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Hydrothermal dissipative nanofluid flow over a stretching riga plate with heat and mass transmission and shape effects

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Abstract

This paper presents computational analyses of the effects of the nanoparticle’s shapes, heat, and mass transmission on the radiative nanofluid flow over a stretching Riga plate. Various nanoparticles shapes are considered, namely bricks- shaped, cylinder- shaped, platelets- shaped, and disk- shaped; those are governed using values of constants \(A\) and \(B\) in the correlations of the nanofluid dynamic viscosity. Besides, several significant influences are assumed such as constant Lorentz force, non-linear thermal radiation, viscous dissipation, heat generation, and convective boundary conditions. The solution methodology is based on similarity analyses and the obtained system is solved numerically. The entropy generation in all the aforementioned cases is examined. The given outcomes are represented in terms of the profiles of velocity, temperature, system entropy, and heat transfer rate together with the contours of the streamlines and isotherms. The findings disclosed that the sphere-shaped nanoparticles give higher values of the skin friction coefficient \(-{C}_{{\text{f}}}{{\text{Re}}}^{1/2}\) while the platelets-shaped cause lower values of \(-{C}_{{\text{f}}}{{\text{Re}}}^{1/2}\). Additionally, the system irreversibility is enhanced as the thermal radiation coefficient \(\left({R}_{{\text{d}}}\right)\), solid volume fraction \(\left(\varphi \right)\), Brinkman number \(\left({\text{Br}},\right)\) or space-dependent heat source coefficient \(\left({Q}_{{\text{E}}}\right)\) is enhanced.

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Abbreviations

\(\left(u,v\right)\) :

Components of rising velocity in growing \((x,y)\) directions \(\left({{\text{ms}}}^{-1}\right)\)

\(\left(x,y\right)\) :

Cartesian coordinate system (m)

\({\rho }_{{\text{hnf}}}\) :

Nanofluid effective density \(\left({{\text{kgm}}}^{-3}\right)\)

\({\mu }_{{\text{nf}}}\) :

The nanofluid's effective dynamic viscosity \(\left({{\text{kgm}}}^{-1}{{\text{s}}}^{-1}\right)\)

\({\left(\rho {c}_{{\text{p}}}\right)}_{{\text{nf}}}\) :

The nanofluid's heat capacity

\(T\) :

The fluid temperature in the boundary layer \(({\text{K}})\)

\({T}_{{\text{f}}}\) :

Temperature at the convective surface \(({\text{K}})\)

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

Temperature of the fluid in the environment \(({\text{K}})\)

\({\rho }_{\text{s}}\) :

Nanoparticle's density (Ag) \(({{\text{Kgm}}}^{-3})\)

\({\rho }_{{\text{f}}}\) :

The fluid's base density \(({{\text{Kgm}}}^{-3})\)

\({\sigma }_{{\text{s}}}\) :

The nanoparticle's conductivity \(\left({\text{S}}\,{\text{cm}}^{-1}\right)\)

\(E\) :

The electrical field

\(P\) :

Pressure (pa)

\(J\) :

The electromotive force

\(V\) :

The vector of velocity

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

The magnetic field is produced by permanent magnets (Tesla)

\(n\) :

Index exponential

\({\text{Bi}}\) :

Biot number

\(M\) :

The parameter of magnetic field

\(Z\) :

The modified Hartmann number

\(d\) :

The dimensionless parameters for the magnets and electrode width

\({R}_{{\text{d}}}\) :

Radiation parameter

\(\psi \) :

The sphericity

\({N}_{{\text{G}}}\) :

The dimensionless value for the entropy generation

\({\mathbb{Q}}_{{\text{T}}}^{*}\) :

The coefficient heat absorption

\({\mathbb{Q}}_{{\text{E}}}^{*}\) :

The coefficient of heat source/sink with exponential space dependence

\({\text{nf}}\) :

Nanofluid (NF)

\({\mu }_{{\text{f}}}\) :

Fluid's dynamic viscosity \(\left(\mathrm{kg }{{\text{m}}}^{-1} {{\text{s}}}^{-1}\right)\)

\({q}_{{\text{w}}}\) :

Surface heat flux \(({\text{W}}/{{\text{m}}}^{2})\)

\({\left(\rho {c}_{{\text{p}}}\right)}_{{\text{s}}}\) :

1-Nanoparticle's specific thermal capacity (Ag)\(\left(\mathrm{J }{{\text{m}}}^{-3}{{\text{K}}}^{-1}\right)\)

\({\left(\rho {c}_{p}\right)}_{\text{f}}\) :

Base fluid's specific thermal capacity \(\left(\mathrm{J }{{\text{m}}}^{-3}{{\text{K}}}^{-1}\right)\)

\({k}_{{\text{s}}}\) :

Nanoparticle-1's thermal conductivity (Ag) \(({{\text{Wm}}}^{-1}{{\text{K}}}^{-1})\)

\({k}_{{\text{f}}}\) :

The base fluid's thermal conductivity \(({{\text{Wm}}}^{-1}{{\text{K}}}^{-1})\)

\({\sigma }^{*}\) :

The constant of Stefan−Boltzmann (\({\text{W}}\,{{\text{m}}}^{-2}{{\text{K}}}^{-4})\)

\({k}^{*}\) :

The average absorption factor \(({{\text{m}}}^{-1})\)

\({\sigma }_{{\text{f}}}\) :

The base fluid's electrical conductivity \(\left({\text{S}}\,{\text{cm}}^{-1}\right)\)

\({\sigma }_{{\text{nf}}}\) :

The nanofluid electrical conductivity \(\left({\text{S}}\,{\text{cm}}^{-1}\right)\)

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

Nanoparticle's dynamic viscosity (Ag)\(\left(\mathrm{kg }{{\text{m}}}^{-1} {{\text{s}}}^{-1}\right)\)

\({\mu }_{{\text{f}}}\) :

The fluid's base dynamic viscosity (CNT) \(\left(\mathrm{kg }{{\text{m}}}^{-1} {{\text{s}}}^{-1}\right)\)

\(\Phi \) :

Dissipation of viscosity

\(Q\) :

The density of electric charges

\(s\) :

Solid particles at the nanoscale

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

The representation of the current density \(\left(\mathrm{A }{{\text{m}}}^{-2}\right)\)

\(\varphi \) :

The volume fraction of nanoparticle

\({\text{Pr}}\) :

Prandtl number

\({\text{Nr}}\) :

Thermal radiation parameter

\({\text{Br}}\) :

Brinkman number of rotational

\({\text{Re}}\) :

The coefficient of rotational Reynolds number

\({\text{Ec}}\) :

Eckert number

\(m\) :

The empirical shape factor

\({S}_{{{\text{G}}}_{0}}\) :

The rate at which distinctive feature entropy is produced

\({T}_{{\text{m}}}\) :

Mean temperature of the fluid \(({\text{K}})\)

\({\Omega }^{-1}\) :

The infinitesimal change in temperature

\(f\) :

Basic liquid

References

  1. Choi SU, Eastman JA. Enhancing thermal conductivity of fluids with nanoparticles. Argonne National Lab (ANL), Argonne, IL (United States), 1995.

  2. Lim E-K, Jang E, Lee K, Haam S, Huh Y-M. Delivery of cancer therapeutics using nanotechnology. Pharmaceutics. 2013;5(2):294–317.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  3. Sus C. Enhancing thermal conductivity of fluids with nanoparticles, developments and applications of non-Newtonian flows. ASME, FED, MD. 1995;1995(231):99-I05.

    Google Scholar 

  4. Asokan N, Gunnasegaran P, Wanatasanappan VV. Experimental investigation on the thermal performance of compact heat exchanger and the rheological properties of low concentration mono and hybrid nanofluids containing Al2O3 and CuO nanoparticles. Therm Sci Eng Prog. 2020;20: 100727.

    Article  Google Scholar 

  5. Jiang Y, Zhou X, Wang Y. Effect of nanoparticle shapes on nanofluid mixed forced and thermocapillary convection in minichannel. Int Commun Heat Mass Transf. 2020;118: 104884.

    Article  CAS  Google Scholar 

  6. Saadati H, Hadad K, Rabiee A. Safety margin and fuel cycle period enhancements of VVER-1000 nuclear reactor using water/silver nanofluid. Nucl Eng Technol. 2018;50(5):639–47.

    Article  CAS  Google Scholar 

  7. Buongiorno J. Convective transport in nanofluids. ASME J Heat Transf. 2006;128:240–50.

    Article  Google Scholar 

  8. Agha A, Waheed W, Alamoodi N, Mathew B, Alnaimat F, Abu-Nada E, et al. A review of cyclic olefin copolymer applications in microfluidics and microdevices. Macromol Mater Eng. 2022;307(8):2200053.

    Article  CAS  Google Scholar 

  9. Ahmed SE, Arafa AA, Hussein SA. Cattaneo-Christov double-diffusion and hydrothermal flow of Sutterby tri, hybrid and mono-nanofluids with oxytactic microorganism. Int J Ambient Energy. 2023;44(1):2200–13.

    Article  CAS  Google Scholar 

  10. Hayat T, Aziz A, Muhammad T, Alsaedi A. Significance of homogeneous–heterogeneous reactions in Darcy-Forchheimer three-dimensional rotating flow of carbon nanotubes. J Therm Anal Calorim. 2020;139:183–95.

    Article  CAS  Google Scholar 

  11. Hussein SA. Simulation and interpretation of MHD peristaltic transport of dissipated third grade nanofluid flow across asymmetric channel under the influences of rheological characteristics and inclined magnetic field as well as heat and mass convection. Int J Model Simul. 2023. https://doi.org/10.1080/02286203.2023.2240557.

    Article  Google Scholar 

  12. Abderrahmane A, Al-Khaleel M, Mourad A, Laidoudi H, Driss Z, Younis O, et al. Natural convection within inversed T-shaped enclosure filled by nano-enhanced phase change material: numerical investigation. Nanomaterials. 2022;12(17):2917.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Selimefendigil F, Dilbaz F, Öztop HF. Combined utilization of cylinder and different shaped alumina nanoparticles in the base fluid for the effective cooling system design of lithium-ion battery packs. Energies. 2023;16(9):3966.

    Article  CAS  Google Scholar 

  14. Hussein SA. Numerical simulation for peristaltic transport of radiative and dissipative MHD Prandtl nanofluid through the vertical asymmetric channel in the presence of double diffusion convection. Numer Heat Transf B: Fund. 2023;85(4):385–411.

    Article  Google Scholar 

  15. Rashid FL, Hussein AK, Malekshah EH, Abderrahmane A, Guedri K, Younis O. Review of heat transfer analysis in different cavity geometries with and without nanofluids. Nanomaterials. 2022;12(14):2481.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  16. Ahmed SE, Arafa AA, Hussein SA, Morsy Z. Time-dependent squeezing flow of variable properties ternary nanofluids between rotating parallel plates with variable magnetic and electric fields. Numer Heat Transf A Appl. 2023. https://doi.org/10.1080/10407782.2023.2272292.

    Article  Google Scholar 

  17. Safdar R, Jawad M, Hussain S, Imran M, Akgül A, Jamshed W. Thermal radiative mixed convection flow of MHD Maxwell nanofluid: Implementation of Buongiorno’s model. Chinese J Phys. 2022;77:1465–78.

    Article  Google Scholar 

  18. Ahmed SE, Arafa AA, Hussein SA. A novel model of non-linear radiative Williamson nanofluid flow along a vertical wavy cone in the presence of gyrotactic microorganisms. Int J Model Simul. 2023. https://doi.org/10.1080/02286203.2023.2180023.

    Article  Google Scholar 

  19. Waqas M, Khan W, Pasha AA, Islam N, Rahman MM. Dynamics of bioconvective Casson nanoliquid from a moving surface capturing gyrotactic microorganisms, magnetohydrodynamics and stratifications. Therm Sci Eng Prog. 2022;36: 101492.

    Article  CAS  Google Scholar 

  20. Saeed AM, Abderrahmane A, Qasem NA, Mourad A, Alhazmi M, Ahmed SE, et al. A numerical investigation of a heat transfer augmentation finned pear-shaped thermal energy storage system with nano-enhanced phase change materials. J Energy Storage. 2022;53: 105172.

    Article  Google Scholar 

  21. Ahmed SE, Arafa AA, Hussein SA. Dissipated-radiative compressible flow of nanofluids over unsmoothed inclined surfaces with variable properties. Numer Heat Transf A: Appl. 2023;84(5):507–28.

    Article  Google Scholar 

  22. Selimefendigil F, Omri M, Aich W, Besbes H, Ben Khedher N, Alshammari BM, et al. Numerical study of thermo-electric conversion for teg mounted wavy walled triangular vented cavity considering nanofluid with different-shaped nanoparticles. Mathematics. 2023;11(2):483.

    Article  Google Scholar 

  23. Shamshuddin M, Rajput GR, Jamshed W, Shahzad F, Salawu S, Abderrahmane A, et al. MHD bioconvection microorganism nanofluid driven by a stretchable plate through porous media with an induced heat source. Waves Random Complex Media. 2022. https://doi.org/10.1080/17455030.2022.2126024.

    Article  Google Scholar 

  24. Ahmed SE, Raizah Z, Arafa AA, Hussein SA. FEM treatments for MHD highly mixed convection flow within partially heated double-lid driven odd-shaped enclosures using ternary composition nanofluids. Int Commun Heat Mass Transf. 2023;145: 106854.

    Article  CAS  Google Scholar 

  25. Asjad MI, Usman M, Kaleem MM, Akgül A. Numerical solutions of fractional Oldroyd-B hybrid nanofluid through a porous medium for a vertical surface. Waves Random Complex Media. 2022. https://doi.org/10.1080/17455030.2022.2128233.

    Article  Google Scholar 

  26. Selimefendigil F, Öztop HF. Effects of flow separation and shape factor of nanoparticles in heat transfer fluid for convection thorough phase change material (PCM) installed cylinder for energy technology applications. J Energy Storage. 2021;41: 102945.

    Article  Google Scholar 

  27. Shahzad A, Imran M, Tahir M, Khan SA, Akgül A, Abdullaev S, et al. Brownian motion and thermophoretic diffusion impact on Darcy-Forchheimer flow of bioconvective micropolar nanofluid between double disks with Cattaneo-Christov heat flux. Alex Eng J. 2023;62:1–15.

    Article  Google Scholar 

  28. Hussein SA, Ahmed SE, Arafa AA. Numerical treatment of thermal and concentration convection along with induced magnetic field on peristaltic pumping of a magnetic six-constant Jeffrey nanofluid through a vertical divergent channel. Numer Heat Transf A Appl. 2023;84(8):877–904.

    Article  Google Scholar 

  29. Anjum N, Khan W, Hobiny A, Azam M, Waqas M, Irfan M. Numerical analysis for thermal performance of modified Eyring Powell nanofluid flow subject to activation energy and bioconvection dynamic. Case Stud Therm Eng. 2022;39: 102427.

    Article  Google Scholar 

  30. Tabrez M, Azeem KW. Exploring physical aspects of viscous dissipation and magnetic dipole for ferromagnetic polymer nanofluid flow. Waves Random Complex Media. 2022. https://doi.org/10.1080/17455030.2022.2135794.

    Article  Google Scholar 

  31. Arafa AA, Hussein SA, Ahmed SE. Hydrothermal bioconvective Bödewadt ternary composition nanofluids flow over a stretching rotating disk through a heat generating porous medium. J Magn Magn Mater. 2023;586: 171174.

    Article  CAS  Google Scholar 

  32. Hussain Z, Azeem KW. Impact of thermal-solutal stratifications and activation energy aspects on time-dependent polymer nanoliquid. Waves Random Complex Media. 2022. https://doi.org/10.1080/17455030.2022.2128229.

    Article  Google Scholar 

  33. Ahmed SE, Abderrahmane A, Alotaibi S, Younis O, Almasri RA, Hussam WK. Enhanced heat transfer for NePCM-melting-based thermal energy of finned heat pipe. Nanomaterials. 2021;12(1):129.

    Article  PubMed  PubMed Central  Google Scholar 

  34. Sharma RP, Mishra S, Tinker S, Kulshrestha B. Effect of non-linear thermal radiation and binary chemical reaction on the williamson nanofluid flow past a linearly stretching sheet. Int J Appl Comput Math. 2022;8(4):171.

    Article  Google Scholar 

  35. Sharma RP, Gorai D, Das K. Comparative study on hybrid nanofluid flow of Ag–CuO/H2O over a curved stretching surface with Soret and Dufour effects. Heat Transf. 2022;51(7):6365–83.

    Article  Google Scholar 

  36. Ahmed SE, Arafa AA, Hussein SA. Bioconvective flow of a variable properties hybrid nanofluid over a spinning disk with Arrhenius activation energy, Soret and Dufour impacts. Numer Heat Transf A: Applicat. 2024;85(6):900–22.

    Article  Google Scholar 

  37. Eastman JA, Choi S, Li S, Yu W, Thompson L. Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Appl Phys Lett. 2001;78(6):718–20.

    Article  CAS  Google Scholar 

  38. Xie H-Q, Wang J-C, Xi T-G, Liu Y. Thermal conductivity of suspensions containing nanosized SiC particles. Int J Thermophys. 2002;23:571–80.

    Article  CAS  Google Scholar 

  39. Timofeeva EV, Routbort JL, Singh D. Particle shape effects on thermophysical properties of alumina nanofluids. J Appl Phys. 2009. https://doi.org/10.1063/1.3155999.

    Article  Google Scholar 

  40. Hamilton RL, Crosser O. Thermal conductivity of heterogeneous two-component systems. Ind Eng Chem Fundam. 1962;1(3):187–91.

    Article  CAS  Google Scholar 

  41. Khan I. Shape effects of MoS2 nanoparticles on MHD slip flow of molybdenum disulphide nanofluid in a porous medium. J Mol Liq. 2017;233:442–51.

    Article  CAS  Google Scholar 

  42. Singh D, Timofeeva E, Yu W, Routbort J, France D, Smith D, et al. An investigation of silicon carbide-water nanofluid for heat transfer applications. J Appl Phys. 2009. https://doi.org/10.1063/1.3082094.

    Article  Google Scholar 

  43. Hassan M, Fetecau C, Majeed A, Zeeshan A. Effects of iron nanoparticles’ shape on convective flow of ferrofluid under highly oscillating magnetic field over stretchable rotating disk. J Magn Magn Mater. 2018;465:531–9.

    Article  CAS  Google Scholar 

  44. Bj G, Bc P. Scrutinization of different shaped nanoparticle of molybdenum disulfide suspended nanofluid flow over a radial porous fin. Int J Numer method H. 2020;30(7):3685–99.

    Google Scholar 

  45. Gireesha B, Sowmya G, Gorla RSR. Nanoparticle shape effect on the thermal behaviour of moving longitudinal porous fin. J Nanomater Nanoeng Nanosyst. 2020;234(3–4):115–21.

    Google Scholar 

  46. Babazadeh H, Zeeshan A, Jacob K, Hajizadeh A, Bhatti M. Numerical modelling for nanoparticle thermal migration with effects of shape of particles and magnetic field inside a porous enclosure. IJST-T MECH ENG. 2021;45:801–11.

    Google Scholar 

  47. Bejan AA. Study of entropy generation in fundamental convective heat transfer. J Heat Transf. 1979;101(4):718–25.

    Article  Google Scholar 

  48. Bejan A. Entropy generation minimization: The new thermodynamics of finite-size devices and finite-time processes. J Appl Phys. 1996;79(3):1191–218.

    Article  CAS  Google Scholar 

  49. Butt AS, Munawar S, Ali A, Mehmood A. Entropy generation in the Blasius flow under thermal radiation. Phys Scr. 2012;85(3): 035008.

    Article  Google Scholar 

  50. Berrehal H, Maougal A. Entropy generation analysis for multi-walled carbon nanotube (MWCNT) suspended nanofluid flow over wedge with thermal radiation and convective boundary condition. J Mech Sci Technol. 2019;33(1):459–64.

    Article  Google Scholar 

  51. Ellahi R, Hassan M, Zeeshan A. Shape effects of nanosize particles in Cu–H2O nanofluid on entropy generation. Int J Heat Mass Trans. 2015;81:449–56.

    Article  CAS  Google Scholar 

  52. Monaledi RL, Makinde OD. Inherent irreversibility in Cu-H 2 O nanofluid couette flow with variable viscosity and nonlinear radiative heat transfer. Int J Fluid Mech Res. 2019;46(6):525–43.

    Article  Google Scholar 

  53. Ellahi R, Hassan M, Zeeshan A, Khan AA. The shape effects of nanoparticles suspended in HFE-7100 over wedge with entropy generation and mixed convection. Appl Nanosci. 2016;6(5):641–51.

    Article  CAS  Google Scholar 

  54. Riaz A, Bhatti MM, Ellahi R, Zeeshan A. Mathematical analysis on an asymmetrical wavy motion of blood under the influence entropy generation with convective boundary conditions. Symmetry. 2020;12(1):102.

    Article  Google Scholar 

  55. Riaz A, Abbas T, Zeeshan A, Doranehgard MH. Entropy generation and MHD analysis of a nanofluid with peristaltic three dimensional cylindrical enclosures. Int J Numer Method H. 2021;31(8):2698–714.

    Article  Google Scholar 

  56. Gireesha B, Mahanthesh B. Perturbation solution for radiating viscoelastic fluid flow and heat transfer with convective boundary condition in nonuniform channel with Hall current and chemical reaction. Int Sch Res Notices. 2013;2013:1–14.

    Google Scholar 

  57. Seth G, Sharma R, Kumbhakar B. Heat and mass transfer effects on unsteady MHD natural convection flow of a chemically reactive and radiating fluid through a porous medium past a moving vertical plate with arbitrary ramped temperature. J Appl Fluid Mech. 2015;9(1):103–17.

    Google Scholar 

  58. Thumma T, Mishra S, Abbas MA, Bhatti MM, Abdelsalam SI. Three-dimensional nanofluid stirring with non-uniform heat source/sink through an elongated sheet. Appl Math Comput. 2022;421: 126927.

    Article  Google Scholar 

  59. Gireesha B, Mahanthesh B, Krupalakshmi K. Hall effect on two-phase radiated flow of magneto-dusty-nanoliquid with irregular heat generation/consumption. Results Phys. 2017;7:4340–8.

    Article  Google Scholar 

  60. Hussain SM, Jain J, Seth G, Rashidi M. Free convective heat transfer with hall effects, heat absorption and chemical reaction over an accelerated moving plate in a rotating system. J Magn Magn Mater. 2017;422:112–23.

    Article  CAS  Google Scholar 

  61. Pantokratoras A, Magyari E. EMHD free-convection boundary-layer flow from a Riga-plate. J Eng Math. 2009;64:303–15.

    Article  CAS  Google Scholar 

  62. Xu L, Lee EW. Variational iteration method for the magnetohydrodynamic flow over a nonlinear stretching sheet. Abstr Appl Anal. 2013;2013:1–5.

    CAS  Google Scholar 

  63. Hayat T, Hussain Q, Javed T. The modified decomposition method and Padé approximants for the MHD flow over a non-linear stretching sheet. Nonlinear Anal Real World Appl. 2009;10(2):966–73.

    Article  Google Scholar 

  64. Mabood F, Yusuf T, Khan W. Cu–Al2O3–H2O hybrid nanofluid flow with melting heat transfer, irreversibility analysis and nonlinear thermal radiation. J Therm Anal Calorim. 2021;143(2):973–84.

    Article  CAS  Google Scholar 

  65. Berrehal H, Sowmya G, Makinde OD. Shape effect of nanoparticles on MHD nanofluid flow over a stretching sheet in the presence of heat source/sink with entropy generation. Int J Numer Method H. 2022;32(5):1643–63.

    Article  Google Scholar 

  66. Wang C. Free convection on a vertical stretching surface. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik. 1989;69(11):418–20.

    Article  Google Scholar 

  67. Acharya N, Maity S, Kundu PK. Influence of inclined magnetic field on the flow of condensed nanomaterial over a slippery surface: the hybrid visualization. Appl Nanosci. 2020;10(2):633–47.

    Article  CAS  Google Scholar 

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through a large group Research Project under grant number RGP2/64/4.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Khalid University, Abha, Saudi Arabia

    Sameh E. Ahmed

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

    Anas A. M. Arafa

  3. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

    Sameh A. Hussein

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Ahmed, S.E., Arafa, A.A.M. & Hussein, S.A. Hydrothermal dissipative nanofluid flow over a stretching riga plate with heat and mass transmission and shape effects. J Therm Anal Calorim (2024). https://doi.org/10.1007/s10973-024-13061-3

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