### Abstract

Language | English |
---|---|

Pages | 1-14 |

Number of pages | 14 |

Journal | Review of Applied Physics |

Volume | 1 |

Issue number | 1 |

Publication status | Published - 2012 |

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### Keywords

- thermal convection
- analytic solutions
- navier-stokes equations

### Cite this

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*Review of Applied Physics*, vol. 1, no. 1, pp. 1-14.

**Exact solutions for thermal problems : buoyancy, marangoni, vibrational and magnetic-field-controlled flows.** / Lappa, Marcello.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Exact solutions for thermal problems

T2 - Review of Applied Physics

AU - Lappa, Marcello

PY - 2012

Y1 - 2012

N2 - In general, the thermal‐convection (Navier‐Stokes and energy) equations are nonlinear partial differential equations that in most cases require the use of complex algorithms in combination with opportune discretization techniques for obtaining reliable numerical solutions. There are some cases, however, in which such equations admit analytical solutions. Such exact solutions have enjoyed a widespread use in the literature as basic states for determining the linear stability limits in some idealized situations. This review article provides a synthetic review of such analytical expressions for a variety of situations of interest in materials science (especially crystal growth and related disciplines), including thermogravitational (buoyancy), thermocapillary (Marangoni), thermovibrational convection as well as “mixed” cases and flow controlled via static and uniform magnetic fields.

AB - In general, the thermal‐convection (Navier‐Stokes and energy) equations are nonlinear partial differential equations that in most cases require the use of complex algorithms in combination with opportune discretization techniques for obtaining reliable numerical solutions. There are some cases, however, in which such equations admit analytical solutions. Such exact solutions have enjoyed a widespread use in the literature as basic states for determining the linear stability limits in some idealized situations. This review article provides a synthetic review of such analytical expressions for a variety of situations of interest in materials science (especially crystal growth and related disciplines), including thermogravitational (buoyancy), thermocapillary (Marangoni), thermovibrational convection as well as “mixed” cases and flow controlled via static and uniform magnetic fields.

KW - thermal convection

KW - analytic solutions

KW - navier-stokes equations

M3 - Article

VL - 1

SP - 1

EP - 14

JO - Review of Applied Physics

JF - Review of Applied Physics

SN - 2327-1604

IS - 1

ER -