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A hydrodynamic and hydromagnetic comparative analysis of triple diffusive nanofluid flow over a horizontal plate with quadratic mixed convection

对流水平板上二次混合的三重扩散纳米流体的流体力学和流体磁学对比分析

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Abstract

The triple diffusion amalgamated with the convection occurs when the fluid flow is under the influence of two different densities with varied diffusion rates. The primary objective of this analysis is to compare hydrodynamic and hydromagnetic nanofluid flow over a horizontally placed plate for triple diffusive systems with mixed convection of quadratic nature. The additional novel features of the envisaged model are the consideration of variable thermal conductivity and nonlinear thermal radiative heat flux. The problem is comprised of a set of equations that are solved with the aid of the MATLAB bvp4c package. To visualize the impacts of the parameters with associated profiles, graphical illustrations are given. Graphs are utilized to evaluate how significant changes in the key parameters impact the related fields and their corresponding physical quantities. It is inferred that liquid velocity surges for numerous estimates of the Dufour parameter of salt 1 and salt 2. It is verified that the hydrodynamic flow is dominant in comparison to hydromagnetic. In addition, a comparison between the published results in a specific scenario and the current research is also included. An excellent correlation is attained.

摘要

当两种不同密度和扩散速率的纳米流体混合时,会发生三重扩散和对流现象。本文主要目的是比较对流水平板上二次混合的三重扩散纳米流体的流体力学和流体磁学。文中建立的模型其他新特征考虑了可变导热系数和非线性热辐射热通量。该问题由一组方程组成,借助MATLAB bvp4c 包进行求解。为了使参数与相关剖面的影响可视化,给出了图形说明,并利用图表来评估关键参数变化是如何影响相关场及其相应的物理量。通过对盐1 和盐2 的Dufour 参数的多次估计,可以推断出流体流速的波动。验证了流体动力流相对于流体磁流的优势。此外,还将特定情景下已发表的结果与当前研究结果进行了比较。

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Abbreviations

β :

Biot number

ρ :

Density, kg/m3

μ :

Dynamic viscosity, kg/ms

C p :

Specific heat capacity, J/(kg·K)

ε :

Variable thermal conductivity parameter, W/(m·K)

γ :

Nonlinear mixed convection parameter

β 1, β 2 :

Coefficients of thermal expansion

β c1, βc2 :

Nonlinear fluid expansion coefficients

β 3, β 4, β 5, β 6 :

Coefficients of thermal expansion of solute

u, v :

Velocity components, m/s

T :

Temperature, K

C 2, C 1 :

Concentrations of salt 2 and 1, mol/m3

T w :

Temperature of wall, K

Nr :

Nanoparticle buoyancy ratio parameter

Sh x :

Sherwood number of nanofluid

Sh 2x , Sh 1x :

Mass transportation rates

Nc 1, Nc 2 :

Buoyancy ratio parameters of salt 1 and 2

D B :

Diffusion coefficients, m2/s

B 0 :

Coefficient of magnetic field, A/m

K :

Thermal conductivity, W/(m·K)

Sc :

Schmidt number

C 2w, C 1w :

Liquid concentrations at the wall, mol/m3

h f :

Heat transfer coefficient, W·K/m2

p :

Pressure, N/m2

Le :

Lewis number

C 1∞, C 2∞ :

Ambient concentration of fluid hydrogen and liquid oxygen, mol/m3

Le 1, Le 2 :

Regular Lewis number of salt 1 and 2

\({N_{{d_1}}},{N_{{d_2}}}\) :

Dufour and Soret type diffusivity, m2/s

D T :

Thermophoretic diffusion coefficient, m2/s

N b :

Brownian motion parameter

Pr :

Prandtl number

v F :

Kinematic viscosity, kg/(m·s)

σ :

Electrical conductivity, s/m

k s :

Coefficient of heterogeneous reaction

Ld 2, Ld 1 :

Solutal Dufour Lewis number of salt 2 and salt 1

Nd 1 , Nd 2 :

Dufour and Soret type diffusivity, m2/s

N t :

Thermophoresis parameter, m2/s

References

  1. CHOI S, EASTMAN J A. Enhancing thermal conductivity of fluids with nanoparticles [R]. Argonne, IL (United States) Argonne National Lab.(ANL), 1995.

  2. DAS S, CHOI S, YU W, et al. Nanofluids [M]// Science and Technology. John Wiley & Sons, 2007.

  3. JANG P S, CHOI S U S. Effects of various parameters on nanofluid thermal conductivity [J]. Journal of Heat Transfer, 2007, 129(5): 617–623. DOI: https://doi.org/10.1115/1.2712475.

    Article  Google Scholar 

  4. RAMZAN M, GUL H, MALIK M Y, et al. Entropy minimization analysis of a partially ionized casson nanofluid flow over a bidirectional stretching sheet with surface catalyzed reaction [J]. Arabian Journal for Science and Engineering, 2022, 47(12): 15209–15221. DOI: https://doi.org/10.1007/s13369-021-06492-9.

    Article  Google Scholar 

  5. AHMAD S, KHAN M N, NADEEM S. Unsteady three dimensional bioconvective flow of Maxwell nanofluid over an exponentially stretching sheet with variable thermal conductivity and chemical reaction [J]. International Journal of Ambient Energy, 2022, 43(1): 6542–6552. DOI: https://doi.org/10.1080/01430750.2022.2029765.

    Article  Google Scholar 

  6. ARIF U, MEMON M A, SAIF R S, et al. Triple diffusion with heat transfer under different effects on magnetized hyperbolic tangent nanofluid flow [J]. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 2022: 095440892210791. DOI: https://doi.org/10.1177/09544089221079139.

  7. MANDAL S, SHIT G C. Entropy analysis of unsteady MHD three-dimensional flow of Williamson nanofluid over a convectively heated stretching sheet [J]. Heat Transfer, 2022, 51(2): 2034–2062. DOI: https://doi.org/10.1002/htj.22387.

    Article  Google Scholar 

  8. KUMAR R N, PUNITH GOWDA R J, ALAM M M, et al. Inspection of convective heat transfer and KKL correlation for simulation of nanofluid flow over a curved stretching sheet [J]. International Communications in Heat and Mass Transfer, 2021, 126: 105445. DOI: https://doi.org/10.1016/j.icheatmasstransfer.2021.105445.

    Article  Google Scholar 

  9. KUMAR R N, SURESHA S, PUNITH GOWDA R J, et al. Exploring the impact of magnetic dipole on the radiative nanofluid flow over a stretching sheet by means of KKL model [J]. Pramana, 2021, 95(4): 180. DOI: https://doi.org/10.1007/s12043-021-02212-y.

    Article  Google Scholar 

  10. PUNITH GOWDA R J, RAUF A, KUMAR R N, et al. Slip flow of Casson - Maxwell nanofluid confined through stretchable disks [J]. Indian Journal of Physics, 2022, 96(7): 2041–2049. DOI: https://doi.org/10.1007/s12648-021-02153-7.

    Article  Google Scholar 

  11. ZEESHAN, AHAMMAD N A, ALI SHAH N, et al. Analysis of error and stability of nanofluid over horizontal channel with heat/mass transfer and nonlinear thermal conductivity [J]. Mathematics, 2023, 11(3): 690. DOI: https://doi.org/10.3390/math11030690.

    Article  Google Scholar 

  12. KARVELAS E G, LAMPROPOULOS N K, BENOS L T, et al. On the magnetic aggregation of Fe3O4 nanoparticles [J]. Computer Methods and Programs in Biomedicine, 2021, 198: 105778. DOI: https://doi.org/10.1016/j.cmpb.2020.105778.

    Article  Google Scholar 

  13. REKHA M B, SARRIS I E, MADHUKESH J K, et al. Activation energy impact on flow of AA7072-AA7075/water-based hybrid nanofluid through a cone, wedge and plate [J]. Micromachines, 2022, 13(2): 302. DOI: https://doi.org/10.3390/mi13020302.

    Article  Google Scholar 

  14. ISHTIAQ B, ZIDAN A M, NADEEM S, et al. Scrutinization of MHD stagnation point flow in hybrid nanofluid based on the extended version of Yamada-Ota and Xue models [J]. Ain Shams Engineering Journal, 2023, 14(3): 101905. DOI: https://doi.org/10.1016/j.asej.2022.101905.

    Article  Google Scholar 

  15. BAIG M N J, SALAMAT N, DURAIHEM F Z, et al. Exact analytical solutions of stagnation point flow over a heated stretching cylinder: A phase flow nanofluid model [J]. Chinese Journal of Physics, 2023. DOI: https://doi.org/10.1016/j.cjph.2023.03.017.

  16. NADEEM S, ISHTIAQ B, BEN HAMIDA M B, et al. Reynolds nano fluid model for Casson fluid flow conveying exponential nanoparticles through a slandering sheet [J]. Scientific Reports, 2023, 13(1): 1–12. DOI: https://doi.org/10.1038/s41598-023-28515-1.

    Article  Google Scholar 

  17. NADEEM S, ISHTIAQ B, AKKURT N, et al. Entropy optimized flow of hybrid nanofluid with partial slip boundary effects and induced magnetic field [J]. International Journal of Modern Physics B, 2023: 2350252. DOI: https://doi.org/10.1142/s0217979223502521.

  18. GRIFFITHS R W. The influence of a third diffusing component upon the onset of convection [J]. Journal of Fluid Mechanics, 1979, 92(4): 659–670. DOI: https://doi.org/10.1017/s0022112079000811.

    Article  MATH  Google Scholar 

  19. KUZNETSOV A V, NIELD D A. Double-diffusive natural convective boundary-layer flow of a nanofluid past a vertical plate [J]. International Journal of Thermal Sciences, 2011, 50(5): 712–717. DOI: https://doi.org/10.1016/j.ijthermalsci.2011.01.003.

    Article  Google Scholar 

  20. RIONERO S. Triple diffusive convection in porous media [J]. Acta Mechanica, 2013, 224(2): 447–458. DOI: https://doi.org/10.1007/s00707-012-0749-2.

    Article  MathSciNet  MATH  Google Scholar 

  21. SHIVAKUMARA I S, NAVEEN KUMAR S B. Linear and weakly nonlinear triple diffusive convection in a couple stress fluid layer [J]. International Journal of Heat and Mass Transfer, 2014, 68: 542–553. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2013.09.051.

    Article  Google Scholar 

  22. SAJID T, JAMSHED W, SHAHZAD F, et al. Insightful into dynamics of magneto Reiner-Philippoff nanofluid flow induced by triple-diffusive convection with zero nanoparticle mass flux [J]. Ain Shams Engineering Journal, 2023, 14(4): 101946. DOI: https://doi.org/10.1016/j.asej.2022.101946.

    Article  Google Scholar 

  23. PATIL P M, BENAWADI S, SHEREMET M A. The unsteady nonlinear convective flow of a nanofluid due to impulsive motion: Triple diffusion and magnetic effects [J]. Thermal Science and Engineering Progress, 2022, 35: 101456. DOI: https://doi.org/10.1016/j.tsep.2022.101456.

    Article  Google Scholar 

  24. NOOR ARSHIKA S, TARANNUM S, PRANESH S. Heat and mass transfer of triple diffusive convection in viscoelastic liquids under internal heat source modulations [J]. Heat Transfer, 2022, 51(1): 239–256. DOI: https://doi.org/10.1002/htj.22305.

    Article  Google Scholar 

  25. SHUKLA S, GUPTA U. LTNE effects on triple-diffusive convection in nanofluids [J]. Journal of Heat Transfer, 2022, 144(9): 092501. DOI: https://doi.org/10.1115/1.4054837.

    Article  Google Scholar 

  26. AHMED M F, ZAIB A, ALI F, et al. Numerical computation for gyrotactic microorganisms in MHD radiative Eyring-Powell nanomaterial flow by a static/moving wedge with darcy-forchheimer relation [J]. Micromachines, 2022, 13(10): 1768. DOI: https://doi.org/10.3390/mi13101768.

    Article  Google Scholar 

  27. KHAN M N, AHAMMAD N A, AHMAD S, et al. Thermophysical features of Ellis hybrid nanofluid flow with surface-catalyzed reaction and irreversibility analysis subjected to porous cylindrical surface [J]. Frontiers in Physics, 2022, 10: 986501. DOI: https://doi.org/10.3389/fphy.2022.986501.

    Article  Google Scholar 

  28. ISLAM N, RIASAT S, RAMZAN M, et al. Thermal efficiency appraisal of hybrid nanocomposite flow over an inclined rotating disk exposed to solar radiation with Arrhenius activation energy [J]. Alexandria Engineering Journal, 2023, 68: 721–732.

    Article  Google Scholar 

  29. HAQ I, BILAL M, AHAMMAD N A, et al. Mixed convection nanofluid flow with heat source and chemical reaction over an inclined irregular surface [J]. ACS Omega, 2022, 7(34): 30477–30485. DOI: https://doi.org/10.1021/acsomega.2c03919.

    Article  Google Scholar 

  30. ALQARNI M M, BILAL M, ALLOGMANY R, et al. Mathematical analysis of casson fluid flow with energy and mass transfer under the influence of activation energy from a non-coaxially spinning disc [J]. Frontiers in Energy Research, 2022, 10: 986284. DOI: https://doi.org/10.3389/fenrg.2022.986284.

    Article  Google Scholar 

  31. RAMZAN M, SHAHMIR N, ALI S GHAZWANI H, et al. A numerical study of nanofluid flow over a curved surface with Cattaneo-Christov heat flux influenced by induced magnetic field [J]. Numerical Heat Transfer, Part A: Applications, 2023, 83(2): 197–212. DOI: https://doi.org/10.1080/10407782.2022.2144976.

    Article  Google Scholar 

  32. ADEEL A, MARIA A, YASIR K. Influence of polymers on drag and heat transfer of nanofluid past stretching surface: A molecular approach [J]. Journal of Central South University, 2022, 29(12): 3912–3924. DOI: https://doi.org/10.1007/s11771-022-5219-y.

    Article  Google Scholar 

  33. GHACHEM K, KOLSI L, LARGUECH S, et al. Heat and mass transfer enhancement in triangular pyramid solar still using CNT-water nanofluid [J]. Journal of Central South University, 2021, 28(11): 3434–3448. DOI: https://doi.org/10.1007/s11771-021-4866-8.

    Article  Google Scholar 

  34. JALIL E, MOLAEIMANESH G R. Effects of turbulator shape, inclined magnetic field, and mixed convection nanofluid flow on thermal performance of micro-scale inclined forward-facing step [J]. Journal of Central South University, 2021, 28(11): 3310–3326. DOI: https://doi.org/10.1007/s11771-021-4857-9.

    Article  Google Scholar 

  35. ABBASI A S, KHAN A N. Improving performance of flat plate solar collector using nanofluid water/zinc oxide [J]. Journal of Central South University, 2021, 28(11): 3391–3403. DOI: https://doi.org/10.1007/s11771-021-4863-y.

    Article  Google Scholar 

  36. RAMZAN M, SHAHEEN N, ALI S GHAZWANI H, et al. Nonlinear convective nanofluid flow in an annular region of two concentric cylinders with generalized Fourier law: An application of Hamilton-Crosser nanofluid model [J]. Numerical Heat Transfer, Part A: Applications, 2023: 1–18. DOI: https://doi.org/10.1080/10407782.2023.2175749.

  37. KHAN W A, CULHAM J R, KHAN Z H, et al. Triple diffusion along a horizontal plate in a porous medium with convective boundary condition [J]. International Journal of Thermal Sciences, 2014, 86: 60–67. DOI: https://doi.org/10.1016/j.ijthermalsci.2014.06.035.

    Article  Google Scholar 

  38. KHAN Z H, KHAN W A, TANG Ji-guo, et al. Entropy generation analysis of triple diffusive flow past a horizontal plate in porous medium [J]. Chemical Engineering Science, 2020, 228: 115980. DOI: https://doi.org/10.1016/j.ces.2020.115980.

    Article  Google Scholar 

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Authors and Affiliations

  1. Mechanical Engineering Department, College of Engineering, Umm Al-Qura University, Makkah, 24382, Saudi Arabia

    Abdulkhaliq M-alharbi Khalid

  2. Department of Computer Science, Bahria University, Islamabad, 44000, Pakistan

    Gul Hina & Ramzan Muhammad

  3. Department of Applied Data Science, Noroff University College, Kristiansand, Norway

    Kadry Seifedine

  4. Artificial Intelligence Research Center (AIRC), Ajman University, Ajman, 346, United Arab Emirates

    Kadry Seifedine

  5. Department of Electrical and Computer Engineering, Lebanese American University, Byblos, Lebanon

    Kadry Seifedine

  6. Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia

    Mohammed-saeed Abdulkafi

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  2. Gul Hina
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  3. Ramzan Muhammad
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Contributions

MUHAMMAD Ramzan supervised and considered the idea. HINA Gul wrote the manuscript. KHALID Abdulkhaliq M-alharbi and SEIFEDINE Kadry helped in editing, and validation. ABDULKAFI Mohammed-saeed helped in revising the manuscript.

Corresponding author

Correspondence to Ramzan Muhammad.

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KHALID Abdulkhaliq M-alharbi, HINA Gul, MUHAMMAD Ramzan, SEIFEDINE Kadry, and ABDULKAFI Mohammed-saeed declare that they have no conflict of interest.

Additional information

Foundation item: Project(23UQU4310392DSR003) supported by the Deanship of Scientific Research of Umm Al-Qura University, Saudi Arabia

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Khalid, A.Ma., Hina, G., Muhammad, R. et al. A hydrodynamic and hydromagnetic comparative analysis of triple diffusive nanofluid flow over a horizontal plate with quadratic mixed convection. J. Cent. South Univ. 30, 2616–2626 (2023). https://doi.org/10.1007/s11771-023-5339-z

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