Analytical modelling of temperature distribution in resistive thin-film thermal sensors

The method of modelling the temperature distribution in resistive thin-film thermal sensors is presented. This method is based upon the division of the sensor into the unit subdomains whose structure is substituted by an equivalent structure. In its turn, the equivalent structure of the unit subdomain is divided into four rectangular regions. For each region, the analytical expression of the temperature distribution is determined using the Fourier method. In addition, each heat flux density between the adjacent regions and between the regions and the ambient air is defined as the sum of orthogonal functions with unknown weighting coefficients. To find the unknown weighting coefficients the adjoint boundary conditions on the boundaries between the adjacent regions and the Newton boundary conditions on the boundaries between the regions and the ambient air are used. In general, the determination of the weighting coefficients is reduced to solving a system of linear equations. The present method is used to determine the temperature distribution in the realistic resistive thin-film thermal sensor and the dependencies of the overheating temperature in the centre of meander strips of this sensor on a number of the parameters: the measuring current, the thermal conductivity and the thickness of the substrate, the convective heat transfer coefficient, the surface temperature of an object under investigation, the width of the meander strip, and the distance between meander strips.