A heat-transfer model of the behaviour of a thermoacoustic cooler and its surrounding heat-reservoirs is described. Both the real part and the imaginary part of the heat-transfer exponent affect strongly the optimal performance of the cooler. Both the exergy-efficiency and the cooling load decrease with increase of the imaginary part of the complex exponent when the real part is fixed. The optimal zone on the performance of the thermoacoustic cooler is obtained by numerical analysis. The results obtained herein will be useful for the selection of the operation parameters for a real thermoacoustic cooler. (c) 2007 Elsevier Ltd. All rights reserved.