This research present an iterative approach that can estimate the boundary condition from the temperature measured at the interior point of the fluid field in the inverse natural convection problems. Based on the proposed method, the undetermined boundary condition is first denoted as the unknown variables in a set of nonlinear equations, which are formulated from the measured temperature and the calculated temperature of the inverse problem. Then, a modified Newton-Raphson method is used to estimate the unknown boundary condition. In the example problem, the close agreement between the exact solutions and the estimated results shows the potential of the proposed model in finding the accurate value of the boundary condition in the inverse natural convection problems.

a b s t r a c tA direct error vector analysis of inverse heat conduction problem is presented to detect the measured noise. Based on the reverse matrix approach that the inverse problem is solved directly in a linear domain, and the error vector is formulated from the difference between the measured temperature and the estimated temperature. There is no prior knowledge on the exact solution while the error vector is constructed. The error vector is used to investigate the consistence of the measured data in the domain and lead to detect the noise data. Furthermore, the proper number of the undetermined variable is able to suggest based on the mean value of the error vector and the value of the condition number of the reverse matrix. In the first example, a test problem with the measurement noise is presented. The estimated result is influent by the noise globally. The result shows that the value of error vector is changed significantly at the coordinate of the measurement noise appeared. In other words, the error vector analysis is able to identify the noise data. In the second example, the proper number of series expansion terms is investigated. From the result, it shows that the number of expansion terms with the small mean value and condition number can better approximate to the unknown condition. It means that the proposed method is able to suggest a proper number of expansion terms when the function of the recovered boundary is unknown.

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