### Abstract

Compared to the heat transfer coefficient, the thermal Green's function concept is a more fundamental method of describing the relationship between local wall heat transfer and wall temperature. It is far more amenable to situations involving strong spatial, temporal, and boundary condition variability. The utility of this methodology has been established, in particular for the analysis of the conjugate heat transfer problem. A necessary element in this technique is an inverse theoretical model to infer the Green's function from laboratory thermal response data. This paper presents preliminary results from a first attempt to develop such a measurement theory to extract local approximations to the unsteady thermal Green's function (UTGF) in 3-D boundary layer flows. The flow model used is a linear shear flow, which is a solution valid in the near wall region of laminar flows, as well as the viscous sublayer region of a turbulent boundary layer. This model is governed by the shear velocity, which is a measure of the local wall shear stress. The solution methodology employs the mathematical theory of Green's function solutions to the energy equation for a general 3-D boundary layer flow, where the UTGF of interest is the thermal response to an impulsive heat load. Analytic methods are used to condense the equation from a 3-D to a 2-D transient PDE, and the reduced equation is solved using a Petrov-Galerkin Finite Element Method. These data are used to construct a numerical UTGF uniquely determined by the shear velocity, flow angle, and the thermodynamic properties of the fluid. An error minimization scheme is proposed to find the appropriate value of the shear velocity, thus providing local UTGF, and shear velocity measurements.

Original language | English (US) |
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Title of host publication | American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD |

Publisher | American Society of Mechanical Engineers (ASME) |

Pages | 389-396 |

Number of pages | 8 |

Volume | 374 |

Edition | 4 |

DOIs | |

State | Published - 2003 |

Event | 2003 ASME International Mechanical Engineering Congress - Washington, DC., United States Duration: Nov 15 2003 → Nov 21 2003 |

### Other

Other | 2003 ASME International Mechanical Engineering Congress |
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Country | United States |

City | Washington, DC. |

Period | 11/15/03 → 11/21/03 |

### Fingerprint

### Keywords

- Boundary layer
- Forced convection
- Green's function

### ASJC Scopus subject areas

- Mechanical Engineering
- Fluid Flow and Transfer Processes

### Cite this

*American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD*(4 ed., Vol. 374, pp. 389-396). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/IMECE2003-43252

**Measurement of the unsteady thermal Green's function in a boundary layer flow : A preliminary theory.** / Radtke, Gregg; Ortega, Alfonso; Ganapol, Barry D.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD.*4 edn, vol. 374, American Society of Mechanical Engineers (ASME), pp. 389-396, 2003 ASME International Mechanical Engineering Congress, Washington, DC., United States, 11/15/03. https://doi.org/10.1115/IMECE2003-43252

}

TY - GEN

T1 - Measurement of the unsteady thermal Green's function in a boundary layer flow

T2 - A preliminary theory

AU - Radtke, Gregg

AU - Ortega, Alfonso

AU - Ganapol, Barry D

PY - 2003

Y1 - 2003

N2 - Compared to the heat transfer coefficient, the thermal Green's function concept is a more fundamental method of describing the relationship between local wall heat transfer and wall temperature. It is far more amenable to situations involving strong spatial, temporal, and boundary condition variability. The utility of this methodology has been established, in particular for the analysis of the conjugate heat transfer problem. A necessary element in this technique is an inverse theoretical model to infer the Green's function from laboratory thermal response data. This paper presents preliminary results from a first attempt to develop such a measurement theory to extract local approximations to the unsteady thermal Green's function (UTGF) in 3-D boundary layer flows. The flow model used is a linear shear flow, which is a solution valid in the near wall region of laminar flows, as well as the viscous sublayer region of a turbulent boundary layer. This model is governed by the shear velocity, which is a measure of the local wall shear stress. The solution methodology employs the mathematical theory of Green's function solutions to the energy equation for a general 3-D boundary layer flow, where the UTGF of interest is the thermal response to an impulsive heat load. Analytic methods are used to condense the equation from a 3-D to a 2-D transient PDE, and the reduced equation is solved using a Petrov-Galerkin Finite Element Method. These data are used to construct a numerical UTGF uniquely determined by the shear velocity, flow angle, and the thermodynamic properties of the fluid. An error minimization scheme is proposed to find the appropriate value of the shear velocity, thus providing local UTGF, and shear velocity measurements.

AB - Compared to the heat transfer coefficient, the thermal Green's function concept is a more fundamental method of describing the relationship between local wall heat transfer and wall temperature. It is far more amenable to situations involving strong spatial, temporal, and boundary condition variability. The utility of this methodology has been established, in particular for the analysis of the conjugate heat transfer problem. A necessary element in this technique is an inverse theoretical model to infer the Green's function from laboratory thermal response data. This paper presents preliminary results from a first attempt to develop such a measurement theory to extract local approximations to the unsteady thermal Green's function (UTGF) in 3-D boundary layer flows. The flow model used is a linear shear flow, which is a solution valid in the near wall region of laminar flows, as well as the viscous sublayer region of a turbulent boundary layer. This model is governed by the shear velocity, which is a measure of the local wall shear stress. The solution methodology employs the mathematical theory of Green's function solutions to the energy equation for a general 3-D boundary layer flow, where the UTGF of interest is the thermal response to an impulsive heat load. Analytic methods are used to condense the equation from a 3-D to a 2-D transient PDE, and the reduced equation is solved using a Petrov-Galerkin Finite Element Method. These data are used to construct a numerical UTGF uniquely determined by the shear velocity, flow angle, and the thermodynamic properties of the fluid. An error minimization scheme is proposed to find the appropriate value of the shear velocity, thus providing local UTGF, and shear velocity measurements.

KW - Boundary layer

KW - Forced convection

KW - Green's function

UR - http://www.scopus.com/inward/record.url?scp=1842533028&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842533028&partnerID=8YFLogxK

U2 - 10.1115/IMECE2003-43252

DO - 10.1115/IMECE2003-43252

M3 - Conference contribution

AN - SCOPUS:1842533028

VL - 374

SP - 389

EP - 396

BT - American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD

PB - American Society of Mechanical Engineers (ASME)

ER -