Calculating Radiation View Factor for Various Shapes

[Baltistani]

how is radiation view factor calculated especially for the following cases
1-between a flat surface and a sphere
between two flat surfaces at 90
between two surfaces facing each other
between two spheres

 

[shoaib85]

How I could calculate veiw factor between two sphere tahat are concenteric
please help me
thank you

 

[sramanujam]

shoaib85: please refer to any standard book on heat transfer, view factor between concentric spheres can be easily found out using view factor algebra.
Baltistani: View factor between any pair of surfaces can be found by performing 4 area integrations or 2 contour integrations, but I'm not sure if contour integration can be used always, especially when the distance between any two differential element on both surface is less than unity since it gives negative results.