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International Heat Transfer Conference 11

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)


E. Lundgren
Department of Mathematical Physics and Mechanics, Lund Institute of Technology, Lund, Sweden

U. Marksten
Department of Mathematics, LTH Lund University, Lund Sweden

S.-I. Moller
Department of Mathematical Physics and Mechanics, Lund Institute of Technology, Lund, Sweden

DOI: 10.1615/IHTC11.2000
pages 381-386


It has been observed and reported that in pulse combustors of Helmholtz type the heat transfer is two to five times higher than expected. From experiments, where the temperature profile in the tail pipe of a pulse combustor has been measured, we have no indication why the heat transfer should be enhanced. In the tail pipe of a pulse combustor the radial component of the temperature gradient vanishes in the main part of the of the cross-section of the tail pipe except close to the boundary of the pipe. Evidently, a temperature drop along the tail pipe of up to 500°C/m, indicates that the classical linear constitutive assumption of heat conduction, i.e. Fourier's law, is incapable of describing the phenomenon observed. A powerful coupling between the oscillating velocity field and the oscillating temperature field might be able to explain the observed enhanced heat conduction.
In Fourier's law neither a direct dependence of the heat conduction on the velocity and the velocity gradient, nor an interaction between the velocity and temperature field is given. A first extension would be to introduce a more general constitutive relation for the heat conduction vector. For that reason, in order to describe the observed phenomenon, a new non-linear constitutive relation for the heat conduction vector has been suggested. An additional term, dependent on the velocity gradient operating on the temperature gradient, will effect the heat transfer.
To be able to examine the consequences of the new non-linear constitutive relation suggested, a thermo-mechanical pulsating flow between two parallel plates is considered. By approximating the general constitutive equations in the postulated general equations of motion, analytical solutions of the velocity and temperature fields can be found to be in good agreement with experimental results.
The analytical expressions for the velocity and temperature profiles can then be used in the estimation of the heat transfer, which can be compared with experimental observations.

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