### Abstract

The stability of internally heated inclined plane parallel shear flows is examined numerically for the case of finite value of the Prandtl number, Pr. The transition in a vertical channel has already been studied for 0≤Pr≤100 with or without the application of an external pressure gradient, where the secondary flow takes the form of travelling waves (TWs) that are spanwise-independent (see works of Nagata and Generalis). In this work, in contrast to work already reported (J. Heat Trans. T. ASME 124 (2002) 635-642), we examine transition where the secondary flow takes the form of longitudinal rolls (LRs), which are independent of the steamwise direction, for Pr=7 and for a specific value of the angle of inclination of the fluid layer without the application of an external pressure gradient. We find possible bifurcation points of the secondary flow by performing a linear stability analysis that determines the neutral curve, where the basic flow, which can have two inflection points, loses stability. The linear stability of the secondary flow against three-dimensional perturbations is also examined numerically for the same value of the angle of inclination by employing Floquet theory. We identify possible bifurcation points for the tertiary flow and show that the bifurcation can be either monotone or oscillatory. © 2003 Académie des sciences. Published by Elsevier SAS. All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 9-16 |

Number of pages | 8 |

Journal | Comptes Rendus: Mecanique |

Volume | 332 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2004 |

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### Keywords

- Floquet theory
- heat transfer
- internal heat
- secondary instability
- shear flow
- transition

### Cite this

*Comptes Rendus: Mecanique*,

*332*(1), 9-16. https://doi.org/10.1016/j.crme.2003.10.011

}

*Comptes Rendus: Mecanique*, vol. 332, no. 1, pp. 9-16. https://doi.org/10.1016/j.crme.2003.10.011

**Transition in plane parallel shear flows heated internally.** / Generalis, Sotos C.; Nagata, Masato.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Transition in plane parallel shear flows heated internally

AU - Generalis, Sotos C.

AU - Nagata, Masato

PY - 2004/1

Y1 - 2004/1

N2 - The stability of internally heated inclined plane parallel shear flows is examined numerically for the case of finite value of the Prandtl number, Pr. The transition in a vertical channel has already been studied for 0≤Pr≤100 with or without the application of an external pressure gradient, where the secondary flow takes the form of travelling waves (TWs) that are spanwise-independent (see works of Nagata and Generalis). In this work, in contrast to work already reported (J. Heat Trans. T. ASME 124 (2002) 635-642), we examine transition where the secondary flow takes the form of longitudinal rolls (LRs), which are independent of the steamwise direction, for Pr=7 and for a specific value of the angle of inclination of the fluid layer without the application of an external pressure gradient. We find possible bifurcation points of the secondary flow by performing a linear stability analysis that determines the neutral curve, where the basic flow, which can have two inflection points, loses stability. The linear stability of the secondary flow against three-dimensional perturbations is also examined numerically for the same value of the angle of inclination by employing Floquet theory. We identify possible bifurcation points for the tertiary flow and show that the bifurcation can be either monotone or oscillatory. © 2003 Académie des sciences. Published by Elsevier SAS. All rights reserved.

AB - The stability of internally heated inclined plane parallel shear flows is examined numerically for the case of finite value of the Prandtl number, Pr. The transition in a vertical channel has already been studied for 0≤Pr≤100 with or without the application of an external pressure gradient, where the secondary flow takes the form of travelling waves (TWs) that are spanwise-independent (see works of Nagata and Generalis). In this work, in contrast to work already reported (J. Heat Trans. T. ASME 124 (2002) 635-642), we examine transition where the secondary flow takes the form of longitudinal rolls (LRs), which are independent of the steamwise direction, for Pr=7 and for a specific value of the angle of inclination of the fluid layer without the application of an external pressure gradient. We find possible bifurcation points of the secondary flow by performing a linear stability analysis that determines the neutral curve, where the basic flow, which can have two inflection points, loses stability. The linear stability of the secondary flow against three-dimensional perturbations is also examined numerically for the same value of the angle of inclination by employing Floquet theory. We identify possible bifurcation points for the tertiary flow and show that the bifurcation can be either monotone or oscillatory. © 2003 Académie des sciences. Published by Elsevier SAS. All rights reserved.

KW - Floquet theory

KW - heat transfer

KW - internal heat

KW - secondary instability

KW - shear flow

KW - transition

UR - http://www.scopus.com/inward/record.url?scp=0842306112&partnerID=8YFLogxK

U2 - 10.1016/j.crme.2003.10.011

DO - 10.1016/j.crme.2003.10.011

M3 - Article

VL - 332

SP - 9

EP - 16

JO - Comptes Rendus: Mecanique

JF - Comptes Rendus: Mecanique

SN - 1631-0721

IS - 1

ER -