Two-dimensional inverse problem in estimating heat flux of pin fins

The two-dimensional inverse problem of estimating the unknown heat flux of a pin fin base has been solved using the conjugate gradient method. The advantage of the conjugate gradient method is that no information on the functional form of the unknown quantity is required beforehand. The accuracy of the inverse analysis is examined by using simulated exact and inexact measurements of temperature in an interior location of a pin fin. Numerical results show that good estimations on the heat flux can be obtained for all the test cases considered here. Furthermore, such a technique can be applied to determine the heat flux acting on an internal wall surface, where direct measurements are difficult to make.