Convective Heat Transfer of Wires and Springs for Use in SMA Heat Engines

One type of shape memory allow (SMA) heat engine utilizes a continuous loop of a SMA spring that cycles between hot and cold air reservoirs. As such, an understanding of convective heat transfer to and from the SMA spring is vital for modeling of a SMA heat engine, yet we were unable to find any heat transfer data or correlations for helical springs in the open literature. To fill that need, we present experiments to characterize and quantify the heat transfer coefficients of wires and springs in oblique, air cross-flows.

The experimental setup consists of a steel specimen of a representative size and geometry (helical springs and straight wires) subjected to an air cross-flow in a wind tunnel. Joule heating is applied to the specimen, and the effective heat transfer coefficient is calculated from the input electrical power, measured specimen electrical resistance and measured airflow velocity. The approach is similar to hot-wire anemometry, but here the air velocity is known and we seek the effective heat transfer by solving a nonlinear heat equation with temperature-dependent coefficients. An extensive data set is collected for specimens of four different wire diameters, air speeds between 0 and 16 m/s, angles of attack spanning perpendicular to parallel flow, and spring axial stretch ratios between 2 and 16. Correlations are derived for the relevant dimensionless parameters: Nusselt number, Reynolds number, angle of attack, and stretch ratio. The results on straight wires agree well with known correlations, and the results on springs show an interesting non-monotonic dependence on angle of attack.