Acta Mechanica

, Volume 230, Issue 1, pp 201–211 | Cite as

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

  • Rahul Ramdas Ramteke
  • Nanda KishoreEmail author
Original Paper


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.

List of symbols


Knudsen number (dimensionless)


Nusselt number (dimensionless)


Pressure (dimensionless)


Peclet number (dimensionless)


Prandtl number (dimensionless)


Radial distance (dimensionless)


Radius of sphere (m)


Reynolds number (dimensionless)

\(R_{\infty }\)

Radius of freestream boundary (dimensionless)


Temperature at freestream (K)


Temperature at the surface of sphere (K)


Free stream velocity (m/s)


r-component of velocity (dimensionless)

\(v_{\theta }\)

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

Greek symbols

\(\beta \)

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)


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Chemical EngineeringIndian Institute of Technology GuwahatiGuwahatiIndia

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