An Inverse Natural Convection Problem in Estimating the Location and Strength of a Heat Source

Abstract

The conjugate gradient method was applied for the two-dimensional inverse natural convection problem to determine the location and strength of the unknown transient heat source in a square cavity. The direct, sensitivity and adjoint problems are solved by a commercial code STAR-CD. The alternate use of the regular and modified conjugate gradient methods are employed to alleviate the difficulty in estimating the value at final time. Numerical computations are performed for simulated measurement data. Results for measurement errors, sensor locations and shapes of heat source strength are presented. In order to examine the effectiveness of the present work, the unknown strength of heat source is chosen in the form of step and triangular functions because the functions containing a step change or sharp corner are generally the most difficult cases to estimate in inverse problems.