Construction of three-dimensional temperature distribution using a network of ultrasonic transducers

Although the ultrasonic technique for measuring temperature distributions has drawn much attention in recent years, most studies that adopt this technique focus on two-dimensional (2D) systems. Mathematically, extending from 2D to 3D requires higher construction-performing algorithms, as well as more complicated, but extremely crucial, designs of ultrasonic transducer layouts. Otherwise the ill condition of governing-equation matrices will become more serious. Here, we aim at constructing 3D temperature distributions by using a network of properly-installed ultrasonic transducers that can be controlled to transmit and receive ultrasound. In addition, the proposed method is capable of performing this construction procedure in real time, thus monitoring transient temperature distributions and guarantee the safety of operations related to heating or burning. Numerical simulations include constructions for four kinds of temperature distributions, as well as corresponding qualitative and quantitative analyses. Finally, our study offers a guide in developing non-intrusive experimental methods that measure 3D temperature distributions in real time.