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Thermal Characteristics of 3D Nanofluid Flow over a Convectively Heated Riga Surface in a Darcy–Forchheimer Porous Material with Linear Thermal Radiation: An Optimal Analysis

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Abstract

This paper focuses primarily on the thermal analysis of the steady, three-dimensional flow of CMC (sodium carboxymethyl cellulose) base fluid with Cu nanoparticles through the implantation plate of Riga in a porous Darcy–Forchheimer material with internal heat generation (absorption) effects. Thermophysical feature of CMC is taken into account with Al2O3 nanoparticle in it. Also, thermal radiation and convective boundary constraint are considered into account. Adequate transformations of the issue controlling formulas produce a system of nonlinear ordinary differential equations. The optimal homotopy analysis method is used for calculating the parameters values impacts. The expressions of local Nusselt number and skin friction coefficient are studied and debated. The physical influences of all emerging parameters are debated on graphically forms. The findings suggest that with higher values of Hartmann number, the skin friction in y-direction decreases on the contrary in the case of x-direction, while the Hartmann number increases the rate of heat transportation. Besides, the addition values of thermal radiation and Biot number enhance the rate of heat transport. Comparisons have been made with published literature, and an excellent agreement is clear. This underlines the importance of the study in potential medical and industrial cooling applications.

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References

  1. Choi, S.U.S.: Enhancing thermal conductivity of fluids with nanoparticles. Dev. Appl. Non-Newtonian Flows 66, 99–105 (1995)

    Google Scholar 

  2. Choi, S.U.S.; Zhang, Z.G.; Yu, W.; Lockwood, F.E.; Grulke, E.A.: Anomalously thermal conductivity enhancement in nanotube suspensions. Appl. Phys. Lett. 79, 2252–2254 (2001)

    Google Scholar 

  3. Hady, F.; Ibrahim, F.; Abdel-Gaied, S.; Eid, M.R.: Influence of yield stress on free convective boundary-layer flow of a non-Newtonian nanofluid past a vertical plate in a porous medium. J. Mech. Sci. Technol. 25(8), 2043 (2011)

    Google Scholar 

  4. Hady, F.; Ibrahim, F.; Abdel-Gaied, S.; Eid, M.: Effect of heat generation/absorption on natural convective boundary-layer flow from a vertical cone embedded in a porous medium filled with a non-Newtonian nanofluid. Int. Commun. Heat Mass Transf. 38(10), 1414–1420 (2011)

    Google Scholar 

  5. Abdel-Gaied, S.M.; Eid, M.R.: Natural convection of non-Newtonian power-law fluid over axisymmetric and two-dimensional bodies of arbitrary shape in fluid-saturated porous media. Appl. Math. Mech. 32, 179–188 (2011)

    MathSciNet  MATH  Google Scholar 

  6. Wakif, A.; Boulahia, Z.; Ali, F.; Eid, M.R.; Sehaqui, R.: Numerical analysis of the unsteady natural convection MHD Couette nanofluid flow in the presence of thermal radiation using single and two-phase nanofluid models for Cu–water nanofluids. Int. J. Appl. Comput. Math. 4, 81 (2018)

    MathSciNet  MATH  Google Scholar 

  7. Al-Hossainy, A.F.; Eid, M.R.; Zoromba, M.S.: SQLM for external yield stress effect on 3D MHD nanofluid flow in a porous medium. Phys. Scr. 94, 105208 (2019)

    Google Scholar 

  8. Eid, M.R.; Al-Hossainy, A.; Zoromba, M.S.: FEM for blood-based SWCNTs flow through a circular cylinder in a porous medium with electromagnetic radiation. Commun. Theor. Phys. 71, 1425 (2019)

    MathSciNet  Google Scholar 

  9. Eid, M.R.; Al-Hossainy, A.F.: Synthesis, DFT calculations, and heat transfer performance large-surface TiO2: ethylene glycol nanofluid and coolant applications. Eur. Phys. J. Plus 135, 596 (2020)

    Google Scholar 

  10. Eid, M.R.; Mahny, K.; Dar, A.; Muhammad, T.: Numerical study for Carreau nanofluid flow over a convectively heated nonlinear stretching surface with chemically reactive species. Phys. A 540, 123063 (2020)

    MathSciNet  Google Scholar 

  11. Eid, M.R.: Effects of NP shapes on non-Newtonian bio-nanofluid flow in suction/blowing process with convective condition: Sisko model. J. Non-Equilib. Thermodyn. 45(2), 97–108 (2020)

    Google Scholar 

  12. Al-Hossainy, A.F.; Eid, M.R.: Structure, DFT calculations and heat transfer enhancement in [ZnO/PG+H2O] C hybrid nanofluid flow as a potential solar cell coolant application in a double-tube. J. Mater. Sci. 1, 15 (2020). https://doi.org/10.1007/s10854-020-04089-w

    Article  Google Scholar 

  13. Hady, F.M.; Ibrahim, F.S.; Abdel-Gaied, S.M.; Eid, M.R.: Radiation effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet. Nanoscale Res. Lett. 7, 229 (2012)

    Google Scholar 

  14. Eid, M.R.: Chemical reaction effect on MHD boundary-layer flow of two-phase nanofluid model over an exponentially stretching sheet with a heat generation. J. Mol. Liq. 220, 718–725 (2016)

    Google Scholar 

  15. Eid, M.R.; Mahny, K.L.; Muhammad, T.; Sheikholeslami, M.: Numerical treatment for Carreau nanofluid flow over a porous nonlinear stretching surface. Results Phys. 8, 1185–1193 (2018)

    Google Scholar 

  16. Eid, M.R.; Mahny, K.L.: Flow and heat transfer in a porous medium saturated with a Sisko nanofluid over a nonlinearly stretching sheet with heat generation/absorption. Heat Transf. Asian Res. 47, 54–71 (2018)

    Google Scholar 

  17. Eid, M.R.: Time-dependent flow of water-NPs over a stretching sheet in a saturated porous medium in the stagnation-point region in the presence of chemical reaction. J. Nanofluids 6, 550–557 (2017)

    Google Scholar 

  18. Jagan, K.; Sivasankaran, S.; Bhuvaneswari, M.; Rajan, S.: Effect of non-linear radiation on 3D unsteady MHD nanoliquid flow over a stretching surface with double stratification. Appl Math. Sci. Comput. 2, 109–116 (2019)

    MATH  Google Scholar 

  19. Samrat, S.P.; Sulochana, C.; Ashwinkumar, G.P.: Impact of thermal radiation on an unsteady Casson nanofluid flow over a stretching surface. Int. J. Appl. Comput. Math. 5, 31 (2019)

    MathSciNet  MATH  Google Scholar 

  20. Zangooee, M.R.; Hosseinzadeh, K.H.; Ganji, D.D.: Hydrothermal analysis of MHD nanofluid (TiO2-GO) flow between two radiative stretchable rotating disks using AGM. Case Stud. Therm. Eng. 14, 100460 (2019)

    Google Scholar 

  21. Rasool, G.; Shafiq, A.; Khalique, C.M.; Zhang, T.: Magneto-hydrodynamic Darcy–Forchheimer nanofluid flow over nonlinear stretching sheet. Phys Scr. 94(10), 105221 (2019)

    Google Scholar 

  22. Pantokratoras, A.: Natural convection along a vertical isothermal plate with linear and non-linear Rosseland thermal radiation. Int. J. Therm. Sci. 84, 151–157 (2014)

    Google Scholar 

  23. Sandeep, N.; Reddy, M.G.: Heat transfer of nonlinear radiative magnetohydrodynamic Cu-water nanofluidflow over two different geometries. J. Mol. Liq. 225, 87–94 (2017). https://doi.org/10.1016/j.molliq.2016.11.026

    Article  Google Scholar 

  24. Eid, M.R.; Alsaedi, A.; Muhammad, T.; Hayat, T.: Comprehensive analysis of heat transfer of gold-blood nanofluid (Sisko-model) with thermal radiation. Results Phys. 7, 4388–4393 (2017)

    Google Scholar 

  25. Patel, H.R.; Singh, R.: Thermophoresis, Brownian motion and non-linear thermal radiation effects on mixed convection MHD micropolar fluid flow due to nonlinear stretched sheet in porous medium with viscous dissipation, Joule heating and convective boundary condition. Int. Commun. Heat Mass Transf. 107, 68–92 (2019)

    Google Scholar 

  26. Hosseinzadeh, K.; Asadi, A.; Mogharrebi, A.R.; Khalesi, J.; Mousavisani, S.; Ganji, D.D.: Entropy generation analysis of (CH2OH2) containing CNTs nano fluid flow under effect of MHD and thermal radiation. Case Stud. Therm. Eng. 14, 100482 (2019)

    Google Scholar 

  27. Gailitis, A.K.; Lielausis, O.A.: On the possibility of drag reduction of a flat plate in an electrolyte, Applied Magnetohydrodynnamics. Reports Phys. Inst. 12, 143 (1961)

    Google Scholar 

  28. Ramesh, G.K.; Gireesha, B.J.: Non-linear radiative flow of nanofluid past a moving/stationary Riga plate. Front Heat Mass Transf. 9(1), 1–7 (2017)

    Google Scholar 

  29. Ahmed, N.; Khan, U.; Mohyud-Din, U.: Influence of thermal radiation and viscous dissipation on squeezed flow of water between Riga plates saturated with carbon nanotubes. Colloids Surf. A. 522, 389–398 (2017)

    Google Scholar 

  30. Rasool, G.; Shafiq, A.; Khalique, C.M.: Marangoni forced convective Casson type nanofluid flow in the presence of Lorentz force generated by Riga plate, Discret. Contin. Dyn. Syst. Ser. S (2019).

  31. Rasool, G.; Zhang, T.; Shafiq, A.; Durur, H.: Influence of chemical reaction on Marangoni convective flow of nanoliquid in the presence of Lorentz forces and thermal radiation: a numerical investigation. J. Adv. Nanotechnol. 1(1), 32–49 (2019)

    Google Scholar 

  32. Ajayi, T.; Omowaye, A.; Animasaun, I.L.: Viscous dissipation effects on the motion of Casson fluid over an upper horizontal thermally stratified melting surface of a paraboloid of revolution: boundary layer analysis. J. Appl. Math. 2017, 1697135 (2017)

    MathSciNet  MATH  Google Scholar 

  33. Sandeep, N.; Animasaun, I.: Theoretical exploration of exponential heat source and thermal stratification effects on the motion of 3-dimensional flow of Casson fluid over a low heat energy surface at initial unsteady stage. J. Theoret. Appl. Mech. 47, 61–82 (2017)

    MathSciNet  Google Scholar 

  34. Makinde, O.; Sandeep, N.; Ajayi, T.; Animasaun, I.: Numerical exploration of heat transfer and Lorentz force effects on the flow of MHD Casson fluid over an upper horizontal surface of a thermally stratified melting surface of a paraboloid of revolution. Int. J. Nonlinear Sci. Numer. Simul. 19, 93–106 (2018)

    MathSciNet  MATH  Google Scholar 

  35. Thumma, T.; Wakif, A.; Animasaun, I.L.: Generalized differential quadrature analysis of unsteady three-dimensional MHD radiating dissipative Casson fluid conveying tiny particles. Heat Transf. 49, 2595–2626 (2020)

    Google Scholar 

  36. Cai, Z.; Wu, J.; Du, B.; Zhang, H.: Impact of distribution of carboxymethyl substituents in the stabilizer of carboxymethyl cellulose on the stability of acidified milk drinks. Food Hydrocoll. 76, 150–157 (2018)

    Google Scholar 

  37. Lee, J.; Park, S.; Roh, H.-G.; Oh, S.; Kim, S.; Kim, M.; Kim, D.; Park, J.: Preparation and characterization of superabsorbent polymers based on starch aldehydes and carboxymethyl cellulose. Polymers 10, 605 (2018)

    Google Scholar 

  38. Park, J.-S.; An, S.-J.; Jeong, S.-I.; Gwon, H.-J.; Lim, Y.-M.; Nho, Y.-C.: Chestnut honey impregnated carboxymethyl cellulose hydrogel for diabetic ulcer healing. Polymers 9, 248 (2017)

    Google Scholar 

  39. Gasemloo, S.; Khosravi, M.; Sohrabi, M.R.; Dastmalchi, S.; Gharbani, P.: Response surface methodology (RSM) modeling to improve removal of Cr (VI) ions from tannery wastewater using sulfated carboxymethyl cellulose nanofilter. J. Clean. Prod. 208, 736–742 (2019)

    Google Scholar 

  40. Chen, Y.; Long, Y.; Li, Q.; Chen, X.; Xu, X.: Synthesis of high-performance sodium carboxymethyl cellulose-based adsorbent for effective removal of methylene blue and Pb (II). Int. J. Biol. Macromol. 126, 107–117 (2019)

    Google Scholar 

  41. Renuka, P.; Ganga, B.; Hakeem, A.A.: Effect of space and temperature dependent internal heat generation/absorption on Casson fluid flow in the presence of an inclined magnetic field. Malaya. J. Mat. 6, 428–434 (2018)

    MathSciNet  Google Scholar 

  42. Kumar, K.G.; Rudraswamy, N.; Gireesha, B.: Effects of mass transfer on MHD three dimensional flow of a Prandtl liquid over a flat plate in the presence of chemical reaction. Results Phys. 7, 3465–3471 (2017)

    Google Scholar 

  43. Wakif, A.; Chamkha, A.; Animasaun, I.; Zaydan, M.; Waqas, H.; Sehaqui, R.: Novel physical insights into the thermodynamic irreversibilities within dissipative EMHD fluid flows past over a moving horizontal Riga plate in the coexistence of wall suction and Joule heating effects: a comprehensive numerical investigation. Arab. J. Sci. Eng. 1, 16 (2020). https://doi.org/10.1007/s13369-020-04757-3

    Article  Google Scholar 

  44. Saranya, S.; Ragupathi, P.; Ganga, B.; Sharma, R.; Hakeem, A.A.: Non-linear radiation effects on magnetic/non-magnetic nanoparticles with different base fluids over a flat plate. Adv. Powder Technol. 29(9), 1977–1990 (2018)

    Google Scholar 

  45. Nehad, A.S.; Animasaun, I.L.; Wakif, A.; Koriko, O.; Sivaraj, R.; Adegbie, K.; Abdelmalek, Z.; Vaidya, H.; Ijirimoye, A.; Prasad, K.V.: Significance of suction and dual stretching on the dynamics of various hybrid nanofluids: comparative analysis between type I and type II models. Phys. Scr. 95(9), 095205 (2020)

    Google Scholar 

  46. Rahmati, A.R.; Akbari, O.A.; Marzban, A.; Toghraie, D.; Karimi, R.; Pourfattah, F.: Simultaneous investigations the effects of non-Newtonian nanofluid flow in different volume fractions of solid nanoparticles with slip and no-slip boundary conditions. Therm. Sci. Eng. Prog. 5, 263–277 (2018)

    Google Scholar 

  47. Maleki, H.; Safaei, M.R.; Alrashed, A.A.; Kasaeian, A.: Flow and heat transfer in non-Newtonian nanofluids over porous surfaces. J. Therm. Anal. Calorim. 135, 1655–1666 (2019)

    Google Scholar 

  48. Khan, M.I.; Kiyani, M.Z.; Malik, M.Y.; Yasmeen, T.; Khan, M.W.A.; Abbas, T.: Numerical investigation of magnetohydrodynamic stagnation point flow with variable properties. Alex. Eng. J. 55, 2367–2373 (2016)

    Google Scholar 

  49. Wang, C.: The three-dimensional flow due to a stretching flat surface. Phys. Fluids 27, 1915–1917 (1984)

    MathSciNet  MATH  Google Scholar 

  50. Hayat, T.; Shehzad, S.; Alsaedi, A.: Three-dimensional stretched flow of Jeffrey fluid with variable thermal conductivity and thermal radiation. Appl. Math. Mech. 34, 823–832 (2013)

    MathSciNet  MATH  Google Scholar 

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Correspondence to Mohamed R. Eid.

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Eid, M.R. Thermal Characteristics of 3D Nanofluid Flow over a Convectively Heated Riga Surface in a Darcy–Forchheimer Porous Material with Linear Thermal Radiation: An Optimal Analysis. Arab J Sci Eng 45, 9803–9814 (2020). https://doi.org/10.1007/s13369-020-04943-3

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