Measurement of the unsteady thermal Green's function in a boundary layer flow: A preliminary theory

Gregg Radtke, Alfonso Ortega, Barry D Ganapol

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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 languageEnglish (US)
Title of host publicationAmerican Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD
PublisherAmerican Society of Mechanical Engineers (ASME)
Pages389-396
Number of pages8
Volume374
Edition4
DOIs
StatePublished - 2003
Event2003 ASME International Mechanical Engineering Congress - Washington, DC., United States
Duration: Nov 15 2003Nov 21 2003

Other

Other2003 ASME International Mechanical Engineering Congress
CountryUnited States
CityWashington, DC.
Period11/15/0311/21/03

Fingerprint

Boundary layer flow
Green's function
Measurement theory
Shear flow
Thermal load
Hot Temperature
Laminar flow
Flow velocity
Velocity measurement
Heat transfer coefficients
Shear stress
Boundary layers
Thermodynamic properties
Boundary conditions
Heat transfer
Finite element method
Fluids

Keywords

  • Boundary layer
  • Forced convection
  • Green's function

ASJC Scopus subject areas

  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

Cite this

Radtke, G., Ortega, A., & Ganapol, B. D. (2003). Measurement of the unsteady thermal Green's function in a boundary layer flow: A preliminary theory. In 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.

American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD. Vol. 374 4. ed. American Society of Mechanical Engineers (ASME), 2003. p. 389-396.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Radtke, G, Ortega, A & Ganapol, BD 2003, Measurement of the unsteady thermal Green's function in a boundary layer flow: A preliminary theory. in 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
Radtke G, Ortega A, Ganapol BD. Measurement of the unsteady thermal Green's function in a boundary layer flow: A preliminary theory. In American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD. 4 ed. Vol. 374. American Society of Mechanical Engineers (ASME). 2003. p. 389-396 https://doi.org/10.1115/IMECE2003-43252
Radtke, Gregg ; Ortega, Alfonso ; Ganapol, Barry D. / Measurement of the unsteady thermal Green's function in a boundary layer flow : A preliminary theory. American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD. Vol. 374 4. ed. American Society of Mechanical Engineers (ASME), 2003. pp. 389-396
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