numerical solution to a two-dimensional linear inverse heat conduction problem by conjugate gradient method

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). some heat transfer problems cannot be solved by non-numerical methods. therefore, using numerical methods, a wider range of applied andengineering problems can be modeled and solved. in this paper, the conjugate gradient method is used numerically to estimate of the surface flux using temperature distribution in a two-dimensional heat transfer problem and solve the governing equations. adjust by stopping repetitions at the level where the goal is the least squares, and minimizing the gap between the calculated and measured temperature, just below the noise threshold. that data is infected.compared to other numerical methods developed in, current cgm is more efficient and stable when reversing noisy data. the results show that this method efficiently minimizes the amount of error in the two-dimensional inverse problem with high stability.