where Tt is the transducer temperature at any time (◦C); TA is the oil temperature (◦C); Ti is the initial transducer temperature (◦C); t is time (s); A is the area of the transducer (m2); is the density of the transducer (kgm−3); cp is the specific heat of the transducer (J kg−1 K−1); and V is the volume of the transducer (m3).