One-Dimensional Analytical Model of the Thermal Accelerometer

A simplified model of the thermal (convective) accelerometer is proposed on the basis of solving two one-dimensional equations of convective heat transfer in adjacent domains. The equations, together with corresponding first-kind boundary conditions, have simple analytical solutions and allow qualitative estimation of some parameters of the device. The distance between temperature sensors that is optimal from the viewpoint of maximum response is evaluated. A dependence of the response on the characteristic linear size of the device is found. The model solution, despite its simplicity, is in a good agreement with analytical and numerical solutions oftwo- and three-dimensional convection-diffusion problems in closed cavities. The shortcomings inherent in one-dimensional statement of the problem are revealed.

References

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