Solution22

Solution22 - Chapter 22 Radiation Heat Transfer 22-1...

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Unformatted text preview: Chapter 22 Radiation Heat Transfer 22-1 Chapter 22 RADIATION HEAT TRANSFER View Factors 22-1C The view factor j i F represents the fraction of the radiation leaving surface i that strikes surface j directly. The view factor from a surface to itself is non-zero for concave surfaces. 22-2C The pair of view factors F i j and F j i are related to each other by the reciprocity rule A F A F i ij j ji = where A i is the area of the surface i and A j is the area of the surface j. Therefore, A F A F F A A F 1 12 2 21 12 2 1 21 = = 22-3C The summation rule for an enclosure and is expressed as F i j j N = = 1 1 where N is the number of surfaces of the enclosure. It states that the sum of the view factors from surface i of an enclosure to all surfaces of the enclosure, including to itself must be equal to unity. The superposition rule is stated as the view factor from a surface i to a surface j is equal to the sum of the view factors from surface i to the parts of surface j, F F F 1 2 3 1 2 1 3 = + ( , ) . 22-4C The cross-string method is applicable to geometries which are very long in one direction relative to the other directions. By attaching strings between corners the Crossed-Strings Method is expressed as F i i j =- Crossed strings Uncrossed strings string on surface 2 Chapter 22 Radiation Heat Transfer 22-2 22-5 An enclosure consisting of six surfaces is considered. The number of view factors this geometry involves and the number of these view factors that can be determined by the application of the reciprocity and summation rules are to be determined. Analysis A seven surface enclosure (N=6) involves N 2 2 6 = = 36 view factors and we need to determine 15 2 ) 1 6 ( 6 2 ) 1 ( =- =- N N view factors directly. The remaining 36-15 = 21 of the view factors can be determined by the application of the reciprocity and summation rules. 22-6 An enclosure consisting of five surfaces is considered. The number of view factors this geometry involves and the number of these view factors that can be determined by the application of the reciprocity and summation rules are to be determined. Analysis A five surface enclosure (N=5) involves N 2 2 5 = = 25 view factors and we need to determine N N ( ) (5 )- =- = 1 2 5 1 2 10 view factors directly. The remaining 25-10 = 15 of the view factors can be determined by the application of the reciprocity and summation rules. 22-7 An enclosure consisting of twelve surfaces is considered. The number of view factors this geometry involves and the number of these view factors that can be determined by the application of the reciprocity and summation rules are to be determined. Analysis A twelve surface enclosure (N=12) involves 144 = = 2 2 12 N view factors and we need to determine N N ( ) ( )- =- = 1 2 12 12 1 2 66 view factors directly. The remaining 144-66 = 78 of the view factors can be determined by the application of the reciprocity and summation rules....
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Solution22 - Chapter 22 Radiation Heat Transfer 22-1...

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