Analytical Research of Temperature Distribution and Thermal Stresses within Circular Micro-hotplates - 于慧俐 李绪泉 胡松涛 (东华大学学报（英文版）, 2016)
Micro-hotplate （MHP） technology is one key part in the manufacturing of gas sensors. The pursuit of analytical solutions for the temperature distribution and also thermal stresses within the MHP is of intrinsic scientific interest. In this study, analytical solutions for the temperature field, and both radial and tangential stresses and van Mises stress for circular MHP were obtained. Two geometries were considered： one had a circular heater at the center and the other had a circular heater at the center and an annular heater within the membrane part. Internal heat generation was incorporated in the energy equation for the MHP and different values of convection heat transfer coefficient were used at the upper and lower surfaces of the MHP. It has been shown that the MHP with two heaters can provide more uniform temperature field compared with the MHP with one heater. The main objective of this work is to provide an exact analytical solution for thermal stresses within the circular micro-hcater with a simple geometry as a benchmark, from mathematical point of view, against which the accuracy of new numerical schemes can be checked. To make sure that the analytical procedure is correct, the analytical results are checked against numerical solutions derived from finite element simulation. Since the analytical models for the temperature field and especially for the thermal stresses of MHP ace seldom investigated in the literature, the obtained results are believed to facilitate the design and performance evaluation of MHPs as well.