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Significance of nanoparticle shape factor and buoyancy effects on a parabolic motion of EMHD convective nanofluid past a Riga plate with ramped wall temperature

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Abstract

Riga plate consists of an electromagnetic actuator made of a spanwise network of intermittent electrodes and fixed magnet assembled on a flat surface. Electromagnetohydrodynamic (EMHD) effects play a crucial role in thermoelectric turbines, fluidics network flow control, paper chromatography, and miniature chillers. Driven by these functionality, the convective EMHD flow of water-based nanofluids through a parabolic Riga plate which is affected by applying ramping and isothermal constraints is simultaneously examined here. The modeling additionally includes the influence of radiation effect. The Laplace transform method is utilized to alleviate the ordinary differential equations derived from the rejuvenation of partial differential equations governing the flow. The consequences of contextual factors on energy and momentum distribution are investigated and graphically represented. The prevailing study's significant finding is that increasing the modified Hartmann number enhances the parabolic-velocity distribution of copper–water nanofluid. The escalating values of radiation parameter improve the thermal distribution for both cases. Here, copper–water-based nanofluid shows improved thermal distribution for isothermal wall than ramped wall case.

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Data Availability Statement

No data associated in the manuscript.

Abbreviations

LTM:

Laplace transform method

\(E\) :

Modified Hartmann parameter

EMHD:

Electromagnetohydrodynamic

erf:

Error function

erfc:

Complementary error function

g:

Gravitational constant

Gr:

Thermal Grashof number

\(J_{0}\) :

Current density

\(k\) :

Thermal conductivity (W/mK)

\(k^{*}\) :

Mean absorption coefficient

\(l\) :

Magnets' and electrodes' width

\(m_{0}\) :

Magnetization of magnets

Nu:

Nusselt number

Pr:

Prandtl number

\(q_{r}\) :

Radiative heat flux

\(R\) :

Parameter for radiation

\(S\) :

Width linked with the magnets and electrodes

\(t^{\prime}\) :

Time (s)

\(T\) :

Fluid temperature (K)

\(T_{\infty }\) :

Ambient temperature (K)

\(T_{\omega }\) :

Surface temperature (K)

\(u\) :

Velocity of the fluid in the \(x\)-direction \(\left( {{\rm ms}^{ - 1} } \right)\)

\(U\) :

Dimensionless velocity

\(y\) :

Coordinate axis normal to the plate

\(\rho\) :

Fluid density \(({\rm kgm}^{ - 3} )\)

\(\Theta\) :

Dimensionless temperature

\(\nu\) :

Kinematics viscosity \(({\rm m}^{2}\,{\rm s}^{ - 1} )\)

\(\sigma^{*}\) :

Stefan–Boltzmann constant

\(\zeta\) :

Dimensionless coordinate axis normal to the plate

\(\rho C_{p}\) :

Heat capacitance \(({\rm kg\,m}^{ - 1}{\rm s}^{ - 2} {\rm K}^{ - 1} )\)

\(\beta\) :

Volumetric coefficient of thermal expansion

\(\omega\) :

Conditions at the wall

\(\infty\) :

Free stream conditions

f:

Fluid

nf:

Nanofluid

np:

Nanoparticles

BCs:

Boundary conditions

References

  1. S.U.S. Choi, J.A. Eastman. Enhancing thermal conductivity of fluids with nanoparticles [Internet]. Argonne National Lab. (ANL), Argonne, IL (United States); 1995 Oct. Report No.: ANL/MSD/CP-84938; CONF-951135–29.

  2. M. Turkyilmazoglu, Algebraic solutions of flow and heat for some nanofluids over deformable and permeable surfaces. Int. J. Numer. Methods Heat Fluid Flow. 27(10), 2259–2267 (2017)

    Article  MathSciNet  Google Scholar 

  3. M. Turkyilmazoglu, On the fluid flow and heat transfer between a cone and a disk both stationary or rotating. Math. Comput. Simul. 1(177), 329–340 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Jafarimoghaddam, M. Turkyilmazoglu, A.V. Roşca, I. Pop, Complete theory of the elastic wall jet: a new flow geometry with revisited two-phase nanofluids. Eur. J. Mech. BFluids. 1(86), 25–36 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Rahman, F. Sharif, M. Turkyilmazoglu, M.S. Siddiqui, Unsteady three-dimensional magnetohydrodynamics flow of nanofluids over a decelerated rotating disk with uniform suction. Pramana 96(4), 170 (2022)

    Article  ADS  Google Scholar 

  6. Raza Q, Zubair M, Qureshi A, Alkarni S, Ali B Zain, A, Asogwa K, Shah N, Yook S. Significance of viscous dissipation, nanoparticles, and Joule heat on the dynamics of water: The case of two porous orthogonal disk. Case Studies in Therm. Eng. (2023)

  7. R.J. Punith Gowda, R. Naveen Kumar, B.C. Prasannakumara, Two-phase darcy-forchheimer flow of dusty hybrid nanofluid with viscous dissipation over a cylinder. Int. J. Appl. Comput. Math. 7(3), 95 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  8. S. Ahmad, K. Ali, K.S. Nisar, A.A. Faridi, N. Khan, W. Jamshed et al., Features of Cu and TiO2 in the flow of engine oil subject to thermal jump conditions. Sci Rep. 11(1), 19592 (2021)

    Article  ADS  Google Scholar 

  9. A. Abdulrahman, F. Gamaoun, R.S. Varun Kumar, U. Khan, H. Singh Gill, K.V. Nagaraja et al., Study of thermal variation in a longitudinal exponential porous fin wetted with TiO2−SiO2/ hexanol hybrid nanofluid using hybrid residual power series method. Case Stud. Therm. Eng. 1(43), 102777 (2023)

    Article  Google Scholar 

  10. F. Wang, M.I. Asjad, M. Zahid, A. Iqbal, H. Ahmad, M.D. Alsulami, Unsteady thermal transport flow of Casson nanofluids with generalized Mittag-Leffler kernel of Prabhakar’s type. J. Mater. Res. Technol. 1(14), 1292–1300 (2021)

    Article  Google Scholar 

  11. E.V. Timofeeva, J.L. Routbort, D. Singh, Particle shape effects on thermophysical properties of alumina nanofluids. J. Appl. Phys. 106(1), 014304 (2009)

    Article  ADS  Google Scholar 

  12. M. Sahu, J. Sarkar. Steady-state energetic and exergetic performances of single-phase natural circulation loop with hybrid nanofluids. J. Heat. Transf. [Internet] 12 ;141(8) (2019 ).

  13. B.R. Sreenivasa, J. Faqeeh, A. Alsaiari, H.A.H. Alzahrani, M.Y. Malik, Numerical study of heat transfer mechanism in the flow of ferromagnetic hybrid nanofluid over a stretching cylinder. Waves Random Complex Media. 2;0(0):1–17 (2022)

  14. G.K. Ramesh, J.K. Madhukesh, N.A. Shah, S.-J. Yook, Flow of hybrid CNTs past a rotating sphere subjected to thermal radiation and thermophoretic particle deposition. Alex. Eng. J. 64, 969–979 (2023)

    Article  Google Scholar 

  15. K. Ramesh, K.K. Asogwa, T. Oreyeni, M.G. Reddy, A. Verma, EMHD radiative titanium oxide-iron oxide/ethylene glycol hybrid nanofluid flow over an exponentially stretching sheet. Biomass Conversion and Biorefinery. (2023). https://doi.org/10.1007/s13399-023-04033-y

    Article  Google Scholar 

  16. C.H.N. Raju, C.S. Reddy, A.M. Alyami, S.M. Eldin, Adnan, et al. MHD Eyring–Powell nanofluid flow across a wedge with convective and thermal radiation. Front. Energy Res. 2022;10:1021491

  17. M.C. Jayaprakash, K.K. Asogwa, K.R. Lalitha, Y. Veeranna, G.T. Sreenivasa, Passive control of nanoparticles in stagnation point flow of Oldroyd-B Nanofluid with aspect of magnetic dipole. Part E: J. Process Mech. Eng. (2021). https://doi.org/10.1177/09544089211065550

    Article  Google Scholar 

  18. B.S. Goud, Y.D. Reddy, K.K. Asogwa, Inspection of chemical reaction and viscous dissipation on MHD convection flow over an infinite vertical plate entrenched in porous medium with Soret effect. Biomass Convers. Biorefinery. 29, 1–12 (2022). https://doi.org/10.1007/s13399-022-02886-3

    Article  Google Scholar 

  19. M.D. Alsulami, A. Abdulrahman, R.N. Kumar, R.J. Punith Gowda, B.C. Prasannakumara, Three-dimensional swirling flow of nanofluid with nanoparticle aggregation kinematics using modified krieger-dougherty and maxwell-Bruggeman models: a finite element solution. Mathematics. 11(9), 2081 (2023)

    Article  Google Scholar 

  20. R.N. Kumar, F. Gamaoun, A. Abdulrahman, J.S. Chohan, R.J.P. Gowda, Heat transfer analysis in three-dimensional unsteady magnetic fluid flow of water-based ternary hybrid nanofluid conveying three various shaped nanoparticles: A comparative study. Int J Mod Phys B. 36(25), 2250170 (2022)

    Article  ADS  Google Scholar 

  21. A.K. Gailitis, O.A. Lielausis, On the possibility of drag reduction of a flat plate in an electrolyte. Appl Magnetohydrodyn Tr Inst Fis Latv SSR. 12, 143 (1961)

    Google Scholar 

  22. S. Eswaramoorthi, K. Loganathan, M. Faisal, T. Botmart, N.A. Shah, Analytical and numerical investigation of Darcy-Forchheimer flow of a nonlinear-radiative non-Newtonian fluid over a Riga plate with entropy optimization. Ain Shams Eng. J. 14(3), 101887 (2023)

    Article  Google Scholar 

  23. K.K. Asogwa, M.D. Alsulami, B.C. Prasannakumara, T. Muhammad, Double diffusive convection and cross diffusion effects on Casson fluid over a Lorentz force driven Riga plate in a porous medium with heat sink: an analytical approach. Int. Commun. Heat Mass Transf. 1(131), 105761 (2022)

    Article  Google Scholar 

  24. S. Bilal, K.K. Asogwa, H. Alotaibi, M.Y. Malik, I. Khan, Analytical treatment of radiative Casson fluid over an isothermal inclined Riga surface with aspects of chemically reactive species. Alex Eng. J. 60(5), 4243–4253 (2021)

    Article  Google Scholar 

  25. Y.-J. Xu, F. Shah, M.I. Khan, R.N. Kumar, R.J.P. Gowda, B.C. Prasannakumara et al., New modeling and analytical solution of fourth grade (non-Newtonian) fluid by a stretchable magnetized Riga device. Int. J. Mod. Phys. C. 6, 2250013 (2021)

    MathSciNet  Google Scholar 

  26. K.K. Asogwa, F. Mebarek-Oudina, I.L. Animasaun, Comparative investigation of water-based Al2O3 Nanoparticles through water-based CuO nanoparticles over an exponentially accelerated radiative Riga plate surface via heat transport. Arab. J. Sci. Eng. (2022). https://doi.org/10.1007/s13369-021-06355-3

    Article  Google Scholar 

  27. Asogwa KK, Uwanta IJ, Momoh AA. Omokhuale E. Heat and mass ransfer over a vertical plate with periodic Suction and heat sink. Research Journal of Applied Sciences, Engineering, and Technology. 2013; 5(1), 07–15. https://doi.org/10.19026/rjaset.5.5077

  28. J. Madhukesh, A. Alhadhrami, R. Naveen Kumar, R. Punith Gowda, B. Prasannakumara, K.R. Varun, Physical insights into the heat and mass transfer in Casson hybrid nanofluid flow induced by a Riga plate with thermophoretic particle deposition. Proc. Inst. Mech. Eng. Part. E. J. Process. Mech. Eng. 30, 09544089211039305 (2021)

    Google Scholar 

  29. K.K. Asogwa, I.J. Uwanta, A.A. Aliero, Flow past an exponentially accelerated infinite vertical plate and temperature with variable mass diffusion. Int. J. Comput. Appl. 45(2), 1–7 (2012)

    Google Scholar 

  30. R. Muthucumaraswamy, P. Sivakumar. MHD flow past a parabolic flow past an infinite isothermal vertical plate in the presence of thermal radiation and chemical reaction. Int. J. Appl. Mech. Eng. ;21(1) (2016)

  31. H.A.H. Alzahrani, A. Alsaiari, J.K. Madhukesh, R. Naveen Kumar, B.M. Prasanna, Effect of thermal radiation on heat transfer in plane wall jet flow of Casson nanofluid with suction subject to a slip boundary condition. Waves Random Complex Media. ;0(0):1–18 (2022)

  32. T.A. Yusuf, R. Naveen Kumar, R.J. Punith Gowda, U.D Akpan. Entropy generation on flow and heat transfer of a reactive MHD Sisko fluid through inclined walls with porous medium. Int. J. Ambient. Energy. 3;0(0):1–10 (2021)

  33. M.D. Shamshuddin, S. Anwar, K.K. Asogwa, J.W.Usman, A semi-analytical approach to investigate the entropy generation in a tangent hyperbolic magnetized hybrid nanofluid flow upon a stretchable rotating disk. J. Magn. Magn. Mater. (2023). 170664. https://doi.org/10.1016/j.jmmm.2023.170664.

  34. M.D. Shamshuddin, K.K. Asogwa, M. Ferdows, Thermo-solutal migrating heat producing and radiative Casson nanofluid flow via bidirectional stretching surface in the presence of bilateral reactions. Numer. Heat Transf. Part A. Appl (2023). https://doi.org/10.1080/10407782.2023.2191873

  35. K. Sajjan, N.A. Shah, N.A. Ahammad, C.S. Raju, M.D. Kumar, W. Weera, Nonlinear Boussinesq and Rosseland approximations on 3D flow in an interruption of Ternary nanoparticles with various shapes of densities and conductivity properties. AIMS Math. 7(10), 18416–18449 (2022)

    Article  MathSciNet  Google Scholar 

  36. N. Ahmed, M. Dutta, Transient mass transfer flow past an impulsively started infinite vertical plate with ramped plate velocity and ramped temperature. Int. J. Phys. Sci. 8(7), 254–263 (2013)

    Google Scholar 

  37. O.B. Silva, D.C. Sobral Filho, A new proposal to guide velocity and inclination in the ramp protocol for the treadmill ergometer. Arq. Bras. Cardiol. 81, 48–53 (2003)

    Article  Google Scholar 

  38. B. Shilpa, V. Leela, Integrated intelligent neuro computing technique for mixed convective flow and heat transfer in heterogeneous permeability media. Waves Random Complex Media 28, 1–22 (2023)

    Article  Google Scholar 

  39. B. Shilpa, V. Leela, B.C. Prasannakumara, P. Nagabhushana, Soret and Dufour effects on MHD double-diffusive mixed convective heat and mass transfer of couple stress fluid in a channel formed by electrically conducting and non-conducting walls. Waves Random Complex Media. 10, 1–22 (2022)

    Article  Google Scholar 

  40. V. Leela, B.C. Prasannakumara, B. Shilpa, R.R. Gangadhara, Computational analysis of ohmic and viscous dissipation effects on MHD mixed convection flow in a vertical channel with linearly varying wall temperatures. Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng. 24, 09544089221080669 (2022)

    Google Scholar 

  41. M. Turkyilmazoglu, Asymptotic suction/injection flow induced by a uniform magnetohydrodynamics free stream couple stress fluid over a flat plate. J. Fluids Eng. 1;144(3) (2022)

  42. M. Turkyilmazoglu, Magnetohydrodynamic two-phase dusty fluid flow and heat model over deforming isothermal surfaces. Phys. Fluids 29(1), 013302 (2017)

    Article  ADS  Google Scholar 

  43. R. Muthucumaraswamy, E. Geetha, Effects of parabolic motion on an isothermal vertical plate with constant mass flux. Ain Shams Eng. J. 5(4), 1317–1323 (2014)

    Article  Google Scholar 

  44. T. Anwar, P. Kumam, W. Watthayu, An exact analysis of unsteady MHD free convection flow of some nanofluids with ramped wall velocity and ramped wall temperature accounting heat radiation and injection/consumption. Sci. Rep. 10(1), 17830 (2020)

    Article  ADS  Google Scholar 

  45. I. Siddique, K. Sadiq, I. Khan, K.S. Nisar, Nanomaterials in convection flow of nanofluid in upright channel with gradients. J. Mater. Res. Technol. 1(11), 1411–1423 (2021)

    Article  Google Scholar 

  46. A. Abbasi, K. Al-Khaled, M.I. Khan, S.U. Khan, A.M. El-Refaey, W. Farooq et al., Optimized analysis and enhanced thermal efficiency of modified hybrid nanofluid (Al2O3, CuO, Cu) with nonlinear thermal radiation and shape features. Case Stud. Therm. Eng. 1(28), 101425 (2021)

    Article  Google Scholar 

  47. S. Rosseland, Astrophysik und Atom-Theoretische Grundlagen (Springer Verlag publisher), Germany, 1931)

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Nigeria Maritime University, Okerenkoko, Delta State, Nigeria

    Kanayo Kenneth Asogwa

  2. Department of Mathematics, University of Technology and Applied Sciences, Nizwa, Oman

    K. Thanesh Kumar

  3. Department of Mathematics, JNTUH College of Engineering, Kukatpally, Hyderabad, Telangana, 500085, India

    B. Shankar Goud

  4. Department of Mechanical Engineering and University Centre for Research and Development, Chandigarh University, Mohali, Punjab, 140413, India

    Jasgurpreet Singh Chohan

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  1. Kanayo Kenneth Asogwa
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Correspondence to Kanayo Kenneth Asogwa.

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Asogwa, K.K., Kumar, K.T., Goud, B.S. et al. Significance of nanoparticle shape factor and buoyancy effects on a parabolic motion of EMHD convective nanofluid past a Riga plate with ramped wall temperature. Eur. Phys. J. Plus 138, 572 (2023). https://doi.org/10.1140/epjp/s13360-023-04170-3

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