Excel functions relational operators

Excel also offers relational or comparison opetacois that allow for testing of relative magnitude of various arguments. These relational operators are shown in Table 14.7. We will use Example 14.5 to demonstrate the use of Excel s logical functions and relational operators. 

To select the proper heat transfer relations to represent the functions, you need to analyze the heat transfer functions that will take place in the unit-tube and/or on the shell side. Some units may have several functions, such as the example in Rubin s recommendations on this subject that is, steam desuperheating and hydrocarbon condensing steam and hydrocarbon condensing, and condensate subcooling. Rubin presents an excellent interpretation of multizone operation for several different sets of conditions. See Figures 10-91Aand 10-91B. 

The preparation of a-hydroxyphosphonates in a mixture of water and polyethylene glycol has been reported (Scheme 4.144) [183]. The chemistry was operationally trivial and involved simply stirring the reagents in the solvent mixture at room temperature. These aqueous reactions generated moderate to excellent yields of the compounds. The method was tolerant of a variety of functional groups including nitro, amino, and an unprotected phenol. Heteroarenes such as imidazole were also successfully functionalized. As with many related reactions, ketones were unreactive under the reaction conditions. This approach is one of the most practical syntheses of a-hydroxyphosphonates due to the simplicity of the reaction and the ability to promote the reaction in water at room temperature. 

---