The inverse estimation of the thermal behavior and the viscosity of fluid between two horizontal concentric cylinders with rotating inner cylinder

This study is intended to provide an inverse approach for estimating the viscosity of fluid and thermal behavior of the concentric cylinders. Finite-difference methods are first employed to discredit the problem domain and then a linear inverse model is constructed to identify the condition for the viscosity of fluid and thermal behavior of the concentric cylinders. The present approach is to rearrange the matrix form of differential governing equation and to estimate coefficients of unknown conditions. Then, the linear least-squares error method is adopted to find the solution. Excluding measurement error, the inverse values from the present study are in excellent agreement with the direct solutions regardless of where the measurement points are located. When the measurement errors are considered, more measuring points are needed in order to increase the congruence of the estimated results to exact solutions. The advantage of applying this method in inverse analysis is that no prior information is needed on the functional form of the unknown quantities, and initial guess and iteration are not required.