This paper presents an extension of a mathematical model for particle attrition inside a fluidized bed by a supersonic air jet and its application to optimize the nozzle design. A new method to calculate grinding efficiency is presented. Also, heat transfer is included in the model because of the large interfacial temperature difference. Numerical simulations are conducted to investigate various nozzle designs, i.e. a range of area ratios (indicative of the jet being over-or under-expanded) and nozzle expansion angles, and different bed fluidization velocities. It is found that the perfectly expanded nozzle (the exit pressure equal to the outside pressure) provides better attrition performance than over- and under-expanded jets. The nozzle expansion angle also has an influence on the grinding efficiency: narrow angled nozzles have higher grinding efficiency. In addition, the analysis of various bed fluidization velocities indicates that increasing the velocity results in a modest improvement of the grinding efficiency. (C) 2011 Elsevier B.V. All rights reserved.