### Abstract

A method is described for solving steady-state fluid flow and heat transfer problems which are governed by elliptic-type differential equations. A contrived transient version of the steady-state problem is constructed by appending time derivatives to all the participating equations, regardless of whether or not such terms have physical reality. Each time derivative is multiplied by a fictive diffusivity coefficient which is varied during the course of an explicit marching procedure in order to achieve rapid, stable convergence to the steady state. The solution method is applied to a three-component laminar flow in a cylindrical enclosure having one rotating wall and coolant throughflow. Recirculation patterns are set up in the enclosure due to the shearing action of the throughflow and to the rotation of the disk. The surface heat transfer is found to decrease as the Reynolds number of the throughflow increases.

Original language | English (US) |
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Pages (from-to) | 273-287 |

Number of pages | 15 |

Journal | Computers and Fluids |

Volume | 1 |

Issue number | 3 |

DOIs | |

State | Published - 1973 |

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### Cite this

*Computers and Fluids*,

*1*(3), 273-287. https://doi.org/10.1016/0045-7930(73)90011-X

**The contrived transient-explicit method for solving steady-state flows : application to a rotating, recirculating flow.** / de Socio, L. M.; Sparrow, E. M.; Eckert, E. R G.

Research output: Contribution to journal › Article

*Computers and Fluids*, vol. 1, no. 3, pp. 273-287. https://doi.org/10.1016/0045-7930(73)90011-X

}

TY - JOUR

T1 - The contrived transient-explicit method for solving steady-state flows

T2 - application to a rotating, recirculating flow

AU - de Socio, L. M.

AU - Sparrow, E. M.

AU - Eckert, E. R G

PY - 1973

Y1 - 1973

N2 - A method is described for solving steady-state fluid flow and heat transfer problems which are governed by elliptic-type differential equations. A contrived transient version of the steady-state problem is constructed by appending time derivatives to all the participating equations, regardless of whether or not such terms have physical reality. Each time derivative is multiplied by a fictive diffusivity coefficient which is varied during the course of an explicit marching procedure in order to achieve rapid, stable convergence to the steady state. The solution method is applied to a three-component laminar flow in a cylindrical enclosure having one rotating wall and coolant throughflow. Recirculation patterns are set up in the enclosure due to the shearing action of the throughflow and to the rotation of the disk. The surface heat transfer is found to decrease as the Reynolds number of the throughflow increases.

AB - A method is described for solving steady-state fluid flow and heat transfer problems which are governed by elliptic-type differential equations. A contrived transient version of the steady-state problem is constructed by appending time derivatives to all the participating equations, regardless of whether or not such terms have physical reality. Each time derivative is multiplied by a fictive diffusivity coefficient which is varied during the course of an explicit marching procedure in order to achieve rapid, stable convergence to the steady state. The solution method is applied to a three-component laminar flow in a cylindrical enclosure having one rotating wall and coolant throughflow. Recirculation patterns are set up in the enclosure due to the shearing action of the throughflow and to the rotation of the disk. The surface heat transfer is found to decrease as the Reynolds number of the throughflow increases.

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U2 - 10.1016/0045-7930(73)90011-X

DO - 10.1016/0045-7930(73)90011-X

M3 - Article

VL - 1

SP - 273

EP - 287

JO - Computers and Fluids

JF - Computers and Fluids

SN - 0045-7930

IS - 3

ER -