AN INVERSE ANALYSIS FOR ESTIMATING THE TIME-VARYING INLET TEMPERATUREIN LAMINAR-FLOW INSIDE A PARALLEL-PLATE DUCT

An inverse problem utilizing the conjugate gradient method of minimiza tion with adjoint problem is used to estimate the timewise variation o f the inlet temperature of a thermally developing, hydrodynamically de veloped laminar flow between parallel plates by utilizing transient te mperature measurements from a single thermocouple located downstream o f the entrance. It is assumed that there is no prior information avail able on the functional form of time dependence of the inlet temperatur e other than that which can be inferred from the measured downstream t emperatures. The effects of functional form of the inlet temperature, sensor position, magnitude of measurement error and data sampling rate on the accuracy of estimates are examined. In order to examine the ac curacy of the method under most strict conditions, timewise variations in the form of step changes were also studied. The inverse analysis c onsidered here could predict the timewise variation of inlet temperatu re even under such strict conditions. The estimates are notably more a ccurate when the thermocouple is placed near the entrance.