Shape memory alloys (SMAs) are metals that undergoa change

Chapter 5, Problem 5.31

(choose chapter or problem)

Shape memory alloys (SMAs) are metals that undergoa change in crystalline structure within a relatively nar-row temperature range. A phase transformation frommartensiteto austenitecan induce relatively largechanges in the overall dimensions of the SMA. Hence,SMAs can be employed as mechanical actuators. Con-sider an SMA rod that is initially Di?2 mm in diame-ter, Li?40 mm long, and at a uniform temperature ofTi?320 K. The specific heat of the SMA varies signif-icantly with changes in the crystalline phase, hence c varies with the temperature of the material. For aparticular SMA, this relationship is well described byc?500 J/kg?K3630 J/kg?Ke(?0.808 K?1|T?336K|). Thedensity and thermal conductivity of the SMA material are??8900 kg/m3and k?23 W/m?K, respectively.The SMA rod is exposed to a hot gas character-ized by T??350 K, h?250 W/m2?K. Plot the rodtemperature versus time for 0?t?60 s for the cases of variable and constant (c?500 J/kg?K) specific heats.Determine the time needed for the rod temperature toexperience 95% of its maximum temperature change.Hint:Neglect the change in the dimensions of the SMArod when calculating the thermal response of the rod.