### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 424-452 |

Number of pages | 29 |

Journal | Journal of computational physics |

Volume | 217 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2006 |

### Keywords

- Nanofluids
- Distributed Lagrange multiplier
- Heat conductivity
- IR-73478
- Fictitious domain method
- Particulate flows
- METIS-232969
- Heat transfer

### Cite this

*Journal of computational physics*,

*217*(2), 424-452. https://doi.org/10.1016/j.jcp.2006.01.016

}

*Journal of computational physics*, vol. 217, no. 2, pp. 424-452. https://doi.org/10.1016/j.jcp.2006.01.016

**A fictitious domain method for particulate flows with heat transfer.** / Yu, Z.; Yu, Zhaosheng; Shao, Xueming; Wachs, Anthony.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - A fictitious domain method for particulate flows with heat transfer

AU - Yu, Z.

AU - Yu, Zhaosheng

AU - Shao, Xueming

AU - Wachs, Anthony

PY - 2006

Y1 - 2006

N2 - The distributed-Lagrange-multiplier/fictitious-domain (DLM/FD) method of Glowinski et al. [R. Glowinski, T.-W. Pan, T.I. Hesla, D.D. Joseph, A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow 25 (1999) 755–794] is extended to deal with heat transfer in particulate flows in two dimensions. The Boussinesq approximation is employed for the coupling between the flow and temperature fields. The fluid-flow equations are solved with the finite-difference projection method on a half-staggered grid. In our operator splitting scheme, the Lagrange multipliers at the previous time level are kept in the fluid equations, and the new Lagrange multipliers for the rigid-body motion constraint and the Dirichlet temperature boundary condition are determined from the reduced saddle-point problem, whereas a very simple scheme based on the fully explicit computation of the Lagrange multiplier is proposed for the problem in which the solid heat conduction inside the particle boundary is also considered. Our code for the case of fixed temperature on the immersed boundary is verified by comparing favorably our results on the natural convection driven by a hot cylinder eccentrically placed in a square box and on the sedimentation of a cold circular particle in a vertical channel to the data in the literature. The code for the case of freely varying temperature on the boundaries of freely moving particles is applied to analyze the motion of a catalyst particle in a box and in particular the heat conductivities of nanofluids and sheared non-colloidal suspensions, respectively. Our preliminary computational results support the argument that the micro-heat-convection in the fluids is primarily responsible for the unusually high heat conductivity of nanofluids. It is shown that the Peclet number plays a negative role in the diffusion-related heat conductivity of a sheared non-colloidal suspension, whereas the Reynolds number does the opposite.

AB - The distributed-Lagrange-multiplier/fictitious-domain (DLM/FD) method of Glowinski et al. [R. Glowinski, T.-W. Pan, T.I. Hesla, D.D. Joseph, A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow 25 (1999) 755–794] is extended to deal with heat transfer in particulate flows in two dimensions. The Boussinesq approximation is employed for the coupling between the flow and temperature fields. The fluid-flow equations are solved with the finite-difference projection method on a half-staggered grid. In our operator splitting scheme, the Lagrange multipliers at the previous time level are kept in the fluid equations, and the new Lagrange multipliers for the rigid-body motion constraint and the Dirichlet temperature boundary condition are determined from the reduced saddle-point problem, whereas a very simple scheme based on the fully explicit computation of the Lagrange multiplier is proposed for the problem in which the solid heat conduction inside the particle boundary is also considered. Our code for the case of fixed temperature on the immersed boundary is verified by comparing favorably our results on the natural convection driven by a hot cylinder eccentrically placed in a square box and on the sedimentation of a cold circular particle in a vertical channel to the data in the literature. The code for the case of freely varying temperature on the boundaries of freely moving particles is applied to analyze the motion of a catalyst particle in a box and in particular the heat conductivities of nanofluids and sheared non-colloidal suspensions, respectively. Our preliminary computational results support the argument that the micro-heat-convection in the fluids is primarily responsible for the unusually high heat conductivity of nanofluids. It is shown that the Peclet number plays a negative role in the diffusion-related heat conductivity of a sheared non-colloidal suspension, whereas the Reynolds number does the opposite.

KW - Nanofluids

KW - Distributed Lagrange multiplier

KW - Heat conductivity

KW - IR-73478

KW - Fictitious domain method

KW - Particulate flows

KW - METIS-232969

KW - Heat transfer

U2 - 10.1016/j.jcp.2006.01.016

DO - 10.1016/j.jcp.2006.01.016

M3 - Article

VL - 217

SP - 424

EP - 452

JO - Journal of computational physics

JF - Journal of computational physics

SN - 0021-9991

IS - 2

ER -