The conjugate gradient method of minimization is applied successfully in the present optimal control algorithm in determining the optimal boundary control function for a concurrent flow problem based on the desired thermal entry length and fluid temperatures. The validity of the present optimal control analysis is examined by means of numerical experiments.. Different desired thermal entry length and fluid temperature distributions are given in three test cases and the corresponding optimal control heat fluxes are determined. The results show that the optimal boundary heat fluxes can be obtained with an arbitrary initial guess within seconds of CPU time on a Pentium III-600 MHz PC.