Analytical modelling of transient processes in thermal microsensors

Abstract

An analytical method is developed to determine the frequency response of thermal microsensors on various input actions. The method has the following algorithm. In a microsensor, the domain of modelling is marked out. This domain is divided into the regions with homogeneous parameters. For each region the non-steady-state heat conduction equation is obtained that is solved by means of the time Fourier transform. The heat flux densities between the regions are determined using adjoint boundary conditions in the frequency domain. After that, the analytical expression for the frequency response of the microsensor is obtained. The model is applied to the concrete membrane thermal microsensors, for which the modulus and argument of the frequency response and the time dependency of the output voltage for the step pulse input signal are determined.