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In this paper a new method based on Pinch Technology is proposed for total cost targeting in Grass-Roots design of heat exchanger networks. This method considers allowable pressure drops and the effect of unequal heat transfer coefficients of streams in the earliest possible step (targeting) of heat exchanger network design. The proposed method uses individual temperature shifting of streams which is related to heat transfer coefficient of streams based on diverse pinch concept. lt also considers the relations between pressure drops, heat transfer coefficients of streams and heat exchanger geometry in shell and tube heat exchangers to satisfy allowable pressure drops and reduce area and cost of heat exchanger networks. This method has been checked by a case study in which the results compared with assumed_h conventional method and fixed pressure drop conventional method .The findings indicate advantage of this new method in comparison with earlier methods.