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Numerical Investigation of Heat Transfer Enhancement in Wavy-Walled Tubes Filled With Porous Media

  • Research Article-Mechanical Engineering
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Abstract

This study investigates heat transfer and pressure drop in wavy-walled tubes filled with porous media under local thermal equilibrium (LTE) conditions. A two-equation k-ω SST turbulence model is implemented for the simulations. A Darcy–Brinkman–Forchheimer (DBF) model simulates the flow within porous domains. Based on Nusselt number, friction factor, and performance evaluation criteria (PEC), effective parameters such as wave amplitude, Darcy number, and particle diameter of porous media are investigated. As a result of the porous material addition to the wake region of wavy-walled tubes, the center of recirculation vortexes is shifted upstream, and the vortex intensity is reduced. Vortexes disappear in some cases. In these regions, the local Nusselt number increases due to the convergence of this phenomenon due to the placement of porous material in the divergent section of the wavy-walled tube. The results show that heat transfer and pressure drop variations are related to the Darcy number and the design point should be outside this region. Also, it was found that the Darcy number reduction increased the interaction between porous material and flow and PEC number decreases as shear stress increases in the convergent section. As a result of reducing the size of porous media particles, there is increased collision between fluid and particles, resulting in streamlines conforming to the tube wall and no reverse low. The results reveal that in this article, the maximum PEC number increases to 1.364, which indicates that affordable energy supply and improvement in energy efficiency are available with new ideas.

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Abbreviations

A s :

Area of the tube wall, (m2)

A w = :

Wave amplitude, (m)

\(c_{{\text{p}}}\) :

Specific heat at constant pressure, (J/kg K)

D :

Tube diameter, (m)

Da:

Darcy number

\(F_{{\text{w}}}\) :

Wave factor, \(\frac{{D_{{{\text{max}}}} }}{{D_{{{\text{min}}}} }} \times \frac{2a}{\lambda }\)

f :

Fanning friction factor

h :

Heat transfer coefficient, (W/m2 K)

\(h_{{\text{p}}}\) :

Porous medium thickness, (m)

K :

Permeability, (m2)

k :

Thermal conductivity, (W/m2 K)

\(k_{{{\text{eff}}}}\) :

Effective thermal conductivity, (W/m2 K)

L :

Length of the tube, (m)

\(\dot{m}\) :

Mass flow rate, (kg/s)

Nu:

Nusselt number

Nu(x):

Local Nusselt number

PEC:

Performance evaluation criteria

\(q^{\prime \prime }\) :

Wall heat flux, (w/m2)

\(q_{m}^{\prime \prime \prime }\) :

Heat generation, (w/m3)

Re:

Reynolds number, \(\rho u_{{{\text{max}}}} D_{{{\text{max}}}} /\mu\)

T :

Temperature, (K)

u :

X-direction velocity, (m/s)

v :

Y-direction velocity, (m/s)

\(v_{{\text{t}}}\) :

Total volume, (m3)

\(v_{{\text{v}}}\) :

The volume of void space, (m3)

w :

Z-direction velocity, (m/s)

X :

Dimensionless length, \(\left( {x/\lambda } \right)\)

\(\varepsilon\) :

Porosity

\(\lambda\) :

Wavelength, (m)

\(\mu\) :

Dynamic viscosity, (kg m/s)

\(\rho\) :

Density, (kg/m3)

\(\sigma_{k}\), \(\sigma_{\omega }\) :

K–ω turbulence model constants for k,ω

eff:

Effective

ex:

Outlet

f:

Fluid

in:

Inlet

w:

Wall

References

  1. Reddy, P.S.; Chamkha, A.J.: Soret and Dufour effects on MHD convective flow of Al2O3–water and TiO2–water nanofluids past a stretching sheet in porous media with heat generation/absorption. Adv. Powder Technol. 27(4), 1207–1218 (2016)

    Google Scholar 

  2. Karbasifar, B.; Akbari, M.; Toghraie, D.: Mixed convection of Water-Aluminum oxide nanofluid in an inclined lid-driven cavity containing a hot elliptical centric cylinder. Int. J. Heat Mass Transf. 116, 1237–1249 (2018)

    Google Scholar 

  3. Toosi, M.H.; Siavashi, M.: Two-phase mixture numerical simulation of natural convection of nanofluid flow in a cavity partially filled with porous media to enhance heat transfer. J. Mol. Liq. 238, 553–569 (2017)

    Google Scholar 

  4. Siavashi, M.; Rostami, A.: Two-phase simulation of non-Newtonian nanofluid natural convection in a circular annulus partially or completely filled with porous media. Int. J. Mech. Sci. 133, 689–703 (2017)

    Google Scholar 

  5. Siavashi, M.; Karimi, K.; Xiong, Q.; Doranehgard, M.H.: Numerical analysis of mixed convection of two-phase non-Newtonian nanofluid flow inside a partially porous square enclosure with a rotating cylinder. J. Therm. Anal. Calorim. 137(1), 267–287 (2019)

    Google Scholar 

  6. Maghsoudi, P.; Siavashi, M.: Application of nanofluid and optimization of pore size arrangement of heterogeneous porous media to enhance mixed convection inside a two-sided lid-driven cavity. J. Therm. Anal. Calorim. 135(2), 947–961 (2019)

    Google Scholar 

  7. Saeedi, A.H.; Akbari, M.; Toghraie, D.: An experimental study on rheological behavior of a nanofluid containing oxide nanoparticle and proposing a new correlation. Physica E 99, 285–293 (2018)

    Google Scholar 

  8. Akhbari, M.; Rahimi, A.; Hatamipour, M.S.: Modeling and experimental study of a triangular channel solar air heater. Appl. Therm. Eng. 170, 114902 (2020)

    Google Scholar 

  9. Cheraghi, M.H.; Ameri, M.; Shahabadi, M.: Numerical study on the heat transfer enhancement and pressure drop inside deep dimpled tubes. Int. J. Heat Mass Transf. 147, 118845 (2020)

    Google Scholar 

  10. Dastmalchi, M.; Sheikhzadeh, G.; Arefmanesh, A.: Optimization of micro-finned tubes in double pipe heat exchangers using particle swarm algorithm. Appl. Therm. Eng. 119, 1–9 (2017)

    Google Scholar 

  11. Rashad, A.; Armaghani, T.; Chamkha, A.J.; Mansour, M.: Entropy generation and MHD natural convection of a nanofluid in an inclined square porous cavity: effects of a heat sink and source size and location. Chin. J. Phys. 56(1), 193–211 (2018)

    Google Scholar 

  12. Mahmoudi, Y.; Karimi, N.: Numerical investigation of heat transfer enhancement in a pipe partially filled with a porous material under local thermal non-equilibrium condition. Int. J. Heat Mass Transf. 68, 161–173 (2014)

    Google Scholar 

  13. Pourrahmani, H.; Moghimi, M.; Siavashi, M.; Shirbani, M.: Sensitivity analysis and performance evaluation of the PEMFC using wave-like porous ribs. Appl. Therm. Eng. 150, 433–444 (2019)

    Google Scholar 

  14. Siavashi, M.; Bahrami, H.R.T.; Saffari, H.: Numerical investigation of porous rib arrangement on heat transfer and entropy generation of nanofluid flow in an annulus using a two-phase mixture model. Numerical Heat Transfer, Part A: Appl.. 71(12), 1251–1273 (2017)

    Google Scholar 

  15. Arabpour, A.; Karimipour, A.; Toghraie, D.: The study of heat transfer and laminar flow of kerosene/multi-walled carbon nanotubes (MWCNTs) nanofluid in the microchannel heat sink with slip boundary condition. J. Therm. Anal. Calorim. 131(2), 1553–1566 (2018)

    Google Scholar 

  16. Rush, T.; Newell, T.; Jacobi, A.: An experimental study of flow and heat transfer in sinusoidal wavy passages. Int. J. Heat Mass Transf. 42(9), 1541–1553 (1999)

    Google Scholar 

  17. Sui, Y.; Teo, C.; Lee, P.S.; Chew, Y.; Shu, C.: Fluid flow and heat transfer in wavy microchannels. Int. J. Heat Mass Transf. 53(13–14), 2760–2772 (2010)

    MATH  Google Scholar 

  18. Laohalertdecha, S.; Wongwises, S.: The effects of corrugation pitch on the condensation heat transfer coefficient and pressure drop of R-134a inside horizontal corrugated tube. Int. J. Heat Mass Transf. 53(13–14), 2924–2931 (2010)

    Google Scholar 

  19. Ahmed, H.E.; Fadhil, O.T.; Jehad, M.G.; Alfellag, M.A.: Enhancement of thermal design of pipe filled partially with porous media using eccentric fluid cores. Arab. J. Sci. Eng. 47, 16171 (2022)

    Google Scholar 

  20. Ramgadia, A.G.; Saha, A.K.: Numerical study of fully developed flow and heat transfer in a wavy passage. Int. J. Therm. Sci. 67, 152–166 (2013)

    Google Scholar 

  21. Pethkool, S.; Eiamsa-Ard, S.; Kwankaomeng, S.; Promvonge, P.: Turbulent heat transfer enhancement in a heat exchanger using helically corrugated tube. Int. Commun. Heat Mass Transfer 38(3), 340–347 (2011)

    Google Scholar 

  22. Nauman, M.M.; Sameer, M.; Mehdi, M.; Iqbal, A.; Esa, Z.: Heat Transfer and Pressure Drop in Wavy-Walled Tubes: A Parameter-BASED CFD Study. Fluids. 5(4), 202 (2020)

    Google Scholar 

  23. Mohamad, A.: Heat transfer enhancements in heat exchangers fitted with porous media Part I: constant wall temperature. Int. J. Therm. Sci. 42(4), 385–395 (2003)

    Google Scholar 

  24. Maerefat, M.; Mahmoudi, S.Y.; Mazaheri, K.: Numerical simulation of forced convection enhancement in a pipe by porous inserts. Heat Transfer Eng. 32(1), 45–56 (2011)

    Google Scholar 

  25. Huang, P.; Yang, C.; Hwang, J.; Chiu, M.: Enhancement of forced-convection cooling of multiple heated blocks in a channel using porous covers. Int. J. Heat Mass Transf. 48(3–4), 647–664 (2005)

    MATH  Google Scholar 

  26. Shi, C.; Wang, M.; Yang, J.; Liu, W.; Liu, Z.: Performance analysis and multi-objective optimization for tubes partially filled with gradient porous media. Appl. Therm. Eng. 188, 116530 (2021)

    Google Scholar 

  27. Mahjoob, S.; Vafai, K.: A synthesis of fluid and thermal transport models for metal foam heat exchangers. Int. J. Heat Mass Transf. 51(15–16), 3701–3711 (2008)

    MATH  Google Scholar 

  28. Hung, T.-C.; Huang, Y.-X.; Yan, W.-M.: Thermal performance of porous microchannel heat sink: Effects of enlarging channel outlet. Int. Commun. Heat Mass Transfer 48, 86–92 (2013)

    Google Scholar 

  29. Hung, T.-C.; Huang, Y.-X.; Yan, W.-M.: Thermal performance analysis of porous-microchannel heat sinks with different configuration designs. Int. J. Heat Mass Transf. 66, 235–243 (2013)

    Google Scholar 

  30. Hung, T.-C.; Yan, W.-M.: Optimization of design parameters for a sandwich-distribution porous-microchannel heat sink. Numerical Heat Transfer, Part A: Applications. 66(3), 229–251 (2014)

    Google Scholar 

  31. Shirvan, K.M.; Ellahi, R.; Mirzakhanlari, S.; Mamourian, M.: Enhancement of heat transfer and heat exchanger effectiveness in a double pipe heat exchanger filled with porous media: Numerical simulation and sensitivity analysis of turbulent fluid flow. Appl. Therm. Eng. 109, 761–774 (2016)

    Google Scholar 

  32. Shirvan, K.M.; Mirzakhanlari, S.; Kalogirou, S.A.; Öztop, H.F.; Mamourian, M.: Heat transfer and sensitivity analysis in a double pipe heat exchanger filled with porous medium. Int. J. Therm. Sci. 121, 124–137 (2017)

    Google Scholar 

  33. Chikh, S.; Allouache, N.: Optimal performance of an annular heat exchanger with a porous insert for a turbulent flow. Appl. Therm. Eng. 104, 222–230 (2016)

    Google Scholar 

  34. Lu, W.;Zhao, C.;Tassou, S. Thermal analysis on metal-foam filled heat exchangers. Part I: Metal-foam filled pipes. International journal of heat and mass transfer. 2006;49(15–16):2751–2761.

  35. Yang, K.;Vafai, K. Restrictions on the validity of the thermal conditions at the porous-fluid interface—an exact solution. Journal of Heat transfer. 2011;133(11).

  36. Yang, C.; Nakayama, A.; Liu, W.: Heat transfer performance assessment for forced convection in a tube partially filled with a porous medium. Int. J. Therm. Sci. 54, 98–108 (2012)

    Google Scholar 

  37. Mahmoudi, Y.; Maerefat, M.: Analytical investigation of heat transfer enhancement in a channel partially filled with a porous material under local thermal non-equilibrium condition. Int. J. Therm. Sci. 50(12), 2386–2401 (2011)

    Google Scholar 

  38. Arasteh, H.; Mashayekhi, R.; Ghaneifar, M.; Toghraie, D.; Afrand, M.: Heat transfer enhancement in a counter-flow sinusoidal parallel-plate heat exchanger partially filled with porous media using metal foam in the channels’ divergent sections. J. Therm. Anal. Calorim. 141(5), 1669–1685 (2020)

    Google Scholar 

  39. Siavashi, M.; Bahrami, H.R.T.; Aminian, E.: Optimization of heat transfer enhancement and pumping power of a heat exchanger tube using nanofluid with gradient and multi-layered porous foams. Appl. Therm. Eng. 138, 465–474 (2018)

    Google Scholar 

  40. Nazar, R.; Tham, L.; Pop, I.; Ingham, D.: Mixed convection boundary layer flow from a horizontal circular cylinder embedded in a porous medium filled with a nanofluid. Transp. Porous Media 86(2), 517–536 (2011)

    Google Scholar 

  41. Mahdavi, M.; Saffar-Avval, M.; Tiari, S.; Mansoori, Z.: Entropy generation and heat transfer numerical analysis in pipes partially filled with porous medium. Int. J. Heat Mass Transf. 79, 496–506 (2014)

    Google Scholar 

  42. Nield, D.A.;Bejan, A. Convection in porous media. Springer (2006)

  43. Alazmi, B.; Vafai, K.: Analysis of variants within the porous media transport models. J Heat Transfer. 122(2), 303–326 (2000)

    Google Scholar 

  44. Menter, F.R.: Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32(8), 1598–1605 (1994)

    Google Scholar 

  45. Bian, Y.; Chen, L.; Zhu, J.; Li, C.: Effects of dimensions on the fluid flow and mass transfer characteristics in wavy-walled tubes for steady flow. Heat Mass Transf. 49(5), 723–731 (2013)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 8415683111, Iran

    Mahdi Amini, Mohammad Reza Tavakoli & Iman Chitsaz

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  1. Mahdi Amini
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Correspondence to Mohammad Reza Tavakoli.

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Amini, M., Tavakoli, M.R. & Chitsaz, I. Numerical Investigation of Heat Transfer Enhancement in Wavy-Walled Tubes Filled With Porous Media. Arab J Sci Eng 48, 12541–12553 (2023). https://doi.org/10.1007/s13369-023-07878-7

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