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Shape and Orientation Effect on Natural Convection Around a Heated Vertical Cone, Which Loses Heat from All Its Surfaces

  • Research Article-Mechanical Engineering
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Abstract

In this study, we present the idea of natural convection heat transfer from vertical cones with active base (i.e. all the surfaces are contributing in heat transfer process) for laminar flow in the range of Rayleigh number from 103 to 106. We did numerical simulations for different r/l ranging from 0.9 to 0.1 and orientation (tip upward and tip downward) keeping the total heat transfer area same for all the cases. From the numerical results, it can be concluded that average Nusselt number of downward tip cone is more compared to upward tip cone at same Rayleigh number for low r/l and for high r/l both give almost the same Nu when suspended in the air. When the cone is placed on the ground, downward tip cone is always more effective in natural convection than the upward tip cone. Average Nu and heat flux increase at particular Ra with decrease in r/l. A detailed study of the parameters like r/l, Rayleigh number on average Nu, heat flux, heat transfer ratio, flow field, and temperature plume can be found in this work. Finally simple and very accurate correlations for predicting average Nu are developed for all the studied cases of cone with varying r/l and Ra which will be very useful in designing heat transfer equipment.

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Data availability

Data will be made available on request.

Abbreviations

A t :

Total heat transfer surface area (m2)

g :

Acceleration due to gravity (m/s2)

h :

Average convective heat transfer coefficient [W/(m2 K)]

k :

Thermal conductivity of fluid [W/(m K)]

l :

Slant length of cone (m)

L c :

Characteristic or reference length scale = l (m)

Nu:

Average surface Nusselt number based on characteristic length scale

Pr:

Prandtl number

p :

Pressure (N/m2)

Q :

Total heat transfer rate (W)

q :

Heat flux (W/m2)

Ra:

Rayleigh number based on reference length scale

r/l :

Base radius to slant length ratio of cone

T :

Temperature of fluid (K)

T w :

Temperature of cone wall (K)

T ∞ :

Ambient temperature (K)

U c :

Characteristic flow velocity = \(\sqrt {g\beta \left( {T_{{\text{w}}} - T_{\infty } } \right)L_{{\text{c}}} }\) (m/s)

v r :

Flow velocity in the radial direction (m/s)

v z :

Flow velocity in the axial direction (m/s)

r, z :

Radial and axial coordinate of cylindrical system in 2D (m)

α :

Thermal diffusivity (m2/s)

β :

Thermal expansion coefficient (1/K)

μ :

Dynamic viscosity (kg/m s)

ν :

Kinematic viscosity (m2/s)

ρ :

Density (kg/m3

References

  1. Andreozzi, A.; Bianco, N.; Iasiello, M.; Naso, V.: Natural convection in a vertical channel with open-cell foams. J. Phys. Conf. Ser. (2020). https://doi.org/10.1088/1742-6596/1599/1/012013

    Article  Google Scholar 

  2. Chamkha, A.; Veismoradi, A.; Ghalambaz, M.; Talebizadehsardari, P.: Phase change heat transfer in an L-shape heatsink occupied with paraffin-copper metal foam. Appl. Therm. Eng. 177, 115493 (2020). https://doi.org/10.1016/j.applthermaleng.2020.115493

    Article  Google Scholar 

  3. Iasiello, M.; Mameli, M.; Filippeschi, S.; Bianco, N.: Simulations of paraffine melting inside metal foams at different gravity levels with preliminary experimental validation. J. Phys. Conf. Ser. (2020). https://doi.org/10.1088/1742-6596/1599/1/012008

    Article  Google Scholar 

  4. Zhang, L.; Bhatti, M.M.; Michaelides, E.E.: Thermally developed coupled stress particle–fluid motion with mass transfer and peristalsis. J. Therm. Anal. Calorim. (2020). https://doi.org/10.1007/s10973-020-09871-w

    Article  Google Scholar 

  5. Al-Arabi, M.; El-Riedy, M.K.: Natural convection heat transfer from isothermal horizontal plates of different shapes. Int. J. Heat Mass Transf. 19, 1399–1404 (1976). https://doi.org/10.1016/0017-9310(76)90069-7

    Article  Google Scholar 

  6. Churchill, S.W.; Chu, H.H.S.: Correlating equations for laminar and turbulent free convection from a horizontal cylinder. Int. J. Heat Mass Transf. 18, 1049–1053 (1975). https://doi.org/10.1016/0017-9310(75)90222-7

    Article  Google Scholar 

  7. Churchill, S.W.: A comprehensive correlating equation for laminar, assisting, forced and free convection. AIChE J. 23, 10–16 (1977). https://doi.org/10.1002/aic.690230103

    Article  Google Scholar 

  8. Fujii, T.; Imura, H.: Natural-convection heat transfer from a plate with arbitrary inclination. Int. J. Heat Mass Transf. 15, 755–767 (1972). https://doi.org/10.1016/0017-9310(72)90118-4

    Article  Google Scholar 

  9. Flack, R.D.; Brun, K.; Schnipke, R.J.: Measurement and prediction of natural convection velocities in triangular enclosures. Int. J. Heat Fluid Flow. 16, 106–113 (1995). https://doi.org/10.1016/0142-727X(94)00001-S

    Article  Google Scholar 

  10. Kitamura, K.; Kimura, F.: Heat transfer and fluid flow of natural convection adjacent to upward-facing horizontal plates. Int. J. Heat Mass Transf. 38, 3149–3159 (1995). https://doi.org/10.1016/0017-9310(95)00066-I

    Article  Google Scholar 

  11. Kuehn, T.H.; Goldstein, R.J.: Numerical solution to the Navier–Stokes equations for laminar natural convection about a horizontal isothermal circular cylinder. Int. J. Heat Mass Transf. 23, 971–979 (1980). https://doi.org/10.1016/0017-9310(80)90071-X

    Article  MATH  Google Scholar 

  12. Merk, H.J.; Prins, J.A.: Thermal convection in laminary boundary layers I. Appl. Sci. Res. Sect. A 4, 11–24 (1953). https://doi.org/10.1007/BF03184660

    Article  MathSciNet  MATH  Google Scholar 

  13. Hering, R.G.; Grosh, R.J.: Laminar free convection from a non-isothermal cone. Int. J. Heat Mass Transf. 5, 1059–1068 (1962). https://doi.org/10.1016/0017-9310(62)90059-5

    Article  Google Scholar 

  14. Hering, R.G.: Laminar free convection from a non-isothermal cone at low Prandtl numbers. Int. J. Heat Mass Transf. 8, 1333–1337 (1965). https://doi.org/10.1016/0017-9310(65)90059-1

    Article  Google Scholar 

  15. Sparrow, E.M.; De Mello, F.; Guinle, L.: Deviations from classical free convection boundary-layer theory at low prandtl numbers. Int. J. Heat Mass Transf. 11, 1403–1406 (1968). https://doi.org/10.1016/0017-9310(68)90185-3

    Article  MATH  Google Scholar 

  16. Roy, S.: Free convection from a vertical cone at high prandtl numbers. J. Heat Transf. 96, 115–117 (1974). https://doi.org/10.1115/1.3450128

    Article  Google Scholar 

  17. Oosthuizen, P.H.; Donaldson, E.: Free convective heat transfer from vertical cones. J. Heat Transf. 94, 330–331 (1972). https://doi.org/10.1115/1.3449945

    Article  Google Scholar 

  18. Alamgir, M.: Over-all heat transfer from vertical cones in laminar free convection: an approximate method. J Heat Transf. Trans ASME. 101, 174–176 (1979). https://doi.org/10.1115/1.3450912

    Article  Google Scholar 

  19. Pop, I.; Takhar, H.S.: Compressibility effects in laminar free convection from a vertical cone. Appl. Sci. Res. 48, 71–82 (1991). https://doi.org/10.1007/BF01998666

    Article  MATH  Google Scholar 

  20. Lewandowski, W.M.; Szymański, S.; Kubski, P.; Radziemska, E.; Bieszk, H.; Wilczewski, T.: Natural convective heat transfer from isothermal conic. Int. J. Heat Mass Transf. 42, 1895–1907 (1999). https://doi.org/10.1016/S0017-9310(98)00283-X

    Article  MATH  Google Scholar 

  21. Haddad, O.M.; Bany-Youness, A.: Numerical simulation of natural convection flow over parabolic bodies. Int. J. Thermophys. 27, 1590–1608 (2006). https://doi.org/10.1007/s10765-006-0109-3

    Article  Google Scholar 

  22. Lee, S.; Yovanovich, M.M.; Jafarpur, K.: Effects of geometry and orientation on laminar natural convection from isothermal bodies. J. Thermophys. Heat Transf. 5, 208–216 (1991). https://doi.org/10.2514/3.249

    Article  Google Scholar 

  23. Triveni, M.K.; Sen, D.; Panua, R.: Laminar natural convection for thermally active partial side walls in a right-angled triangular cavity. Arab. J. Sci. Eng. 39, 9025–9038 (2014). https://doi.org/10.1007/s13369-014-1418-7

    Article  Google Scholar 

  24. Bapuji, P.; Ekambavanan, K.; Pop, I.: Finite difference analysis of laminar free convection flow past a non isothermal vertical cone. Heat Mass Transf. 44, 517–526 (2008). https://doi.org/10.1007/s00231-007-0266-3

    Article  MATH  Google Scholar 

  25. Eslami, M.; Jafarpur, K.: Laminar free convection heat transfer from isothermal convex bodies of arbitrary shape: a new dynamic model. Heat Mass Transf. 48, 301–315 (2012). https://doi.org/10.1007/s00231-011-0885-6

    Article  Google Scholar 

  26. El Moutaouakil, L.; Boukendil, M.; Zrikem, Z.; Abdelbaki, A.: Natural convection and surface radiation heat transfer in a square cavity with an inner wavy body. Int. J. Thermophys. 41, 1–21 (2020). https://doi.org/10.1007/s10765-020-02688-7

    Article  Google Scholar 

  27. Inc ANSYS: ANSYS Fluent release 15 User’s Guide (2013)

  28. Behera, S.; Acharya, S.; Dash, S.K.: Natural convection heat transfer from linearly, circularly and parabolically bent plates: A study of shape effect. Int. J. Therm. Sci. (2020). https://doi.org/10.1016/j.ijthermalsci.2019.106219

    Article  Google Scholar 

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  1. Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, 721 302, India

    Shibajee Behera & Sukanta K. Dash

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  1. Shibajee Behera
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Behera, S., Dash, S.K. Shape and Orientation Effect on Natural Convection Around a Heated Vertical Cone, Which Loses Heat from All Its Surfaces. Arab J Sci Eng 46, 11615–11631 (2021). https://doi.org/10.1007/s13369-021-05546-2

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