In this paper, an approach for the optimum design of heat exchangers has been presented. Traditional design method of heat exchangers involves many trials in order to meet design specifications. This can be avoided through the present design method, which takes the minimization of annual total cost as a design objective. In alternative optimum design methods, such as Lagrange multiplier method, by changing one variable at a time and using a trial-error or a graphical method, optimum results are obtained in a long time. In the present design optimization problem, the total annual cost has been taken as the objective function and heat balance, and rate equation have been taken as equal constraint. The method using the penalty function transforms the constrained problem into a single unconstrained problem. To solve the optimal problem, the method of steepest descent has been used. Initial design variables include the tube-inside coefficient of heat transfer, tube-outside coefficient of heat transfer, temperature difference and outside tube area of heat transfer. The changes in variables are considered simultaneously to reach an optimum solution. The results show that the present approach is a powerful tool for optimum design of heat exchangers and is expected to be beneficial to energy industry. Copyright (C) 2004 John Wiley Sons, Ltd.