A 2-D INVERSE METHOD FOR SIMULTANEOUS ESTIMATION OF THE INLET TEMPERATURE AND WALL HEAT-FLUX IN A LAMINAR CIRCULAR DUCT FLOW

A two-dimensional inverse analysis is presented for the estimation of the inlet temperature of the fluid flow and wall Beat flux in a therma lly developing hydrodynamically developed laminar flow in a duct. The inverse analysis is based on Be temperature reading located at a strea m inside Be duct at several different points. At the beginning of the study, finite difference methods are employed to discretize the proble m, and then a linear inverse model is constructed to identify Be unkno wn conditions. The present approach is to rearrange the matrix forms o f the differential governing equation and estimate the inlet temperatu re of the fluid and unknown surface conditions of the duct. The linear least squares method is adopted to find the solution. The advantage o f applying this method in inverse analysis is that no prior informatio n is needed on the functional form of the unknown quantities, no initi al guess is required, and the number of iterations in Be calculation p rocess is limited to one. The effects of sensor position, magnitude of measurement error, and number of measurements on Be accuracy of estim ates are examined. The results show that the preferred position of the sensor is closer to Be inlet region and only few measuring points are sufficient to estimate the wall heat flux and inlet temperatures of B e fluid when the measurement errors are neglected. When the measuremen t errors are considered, more measuring points are needed in order to increase the congruence of Be estimated results to exact solutions.