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Effect of moving walls on heat transfer and entropy generation in a nanofluid-filled enclosure

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Abstract

In this work, a numerical investigation of mixed convection has been carried out in a two-sided lid-driven enclosure filled with copper–water nanofluid. Three different cases have been discussed depending on the direction of moving vertical walls to analyze the behavior of fluid flow and heat transfer in nanofluid. The buoyancy effects are incorporated using two discrete heat sources placed on the bottom wall maintaining a fixed distance from both the side walls. The stationary part of the bottom wall is kept insulated while other walls are maintained at constant low temperature. A two-dimensional computational visualization technique has been employed to demonstrate the main findings of the presented work. The effect of higher nanoparticle volume fraction (up to 20%) with variations of Reynolds number and Richardson number is studied to find the rate of heat transfer. The results are presented using streamlines, isotherms, and energy flux vectors. The thermodynamic optimization of the system is analyzed by using Nusselt number and entropy generation.

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References

  1. Kakac S, Pramuanjaroenkij A (2016) Single-phase and two-phase treatments of convective heat transfer enhancement with nanofluids: a state-of-the-art review. Int J Thermal Sci 100:75–97

    Article  Google Scholar 

  2. Choi SUS (1995) Enhancing thermal conductivity of fluids with nanoparticles. ASME Fluids Eng Div 251:99–105

    Google Scholar 

  3. Tiwari RK, Das MK (2007) Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int J Heat Mass Transf 50:2002–2018

    Article  MATH  Google Scholar 

  4. Nayak AK, Bhattacharyya S (2011) Double-diffusive convection in a cubical lid-driven cavity with opposing temperature and concentration gradients. Theor Comput Fluid Dyn 26(6):565–581

    Article  Google Scholar 

  5. Maiga SEB, Palm SJ, Nguyen CT, Roy G, Galanis N (2005) Heat transfer enhancement by using nanofluids in forced convection flows. Int J Heat Fluid Flow 26:530–546

    Article  Google Scholar 

  6. Oztop HF, Dagtekin I (2004) Mixed convection in two-sided lid-driven differentially heated square cavity. Int J Heat Mass Transf 47:1761–1769

    Article  MATH  Google Scholar 

  7. Talebi F, Mahmoudi AH, Shahi M (2010) Numerical study of mixed convection flows in a square lid-driven cavity utilizing nanofluid. Int Commun Heat Mass Transf 37:79–90

    Article  Google Scholar 

  8. Muthtamilselvan M, Kandaswamy P, Lee J (2010) Heat transfer enhancement of copper-water nanofluids in a lid-driven enclosure. Commun Nonlinear Sci Numer Simul 15(6):1501–1510

    Article  MathSciNet  MATH  Google Scholar 

  9. Patankar SV (1980) Numerical heat transfer and fluid flow. Hemisphere, Washington, DC

    MATH  Google Scholar 

  10. Sebdani SM, Mahmoodi M, Hashemi SM (2012) Effect of nanofluid variable properties on mixed convection in a square cavity. Int J Thermal Sci 52:112–126

    Article  Google Scholar 

  11. Moumni H, Welhezi H, Djebali R, Sediki E (2015) Accurate finite volume investigation of nanofluid mixed convection in two-sided lid-driven cavity including discrete heat sources. Appl Math Model 39(14,15):4164–4179

    Article  MathSciNet  Google Scholar 

  12. Hooman K (2010) Energy flux vector as new tool for convection visualization. Int J Numer Method Heat Fluid Flow 20:240–249

    Article  Google Scholar 

  13. Nayak RK, Bhattacharyya S, Pop I (2015) Numerical study on mixed convection and entropy generation of Cu water nanofluid in a differentially heated skewed enclosure. Int J Heat Mass Transf 85:620–634

    Article  Google Scholar 

  14. Nayak RK, Bhattacharyya S, Pop I (2015) Numerical study on mixed convection and entropy generation of a nanofluid in a lid-driven square enclosure. ASME J Heat Transf 138(1):012503-1–012503-11

    Article  Google Scholar 

  15. Buongiorno J (2005) Convective transport in nanofluids. ASME J Heat Transf 128(3):240–250

    Article  Google Scholar 

  16. Wong KV, Leon OD (2010) Applications of nanofluids: current and future. Adv Mech Eng 2:519–659

    Google Scholar 

  17. Wen D, Lin G, Vafaei S, Zhang K (2007) Review of nanofluids for heat transfer applications. Particuology 7(2):141–150

    Article  Google Scholar 

  18. Mahian O, Kianifar A, Kalogirou SA, Pop I, Wongwises S (2013) A review of the applications of nanofluids in solar energy. Int J Heat Mass Transf 57(2):582–594

    Article  Google Scholar 

  19. Garoosi F, Jahanshaloo L, Rashidi MM, Badakhsh A, Ali ME (2015) Numerical simulation of natural convection of the nanofluid in heat exchangers using a Buongiorno model. Appl Math Comput 254:183–203

    MathSciNet  Google Scholar 

  20. Garoosi F, Bagheri G, Rashidi MM (2015) Two phase simulation of natural convection and mixed convection of the nanofluid in a square cavity. Powder Technol 275:239–256

    Article  Google Scholar 

  21. Garoosi F, Rohani B, Rashidi MM (2015) Two-phase mixture modeling of mixed convection of nanofluids in a square cavity with internal and external heating. Powder Technol 275:304–321

    Article  Google Scholar 

  22. Bejan A (1979) A study of entropy generation in fundamental convective heat transfer. J Heat Transf 4:718–725

    Article  Google Scholar 

  23. Baytas AC (2000) Entropy generation for natural convection in an inclined porous cavity. Int J Heat Mass Transf 43(12):2089–2099

    Article  MATH  Google Scholar 

  24. Magherbi M, Abbassi H, Brahim AB (2003) Entropy generation at the onset of natural convection. Int J Heat Mass Transf 46(18):3441–3450

    Article  MATH  Google Scholar 

  25. Varol Y, Oztop HF, Koca A (2008) Entropy generation due to conjugate natural convection in enclosures bounded by vertical solid walls with different thicknesses. Int Commun Heat Mass Transf 35(5):648–656

    Article  Google Scholar 

  26. Ilis GG, Mobedi M, Sunden B (2008) Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls. Int Commun Heat Mass Transf 35(6):696–703

    Article  Google Scholar 

  27. Khorasanizadeh H, Nikfar M, Amani J (2013) Entropy generation of Cu water nanofluid mixed convection in a cavity. Eur J Mech B 37:143–152

    Article  MathSciNet  MATH  Google Scholar 

  28. Mahmoudi AH, Shahi M, Talebi F (2010) Effect of inlet and outlet location on the mixed convective cooling inside the ventilated cavity subjected to an external nanofluid. Int Commun Heat Mass Transf 37:1158–1173

    Article  Google Scholar 

  29. Wasp EJ, Kenny JP, Gandhi RL (1977) Solid-liquid flow slurry pipeline transportation. Ser Bulk Mater Handl 1(4):48

    Google Scholar 

  30. Brinkman HC (1952) The viscosity of concentrated suspensions and solutions. J Chem Phys 20(4):571–581

    Article  Google Scholar 

  31. Anandalakshmi R, Basak T (2015) Natural convection in rhombic enclosures with isothermally heated side or bottom wall: entropy generation analysis. Eur J Mech B 54:27–44

    Article  MathSciNet  Google Scholar 

  32. Malik S, Nayak AK (2017) MHD convection and entropy generation of nanofluid in a porous enclosure with sinusoidal heating. Int J Heat Mass Transf 111:329–345

    Article  Google Scholar 

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Acknowledgements

The author Mr. Sumit Malik would like to thank Ministry of Human Resource and Development with Grant Number MHR-02-23-200-429 for their funding.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute Technology of Roorkee, Roorkee, 247667, India

    Sumit Malik & A. K. Nayak

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  1. Sumit Malik
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  2. A. K. Nayak
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Correspondence to A. K. Nayak.

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Malik, S., Nayak, A.K. Effect of moving walls on heat transfer and entropy generation in a nanofluid-filled enclosure. J Eng Math 110, 147–165 (2018). https://doi.org/10.1007/s10665-017-9941-7

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  • DOI: https://doi.org/10.1007/s10665-017-9941-7

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