmi
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  2. R. Sivaraj
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Contributions

The mathematical model was formulated and solved, and the manuscript was written by Mrs. P. V. The mathematical model, solution procedure and numerical results were verified, and the manuscript writing was improved by Dr. R. S.

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Correspondence to R. Sivaraj.

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Vijayalakshmi, P., Sivaraj, R. Heat transfer analysis on micropolar alumina–silica–water nanofluid flow in an inclined square cavity with inclined magnetic field and radiation effect. J Therm Anal Calorim 148, 473–488 (2023). https://doi.org/10.1007/s10973-022-11758-x

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