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              <p>Nonlinear temperature field near the stack ends of a standing-wavethermoacoustic refrigeratorArganthaël Bersona,⇑, Gaëlle Poignandb, Philippe Blanc-Benonc, Geneviève Comte-BellotcaDepartment of Chemistry, University of Durham, South Road, Durham DH1 3LE, United KingdombLaboratoire d’Acoustique de l’Université du Main, UMR CNRS 6613, Avenue Olivier Messiaen, 72085 Le Mans Cedex 9, FrancecLaboratoire de Mécanique des Fluides et d’Acoustique, UMR CNRS 5509, École Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully-Cedex, Francearticle  infoArticle history:Received 4 January 2011Received in revised form 27 May 2011Available online 28 June 2011Keywords:ThermoacousticsTemperature-fluctuation measurementsConstant-voltage anemometryOscillating flowsabstractThe nonlinear temperature field in the vicinity of the stack of a standing-wave thermoacoustic refriger-ator is investigated both theoretically and experimentally. First, the problem is addressed theoretically bya one-dimensional nonlinear model that predicts the generation of thermal harmonics near the ends ofthe stack. The model relies on a relaxation-time approximation to describe transverse heat transferbetween the stack walls and the working fluid. It extends a previous model proposed by [Gusev et al.,Thermal wave harmonics generation in the hydrodynamical heat transport in thermoacoustics, J. Acoust.Soc. Am. 109 (2001) pp. 84–90], by including the effect of axial conduction on temperature fluctuations.Second, the nonlinear temperature field is investigated experimentally. The amplitude of temperaturefluctuations behind the stack at the fundamental frequency and second harmonic are measured usingcold-wire anemometry. The measurements rely on a procedure recently developed by the authors thatallows a full correction of the thermal inertia of the sensor. Experimental results are in good agreementwith the predictions of the model. The generation of thermal harmonics behind the stack is thus vali-dated. The influence of the Péclet number on the thermal field, which depends on the diffusivity of theworking fluid and on the acoustic frequency and pressure level, is also demonstrated.</p>
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