Table 4 The results of optimization obtained from analytical method Parameters Value Unit Cooling channel diameter d 12 mm Cooling channels pitch  x 57.7 mm Cooling channels depth  y 45.2 mm Velocity of cooling water u 1.0 m/s Reynolds number Re 11952   Total flow rate of coolant  40.7  l/min Heat transfer coefficient α  4667  W/m2.°K  (a) An un-optimized design (b) Optimized design Fig. 17 Comparison of temperature profile between un-optimized and optimized conformal cooling channels  Fig. 18 Comparison of warpage between conventional straight cooling channel and conformal cooling channel  and a lower warpage than straight cooling channels. These are the advantages of conformal cooling channels. The structure of the milled groove cooling channels for the core side of the mold is illustrated in Fig. 19. This construction allows reducing manufacturing cost as mentioned in Section 2. The parameters of real U-shape cross-section were calculated by the formula (1). These data will be used for the milling process when making the mold.    6. Conclusion  Conformal cooling channels offer the benefit of uniform cooling that, in turn, reduce the cooling time and increase the quality of molded part, especially for products with large size and free-from shape. Besides solid free-form fabrication technique, milled grove cooling channels is an alternative method which can be used to make conformal cooling channels. The strong points of milled groove cooling method are the easiness of machining by CNC milling machine and easily applicable for all kinds of popular mold material. Using milled groove cooling channels, designers have more freedom to deploy the cooling channels layout and the ability of avoiding the  interference with other components in the mold.  Cooling design optimization of injection molding for a complex free-form molded part requires a complicated analysis steps, optimization strategy, and appropriate computer aided tools. This study presents a systematic method for optimizing the milled groove cooling channels in order to obtain the target mold temperature and reduce the cooling time and the non-uniformity of temperature distribution of the molded part. To increase the computational effectiveness, both analytical method and simulation-based method were used successively. The relation between the thermal behavior of the mold and the cooling channels layout parameters has been investigated meticulously. The feasibility of analysis method was proven by comparing the results of this method with DOE approximation. It can be concluded that the analytical method is applicable for optimizing of conformal cooling channels with a moderate preciseness.  When the fidelity of the optimization result is considered, the support of CAE tools, API programming language, and the combination optimization techniques are important to increase the preciseness of the analysis results and to reduce the simulation cost. The proposed method has been tested in various practical cases in which the plastic car fender is one of the typical case studies. The results obtained from the case studies point out that the proposed method of conformal cooling channels optimization can be used successfully with less time-consuming and less effort of designers to improve the part quality and the productivity of plastic production. Although milled groove cooling channels increase the cooling effect of the cooling system in the injection mold, its manufacturing cost hinders the popular use of this kind of cooling channels. Nevertheless, the initial extra investment in mold making is acceptable in mass production and industrial application if the productivity and part quality improves considerably. The future work is required for calculating the exact value of break-even point. Physical experiments are required for verifying the simulation results. Investigating the manufacturing cost, finding the way to reduce the manufacturing cost of milled groove cooling channels and adding the cost factor in optimization will be the objects of further researches.   ACKNOWLEDGEMENT  This work was supported by Research Fund of the University of Ulsan (2009). The authors would like to thank the reviewers for their valuable comments and suggestions.   REFERENCES 1. Chen, X., Lam, Y. C. and Li, D. Q., “Analysis of thermal residual stress in plastic injection molding,” J. Mater. Process. Technol., Vol. 101, No. 1-3, pp. 275-280, 2000. 2. Wang, T. H. and Young, W. B., “Study on residual stresses of thin-walled injection molding,” Eur. Polymer J., Vol. 41, No. 10, pp. 2511-2517, 2005. 3. Tang, L. Q., Chassapis, C. and Manoochehri, S., “Optimal cooling sytem design for multi-cavity injection molding,” Finite Element in Analysis and Design, Vol. 26, No. 3, pp. 229-251, 1997. 4. Lin, Z. C. and Chou, M. 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H. and Sbarski, I., “New cooling channels design for injection molding,” Proc. of the Word Congress on Engineering, Vol. I, 2009.  10. Park, H. S. and Pham, N. H., “Design of conformal cooling 塑料注射模具设计U型铣槽英文文献和中文翻译(5):http://www.751com.cn/fanyi/lunwen_50472.html