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Flow and heat transfer in non-Newtonian nanofluids over porous surfaces

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Abstract

In the present study, heat transfer and fluid flow of a pseudo-plastic non-Newtonian nanofluid over permeable surface has been solved in the presence of injection and suction. Similarity solution method is utilized to convert the governing partial differential equations into ordinary differential equations, which then is solved numerically using Runge–Kutta–Fehlberg fourth–fifth order (RKF45) method. The Cu, CuO, TiO2 and Al2O3 nanoparticles are considered in this study along with sodium carboxymethyl cellulose (CMC)/water as base fluid. Validation has been done with former numerical results. The influence of power-law index, volume fraction of nanoparticles, nanoparticles type and permeability parameter on nanofluid flow and heat transfer was investigated. The results of the study illustrated that the flow and heat transfer of non-Newtonian nanofluid in the presence of suction and injection has different behaviors. For injection and the impermeable plate, the non-Newtonian nanofluid shows a better heat transfer performance compared to Newtonian nanofluid. However, changing the type of nanoparticles has a more intense influence on heat transfer process during suction. It was also observed that in injection, contrary to the other two cases, the usage of non-Newtonian nanofluid can decrease heat transfer in all cases.

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Abbreviations

a :

Constant

c :

Constant

C p :

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

f :

Non-dimensional stream function

f w :

Constant for transpiration rate

h :

Heat transfer coefficient (W m−2 K−1)

k :

Thermal conductivity (W m−1 K−1)

Pr:

Prandtl number

n :

The power-law exponent

T :

Temperature of the fluid (K)

U ∞ :

Velocity of the free stream (ms−1)

u, v :

Components of velocity in x and y directions (ms−1)

x :

Coordinate along the plate (m)

y :

Coordinate normal to the plate surface (m)

α :

Thermal diffusivity (m2 s−1)

η :

Variable for similarity solution

θ :

Non-dimensional temperature

μ :

Dynamic viscosity (kg m−1 s−1)

ν :

Kinematic viscosity (m2 s−1)

ρ :

Fluid density (kg m−3)

φ :

Volume fraction of nanoparticles

ψ :

Stream function

f :

Fluid

w:

Condition at the surface of the plate

∞:

Ambient condition

nf :

Nanofluid

s :

Solid

References

  1. Zainali A, Tofighi N, Shadloo MS, Yildiz M. Numerical investigation of Newtonian and non-Newtonian multiphase flows using ISPH method. Comput Methods Appl Mech Eng. 2013;254:99–113.

    Article  Google Scholar 

  2. Sui J, Zheng L, Zhang X, Chen G. Mixed convection heat transfer in power law fluids over a moving conveyor along an inclined plate. Int J Heat Mass Transf. 2015;85:1023–33.

    Article  Google Scholar 

  3. Jalil M, Asghar S. Flow of power-law fluid over a stretching surface: a Lie group analysis. Int J Non-Linear Mech. 2013;48:65–71.

    Article  Google Scholar 

  4. Ahmed J, Mahmood T, Iqbal Z, Shahzad A, Ali R. Axisymmetric flow and heat transfer over an unsteady stretching sheet in power law fluid. J Mol Liq. 2016;221:386–93.

    Article  CAS  Google Scholar 

  5. Guha A, Pradhan K. Natural convection of non-Newtonian power-law fluids on a horizontal plate. Int J Heat Mass Transf. 2014;70:930–8.

    Article  Google Scholar 

  6. Megahed AM. Flow and heat transfer of a non-Newtonian power-law fluid over a non-linearly stretching vertical surface with heat flux and thermal radiation. Meccanica. 2015;50:1693–700.

    Article  Google Scholar 

  7. Kishan N, Reddy BS. MHD effects on non-Newtonian power-law fluid past a continuously moving porous flat plate with heat flux and viscous dissipation. Int J Appl Mech Eng. 2013;18:425–45.

    Article  Google Scholar 

  8. Srinivasacharya D, Reddy GS. Chemical reaction and radiation effects on mixed convection heat and mass transfer over a vertical plate in power-law fluid saturated porous medium. J Egypt Math Soc. 2016;24:108–15.

    Article  Google Scholar 

  9. Kannan T, Moorthy MB. Effects of variable viscosity on power-law fluids over a permeable moving surface with slip velocity in the presence of heat generation and suction. J Appl Fluid Mech. 2016;9:2791–801.

    Article  Google Scholar 

  10. El-Aziz MA, Afify AA. Lie group analysis of hydromagnetic flow and heat transfer of a power-law fluid over stretching surface with temperature-dependent viscosity and thermal conductivity. Int J Mod Phys C. 2016;27:1650150.

    Article  CAS  Google Scholar 

  11. Kavitha P, Kishan N. Suction/injection effects on MHD flow of a non-Newtonian power-law fluid past a continuously moving porous flat plate with heat flux and viscous dissipation. Int J Appl Comput Math. 2017;3:2389–408.

    Article  Google Scholar 

  12. Ahmed A, Siddique JI, Sagheer M. Dual solutions in a boundary layer flow of a power law fluid over a moving permeable flat plate with thermal radiation, viscous dissipation and heat generation/absorption. Fluids. 2018;3:6.

    Article  CAS  Google Scholar 

  13. Saritha K, Rajasekhar MN, Reddy BS. Heat and mass transfer of laminar boundary layer flow of non-Newtonian power law fluid past a porous flat plate with Soret and Dufour effects. Phys Sci Int J. 2016;11:1–13.

    Article  Google Scholar 

  14. Nejad MM, Javaherdeh K, Moslemi M. MHD mixed convection flow of power law non-Newtonian fluids over an isothermal vertical wavy plate. J Magn Magn Mater. 2015;389:66–72.

    Article  CAS  Google Scholar 

  15. Rajput GR, Prasad JK, Timol MG. Similarity flow solution of MHD boundary layer model for non-Newtonian power-law fluids over a continuous moving surface. Gen. 2014;24:97–102.

    Google Scholar 

  16. Naikoti K, Borra SR. Quasi-linearization approach to MHD effects on boundary layer flow of power-law fluids past a semi infinite flat plate with thermal dispersion. Int J Nonlinear Sci. 2011;11:301–11.

    Google Scholar 

  17. RamReddy C, Naveen P, Srinivasacharya D. nonlinear convective flow of non-Newtonian fluid over an inclined plate with convective surface condition: a Darcy–Forchheimer model. Int J Appl Comput Math. 2018;4:51.

    Article  Google Scholar 

  18. Mahmoud MA. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Math Comput Model. 2011;54:1228–37.

    Article  Google Scholar 

  19. Li B, Zheng L, Zhang X. Heat transfer in pseudo-plastic non-Newtonian fluids with variable thermal conductivity. Energy Convers Manag. 2011;52:355–8.

    Article  Google Scholar 

  20. Yazdi MH, Hashim I, Sopian KB. Slip boundary layer flow of a power-law fluid over moving permeable surface with viscous dissipation and prescribed surface temperature. Int Rev Mech Eng. 2014;8:502–10.

    Google Scholar 

  21. Si X, Li H, Shen Y, Zheng L. Effects of nonlinear velocity slip and temperature jump on pseudo-plastic power-law fluid over moving permeable surface in presence of magnetic field. Appli Math Mech. 2017;38:333–42.

    Article  Google Scholar 

  22. Choi SU, Eastman JA. Enhancing thermal conductivity of fluids with nanoparticles. Argonne: Argonne National Lab; 1995.

    Google Scholar 

  23. Safaei MR, Ahmadi G, Goodarzi MS, Safdari Shadloo M, Goshayeshi HR, Dahari M. Heat transfer and pressure drop in fully developed turbulent flows of graphene nanoplatelets–silver/water nanofluids. Fluids. 2016;1:20.

    Article  CAS  Google Scholar 

  24. Rashidi MM, Nasiri M, Shadloo MS, Yang Z. Entropy generation in a circular tube heat exchanger using nanofluids: effects of different modeling approaches. Heat Transf Eng. 2017;38:853–66.

    Article  CAS  Google Scholar 

  25. Goodarzi M, Amiri A, Goodarzi MS, Safaei MR, Karimipour A, Languri EM, Dahari M. Investigation of heat transfer and pressure drop of a counter flow corrugated plate heat exchanger using MWCNT based nanofluids. Int Commun Heat Mass Transf. 2015;66:172–9.

    Article  CAS  Google Scholar 

  26. Bahmani MH, Sheikhzadeh G, Zarringhalam M, Akbari OA, Alrashed AA, Shabani GA, Goodarzi M. Investigation of turbulent heat transfer and nanofluid flow in a double pipe heat exchanger. Adv Powder Technol. 2018;29(2):273–82.

    Article  CAS  Google Scholar 

  27. Safaei MR, Gooarzi M, Akbari OA, Shadloo MS, Dahari M. Performance evaluation of nanofluids in an inclined ribbed microchannel for electronic cooling applications. In: Sohel Murshed SM, editor. Electronics cooling. InTech; 2016. https://doi.org/10.5772/62898. https://mts.intechopen.com/books/electronics-cooling/performance-evaluation-of-nanofluids-in-an-inclined-ribbed-microchannel-for-electronic-cooling-appli.

  28. Karimipour A, D’Orazio A, Shadloo MS. The effects of different nano particles of Al2O3 and Ag on the MHD nano fluid flow and heat transfer in a microchannel including slip velocity and temperature jump. Phys E. 2017;86:146–53.

    Article  CAS  Google Scholar 

  29. Nojoomizadeh M, D’Orazio A, Karimipour A, Afrand M, Goodarzi M. Investigation of permeability effect on slip velocity and temperature jump boundary conditions for FMWNT/Water nanofluid flow and heat transfer inside a microchannel filled by a porous media. Phys E. 2018;97:226–38.

    Article  CAS  Google Scholar 

  30. Heydari A, Akbari OA, Safaei MR, Derakhshani M, Alrashed AA, Mashayekhi R, Shabani GA, Zarringhalam M, Nguyen TK. The effect of attack angle of triangular ribs on heat transfer of nanofluids in a microchannel. J Therm Anal Calorim. 2018;131:2893–912.

    Article  CAS  Google Scholar 

  31. Goshayeshi HR, Goodarzi M, Dahari M. Effect of magnetic field on the heat transfer rate of kerosene/Fe2O3 nanofluid in a copper oscillating heat pipe. Exp Therm Fluid Sci. 2015;68:663–8.

    Article  CAS  Google Scholar 

  32. Khodabandeh E, Safaei MR, Akbari S, Akbari OA, Alrashed AA. Application of nanofluid to improve the thermal performance of horizontal spiral coil utilized in solar ponds: geometric study. Renew Energy. 2018;122:1–6.

    Article  CAS  Google Scholar 

  33. Goodarzi M, Safaei MR, Vafai K, Ahmadi G, Dahari M, Kazi SN, Jomhari N. Investigation of nanofluid mixed convection in a shallow cavity using a two-phase mixture model. Int J Therm Sci. 2014;75:204–20.

    Article  CAS  Google Scholar 

  34. Abedini E, Zarei T, Afrand M, Wongwises S. Experimental study of transition flow from single phase to two phase flow boiling in nanofluids. J Mol Liq. 2017;231:11–9.

    Article  CAS  Google Scholar 

  35. Abedini E, Zarei T, Rajabnia H, Kalbasi R, Afrand M. Numerical investigation of vapor volume fraction in subcooled flow boiling of a nanofluid. J Mol Liq. 2017;238:281–9.

    Article  CAS  Google Scholar 

  36. Afrand M, Abedini E, Teimouri H. Experimental investigation and simulation of flow boiling of nanofluids in different flow directions. Phys E. 2017;87:248–53.

    Article  CAS  Google Scholar 

  37. Goodarzi M, Kherbeet AS, Afrand M, Sadeghinezhad E, Mehrali M, Zahedi P, Wongwises S, Dahari M. Investigation of heat transfer performance and friction factor of a counter-flow double-pipe heat exchanger using nitrogen-doped, graphene-based nanofluids. Int Commun Heat Mass Transf. 2016;76:16–23.

    Article  CAS  Google Scholar 

  38. Esfe MH, Saedodin S, Naderi A, Alirezaie A, Karimipour A, Wongwises S, Goodarzi M, Bin Dahari M. Modeling of thermal conductivity of ZnO-EG using experimental data and ANN methods. Int Commun Heat Mass Transf. 2015;63:35–40.

    Article  CAS  Google Scholar 

  39. Afrand M. Experimental study on thermal conductivity of ethylene glycol containing hybrid nano-additives and development of a new correlation. Appl Therm Eng. 2017;110:1111–9.

    Article  CAS  Google Scholar 

  40. Esfahani JA, Safaei MR, Goharimanesh M, De Oliveira LR, Goodarzi M, Shamshirband S, Bandarra Filho EP. Comparison of experimental data, modelling and non-linear regression on transport properties of mineral oil based nanofluids. Powder Technol. 2017;317:458–70.

    Article  CAS  Google Scholar 

  41. Dardan E, Afrand M, Isfahani AM. Effect of suspending hybrid nano-additives on rheological behavior of engine oil and pumping power. Appl Therm Eng. 2016;109:524–34.

    Article  CAS  Google Scholar 

  42. Afrand M, Najafabadi KN, Sina N, Safaei MR, Kherbeet AS, Wongwises S, Dahari M. Prediction of dynamic viscosity of a hybrid nano-lubricant by an optimal artificial neural network. Int Commun Heat Mass Transf. 2016;76:209–14.

    Article  CAS  Google Scholar 

  43. Nasiri H, Jamalabadi MY, Sadeghi R, Safaei MR, Nguyen TK, Shadloo MS. A smoothed particle hydrodynamics approach for numerical simulation of nano-fluid flows. J Therm Anal Calorim. 2018. https://doi.org/10.1007/s10973-018-7022-4.

    Article  Google Scholar 

  44. Shamshirband S, Malvandi A, Karimipour A, Goodarzi M, Afrand M, Petković D, Dahari M, Mahmoodian N. Performance investigation of micro-and nano-sized particle erosion in a 90° elbow using an ANFIS model. Powder Technol. 2015;284:336–43.

    Article  CAS  Google Scholar 

  45. Hajmohammadi MR, Maleki H, Lorenzini G, Nourazar SS. Effects of Cu and Ag nano-particles on flow and heat transfer from permeable surfaces. Adv Powder Technol. 2015;26:193–9.

    Article  CAS  Google Scholar 

  46. Akbari OA, Toghraie D, Karimipour A, Safaei MR, Goodarzi M, Alipour H, Dahari M. Investigation of rib’s height effect on heat transfer and flow parameters of laminar water–Al2O3 nanofluid in a rib-microchannel. Appl Math Comput. 2016;290:135–53.

    Google Scholar 

  47. Arani AA, Akbari OA, Safaei MR, Marzban A, Alrashed AA, Ahmadi GR, Nguyen TK. Heat transfer improvement of water/single-wall carbon nanotubes (SWCNT) nanofluid in a novel design of a truncated double-layered microchannel heat sink. Int J Heat Mass Transf. 2017;113:780–95.

    Article  CAS  Google Scholar 

  48. Afrand M, Nadooshan AA, Hassani M, Yarmand H, Dahari M. Predicting the viscosity of multi-walled carbon nanotubes/water nanofluid by developing an optimal artificial neural network based on experimental data. Int Commun Heat Mass Transf. 2016;77:49–53.

    Article  CAS  Google Scholar 

  49. Yarmand H, Gharehkhani S, Shirazi SF, Goodarzi M, Amiri A, Sarsam WS, Alehashem MS, Dahari M, Kazi SN. Study of synthesis, stability and thermo-physical properties of graphene nanoplatelet/platinum hybrid nanofluid. Int Commun Heat Mass Transf. 2016;77:15–21.

    Article  CAS  Google Scholar 

  50. Vafaei M, Afrand M, Sina N, Kalbasi R, Sourani F, Teimouri H. Evaluation of thermal conductivity of MgO-MWCNTs/EG hybrid nanofluids based on experimental data by selecting optimal artificial neural networks. Phys E. 2017;85:90–6.

    Article  CAS  Google Scholar 

  51. Safaei MR, Safdari Shadloo M, Goodarzi MS, Hadjadj A, Goshayeshi HR, Afrand M, Kazi SN. A survey on experimental and numerical studies of convection heat transfer of nanofluids inside closed conduits. Adv Mech Eng. 2016;8:1687814016673569.

    Article  CAS  Google Scholar 

  52. Safaei MR, Jahanbin A, Kianifar A, Gharehkhani S, Kherbeet AS, Goodarzi M, Dahari M. Mathematical modeling for nanofluids simulation: a review of the latest works. In: Akbar NS, editor. Modeling and simulation in engineering sciences. InTech; 2016. https://doi.org/10.5772/64154. https://mts.intechopen.com/books/modeling-and-simulation-in-engineering-sciences/mathematical-modeling-for-nanofluids-simulation-a-review-of-the-latest-works.

  53. Hosseini SM, Safaei MR, Goodarzi M, Alrashed AA, Nguyen TK. New temperature, interfacial shell dependent dimensionless model for thermal conductivity of nanofluids. Int J Heat Mass Transf. 2017;114:207–10.

    Article  CAS  Google Scholar 

  54. Gorla RS, Kumari M. Mixed convection flow of a non-Newtonian nanofluid over a non-linearly stretching sheet. J Nanofluids. 2012;1:186–95.

    Article  CAS  Google Scholar 

  55. Lin Y, Zheng L, Zhang X. Radiation effects on Marangoni convection flow and heat transfer in pseudo-plastic non-Newtonian nanofluids with variable thermal conductivity. Int J Heat Mass Transf. 2014;77:708–16.

    Article  CAS  Google Scholar 

  56. Ramesh GK, Chamkha AJ, Gireesha BJ. Magnetohydrodynamic flow of a non-Newtonian nanofluid over an impermeable surface with heat generation/absorption. J Nanofluids. 2014;3:78–84.

    Article  CAS  Google Scholar 

  57. Uddin MJ, Ferdows M, Bég OA. Group analysis and numerical computation of magneto-convective non-Newtonian nanofluid slip flow from a permeable stretching sheet. Appl Nanosci. 2014;4:897–910.

    Article  CAS  Google Scholar 

  58. Lin Y, Zheng L, Zhang X, Ma L, Chen G. MHD pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation. Int J Heat Mass Transf. 2015;84:903–11.

    Article  CAS  Google Scholar 

  59. Sandeep N, Kumar BR, Kumar MJ. A comparative study of convective heat and mass transfer in non-Newtonian nanofluid flow past a permeable stretching sheet. J Mol Liq. 2015;212:585–91.

    Article  CAS  Google Scholar 

  60. Madhu M, Kishan N, Chamkha A. Boundary layer flow and heat transfer of a non-Newtonian nanofluid over a non-linearly stretching sheet. Int J Numer Methods Heat Fluid Flow. 2016;26:2198–217.

    Article  Google Scholar 

  61. Shadloo MS, Hadjadj A. Laminar-turbulent transition in supersonic boundary layers with surface heat transfer: a numerical study. Numer Heat Transf Part A Appl. 2017;72:40–53.

    Article  CAS  Google Scholar 

  62. Mabood F, Ibrahim SM, Rashidi MM, Shadloo MS, Lorenzini G. Non-uniform heat source/sink and Soret effects on MHD non-Darcian convective flow past a stretching sheet in a micropolar fluid with radiation. Int J Heat Mass Transf. 2016;93:674–82.

    Article  Google Scholar 

  63. Ishak A, Nazar R, Pop I. Mixed convection boundary layer flow adjacent to a vertical surface embedded in a stable stratified medium. Int J Heat Mass Transf. 2008;51:3693–5.

    Article  CAS  Google Scholar 

  64. Zhang H. A study of the boundary layer on a continuous moving surface in power law fluids. University of Science and Technology Beijing, China; 2008.

  65. Jin DX, Wu YH, Zou JT. Studies on heat transfer to pseudoplastic fluid in an agitated tank with helical ribbon impeller. Petro-Chem Equip. 2000;29:7–9.

    Google Scholar 

  66. Abu-Nada E. Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step. Int J Heat Fluid Flow. 2008;29:242–9.

    Article  CAS  Google Scholar 

  67. Zheng L, Zhang X, He J. Suitable heat transfer model for self-similar laminar boundary layer in power law fluids. J Therm Sci. 2004;13:150–4.

    Article  Google Scholar 

  68. Oztop HF, Abu-Nada E. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int J Heat Fluid Flow. 2008;29:1326–36.

    Article  Google Scholar 

  69. Ishak A, Nazar R, Pop I. Local similarity solutions for laminar boundary layer flow along a moving cylinder in a parallel stream. In: Kapur D, editor. Computer mathematics. Lecture notes in computer science, vol 5081. Berlin, Heidelberg: Springer; 2008.

    Google Scholar 

  70. Shadloo MS, Kimiaeifar A, Bagheri D. Series solution for heat transfer of continuous stretching sheet immersed in a micropolar fluid in the existence of radiation. Int J Numer Methods Heat Fluid Flow. 2013;23:289–304.

    Article  Google Scholar 

  71. Shadloo MS, Kimiaeifar A. Application of homotopy perturbation method to find an analytical solution for magnetohydrodynamic flows of viscoelastic fluids in converging/diverging channels. Proc Inst Mech Eng Part C J Mech Eng Sci. 2011;225:347–53.

    Article  CAS  Google Scholar 

  72. Enns RH, McGuire GC, Greene RL. Nonlinear physics with Maple for scientists and engineers. Comput Phys. 1997;11:451–3.

    Article  Google Scholar 

  73. Ishak A. Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition. Appl Math Comput. 2010;217:837–42.

    Google Scholar 

  74. Abu-Nada E, Oztop HF. Effects of inclination angle on natural convection in enclosures filled with Cu–water nanofluid. Int J Heat Fluid Flow. 2009;30:669–78.

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Hamid Maleki

  2. Division of Computational Physics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Mohammad Reza Safaei

  3. Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Mohammad Reza Safaei

  4. Department of Automotive and Marine Engineering Technology, College of Technological Studies, The Public Authority for Applied Education and Training, Adailiyah, Kuwait

    Abdullah A. A. A. Alrashed

  5. Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran

    Alibakhsh Kasaeian

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  1. Hamid Maleki
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Correspondence to Mohammad Reza Safaei.

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Maleki, H., Safaei, M.R., Alrashed, A.A.A.A. et al. Flow and heat transfer in non-Newtonian nanofluids over porous surfaces. J Therm Anal Calorim 135, 1655–1666 (2019). https://doi.org/10.1007/s10973-018-7277-9

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