The conventional conjugate gradient method is improved to utilize its advantage of high accuracy and fast convergence

and to avoid the complicated differentiating and derivation processes for solving nonlinear inverse heat conduction problems. In the present work

the complex-variable-differentiation method is introduced into the conventional conjugate gradient method

which is employed to precisely calculate the sensitivity coefficients. Transient nonlinear inverse heat conduction problems are solved

and then the boundary conditions are identified. Numerical examples are given to show the effectiveness and high accuracy. Compared with the conventional conjugate gradient method

the present algorithm has the advantage of easier implementation and higher accuracy.