Modeling of thermoelectric heat transfer in shape memory alloy actuators: Transient and multiple cycle solutions

In this paper we study the transient and multiple cycle solutions of one-dimensional symmetric thermoelectric shape memory alloy (SMA) actuators. From the model proposed by Bhattacharya et al. 1], an approximately equivalent simpler model governed by an integro-differential equation is derived first, to describe the temperature distribution in SMA. Then a numerical algorithm is proposed to solve the integro-differential equation. It is found that for the transient cooling problem with constant electric current density of magnitude |J| there is a critical value J₀ of |J| such that when |J|>J₀, the temperature in SMA may not be always decreasing. The heat transfer problem and the resulting phase transition of SMA, induced by a piecewise constant electric current source, are also studied. It is found that there exist restrictions on the maximum and minimum values of the current density J ff a repeated complete phase transition to take place in SMA. Explicit expressions for the critical values of J are derived and their physical implications are discussed.