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Combined effects of thermal jump and momentum slip on heat transfer phenomena of unbounded spherical particles

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Abstract

Combined effects of momentum slip and thermal jump on the forced convective heat transfer from spherical particles to Newtonian fluids are reported based on a numerical study. The governing dimensionless conservation equations of the mass, momentum, and energy are solved using in-house computational fluid dynamics-based solver, namely simplified marker and cell algorithm implemented on a staggered grid arrangement in spherical coordinates. The range of parameters considered herein is Reynolds number (\(1 \le Re \le 200\)), dimensionless momentum slip parameter (\(0.01 \le \lambda _\mathrm{v}\le 100\)), dimensionless thermal jump parameter (\(0.01 \le \lambda _\mathrm{T}\le 10\)), and Prandtl number (\(1 \le Pr \le 100\)). The isotherm contours along with the local and surface-mean Nusselt numbers are presented for better understanding of heat transfer phenomena around the spherical particles under the influence of momentum and thermal jump at the interface. The main conclusion of this study is that the effects of the momentum slip parameter and temperature jump on heat transfer act in opposite manner; i.e., large momentum slip (small \(\lambda _\mathrm{v}\) values) on a solid surface increases the convection while a large thermal jump decreases the rate of heat transfer due to the reduction in the magnitude of the temperature gradient at the solid–fluid interface. Finally, the effect of a thermal jump on the rate of heat transfer is more severe than that of velocity slip condition, especially when \(\lambda _\mathrm{T} > 1\) for any combination of the Reynolds and Prandtl numbers.

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Abbreviations

Kn :

Knudsen number (dimensionless)

Nu :

Nusselt number (dimensionless)

p :

Pressure (dimensionless)

Pe :

Peclet number (dimensionless)

Pr :

Prandtl number (dimensionless)

r :

Radial distance (dimensionless)

R :

Radius of sphere (m)

Re :

Reynolds number (dimensionless)

\(R_{\infty }\) :

Radius of freestream boundary (dimensionless)

\(T_{\mathrm{o}}\) :

Temperature at freestream (K)

\(T_\mathrm{w}\) :

Temperature at the surface of sphere (K)

\(U_{\mathrm{o}}\) :

Free stream velocity (m/s)

\(v_{\mathrm{r}}\) :

r-component of velocity (dimensionless)

\(v_{\theta }\) :

\(\theta \)-component of velocity (dimensionless)

\(\beta \) :

Tangential momentum accommodation coefficient (dimensionless)

\(\gamma \) :

Specific heat ratio (dimensionless)

\(\lambda _\mathrm{v}\) :

Momentum slip parameter (dimensionless)

\(\lambda _\mathrm{T}\) :

Thermal jump parameter (dimensionless)

\(\mu \) :

Dynamic viscosity of fluid (dimensionless)

\(\rho \) :

Density of fluid (kg/m\(^{3})\)

\(\sigma _\mathrm{T}\) :

Thermal accommodation coefficient (dimensionless)

References

  1. Meijer, H.E.H., Verbraak, C.P.J.M.: Modeling of extrusion with slip boundary conditions. Polym. Eng. Sci. 28, 758–772 (1988)

    Article  Google Scholar 

  2. Vinogradov, G.V., Malkin, A.Y., Yanovskil, Y.G., Borisenkova, E.K., Yarlykov, B.V., Berezhnaya, G.V.: Viscoelastic properties and flow of narrow distribution polybutadienes and polyisoprenes. J. Polym. Sci. A 10, 1061–1084 (1972)

    Article  Google Scholar 

  3. Kalika, D., Denn, M.M.: Wall slip and extrudate distortion in linear low-density polyethylene. J. Rheol. 31, 815–834 (1987)

    Article  Google Scholar 

  4. Kalyon, D.M., Gevgilili, H.: Wall slip and extrudate distortion of three polymer melts. J. Rheol. 47, 683–699 (2003)

    Article  Google Scholar 

  5. Mennig, G.: Visual observations of slip in flow of polymer melts. J Macromol. Sci. 14, 231–240 (1977)

    Article  Google Scholar 

  6. den Otter, J.L.: Rheological measurements on two uncrosslinked, unfilled synthetic rubbers. Rheol. Acta 14, 329–336 (1975)

    Article  Google Scholar 

  7. Neto, C., Evans, D.R., Bonaccurso, E., Butt, H.-J., Craig, V.S.J.: Boundary slip in Newtonian liquid: A review of experimental studies. Rep. Prog. Phys. 68, 2859–2897 (2005)

    Article  Google Scholar 

  8. Palani, N., Ramalingam, V., Ramadoss, G., Seeniraj, R.V.: Study of slip velocity and application of drift-flux model to slip velocity in a liquid–solid circulating fluidized bed. Adv. Powder Technol. 22, 77–85 (2011)

    Article  Google Scholar 

  9. Hatzikiriakos, S.G., Dealy, J.M.: Wall slip of molten high density polyethylene: II. Capillary rheometer studies. J. Rheol. 36, 703–741 (1992)

    Article  Google Scholar 

  10. Hatzikiriakos, S.G., Dealy, J.M.: Wall slip of molten high density polyethylene: I. Sliding plate rheometer studies. J. Rheol. 35, 497–523 (1991)

    Article  Google Scholar 

  11. Luk, S., Mutharasan, R., Apelian, D.: Experimental observation of wall slip: tube and packed bed flow. Ind. Eng. Chem. Res. 26, 1609–1616 (1987)

    Article  Google Scholar 

  12. Tang, H.S., Kalyon, D.M.: Unsteady circular tube flow of compressible polymeric liquids subject to pressure-dependent wall slip. J. Rheol. 52, 507–525 (2008)

    Article  Google Scholar 

  13. Denn, M.M.: Extrusion instabilities and wall slip. Ann. Rev. Fluid Mech. 22, 265–287 (2001)

    Article  Google Scholar 

  14. Cohen, Y., Metzner, A.B.: Apparent slip flow of polymer solutions. J. Rheol. 29, 67–102 (1985)

    Article  Google Scholar 

  15. Gibbs, S.J., James, K.L., Hall, L.D., Haycock, D.E., Frith, W.J., Ablett, S.: Rheometry and detection of apparent wall slip for Poiseuille flow of polymer solutions and particulate dispersions by nuclear magnetic resonance velocimetry. J. Rheol. 40, 425–440 (1996)

    Article  Google Scholar 

  16. Pit, R., Hervet, H., Leger, L.: Friction and slip of a simple liquid at a solid surface. Tribol. Lett. 7, 147–152 (1999)

    Article  Google Scholar 

  17. Mooney, M.: Explicit formulas for slip and fluidity. J. Rheol. 2, 210–222 (1931)

    Article  Google Scholar 

  18. Chhabra, R.P., Richardson, J.F.: Non-Newtonian Flow and Applied Rheology: Engineering Applications, 2nd edn. Butterworth-Heinemann, Hungary (2008)

    Google Scholar 

  19. Hao, P.F., Wong, C., Yao, Z.H., Zhu, K.Q.: Laminar drag reduction in hydrophobic microchannels. Chem. Eng. Technol. 32, 912–918 (2009)

    Article  Google Scholar 

  20. Khajenoori, M., Safdari, J., Asl, A.H., Mallah, M.H.: Slip and characteristic velocities in a horizontal pulsed-plate extraction column. Chem. Eng. Technol. 38, 1783–1792 (2015)

    Article  Google Scholar 

  21. Kishore, N., Ramteke, R.R.: Forced convective heat transfer from spheres to Newtonian fluids in steady axisymmetric flow regime with velocity slip at fluid–solid interface. Int. J. Therm. Sci. 105, 206–217 (2016)

    Article  Google Scholar 

  22. Neto, C., Evans, D.R., Bonaccurso, E., Butt, H.J., Craig, V.S.J.: Boundary slip in Newtonian liquid: a review of experimental studies. Rep. Prog. Phys. 68, 2859–2897 (2005)

    Article  Google Scholar 

  23. Sochi, T.: Slip at fluid–solid interface. Poly. Rev. 51, 309–340 (2011)

    Article  Google Scholar 

  24. Barnes, H.A.: A review of the slip (wall depletion) of polymer solutions, emulsions and particle suspensions in viscometers: its cause, character, and cure. J. Non-Newton. Fluid Mech. 56, 221–251 (1995)

    Article  Google Scholar 

  25. Luo, H., Pozrikidis, C.: Effect of surface slip on Stokes flow past a spherical particle in infinite fluid and near a plane wall. J. Eng. Math. 62, 1–21 (2008)

    Article  MathSciNet  Google Scholar 

  26. Trofa, M., D’Avino, G., Hulsen, M.A., Greco, F., Mahanthesh, P.L.M.: Numerical simulations of the dynamics of a slippery particle in Newtonian and viscoelastic fluids subjected to shear and Poiseuille flows. J. Non-Newton. Fluid Mech. 228, 46–54 (2016)

    Article  MathSciNet  Google Scholar 

  27. Hall, R.O.A., Martin, D.G.: The evaluation of temperature jump distances and thermal accommodation coefficients from measurements of the thermal conductivity of UO2 packed sphere beds. Nucl. Eng. Des. 101, 249–258 (1987)

    Article  Google Scholar 

  28. Kishore, N., Ramteke, R.R.: Slip in flows of power-law liquids past smooth spherical particles. Acta Mech. 226, 2555–2571 (2015)

    Article  MathSciNet  Google Scholar 

  29. Ramteke, R.R., Kishore, N.: Computational fluid dynamics study on forced convective heat transfer phenomena of spheres in power-law liquids with velocity slip at the interface. Heat Transf. Eng. 39, 162–179 (2018)

    Article  Google Scholar 

  30. Kandlikar, S.G., Garimella, S., Li, D., Colin, S., King, M.R.: Heat Transfer and Fluid Flow in Minichannels and Microchannels. Elsevier, Kidlington (2006)

    Google Scholar 

  31. Smoluchowski, M.: Ueber Wärmeleitung in verdünnten Gasen. Ann. Phys. Chem. 64, 101–130 (1898)

    Article  Google Scholar 

  32. Zade, A.Q., Renksizbulut, M., Friedman, J.: Boundary conditions for multi-component slip-flows based on the kinetic theory of gases. In: Proceedings of the Sixth International ASME Conference on Nanochannels, Microchannels and Minichannels, ICNMM 2008, Darmstadt, Germany, June 23–25 (2008)

  33. Gokcen, T., MacCormack, R.W.: Nonequilibrium effects for Hypersonic transitional flows Using continuum approach. AIAA Paper No. 1987–1115. Presented at the 27th Aerospace Sciences Meeting, p. 1989. Reno, NV, Jan (1987)

  34. Mohajer, B., Aliakbar, V., Shams, M., Moshfegh, A.: Heat transfer analysis of a microspherical particle in the slip flow regime by considering variable properties. Heat Trans. Eng. 36, 596–610 (2015)

    Article  Google Scholar 

  35. Taylor, T.D.: Heat transfer from single spheres in a low Reynolds number slip flow. Phys. Fluids 6, 7–12 (1963)

    Google Scholar 

  36. Strom, H., Sasic, S.: Heat transfer effects on particle motion under rarefied conditions. Int. J. Heat Fluid Flow 43, 277–284 (2013)

    Article  Google Scholar 

  37. Mimaki, H., Endo, Y., Takashima, Y.: Heat transfer from a sphere to rarefied gas mixture. Int. J. Heat Mass Trans. 9, 1435–1448 (1966)

    Article  Google Scholar 

  38. Kavanau, L.L., Drake, R.M.: Heat Transfer from Spheres to a Rarefied Gas in Subsonic Flow. California University, Berkeley (1953)

    Google Scholar 

  39. Vasudeviah, M., Balamurugan, K.: Heat transfer in a slip-flow past a sphere. Fluid Dyn. Res. 22, 281–296 (1998)

    Article  MathSciNet  Google Scholar 

  40. Martin, M.J., Boyd, I.D.: Momentum and heat transfer in a laminar boundary layer with slip flow. J. Thermophys. Heat Trans. 20, 1–6 (2006)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India

    Rahul Ramdas Ramteke & Nanda Kishore

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  1. Rahul Ramdas Ramteke
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Ramteke, R.R., Kishore, N. Combined effects of thermal jump and momentum slip on heat transfer phenomena of unbounded spherical particles. Acta Mech 230, 201–211 (2019). https://doi.org/10.1007/s00707-018-2309-x

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  • DOI: https://doi.org/10.1007/s00707-018-2309-x

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