A 6cm dismeter sphere is suspended inside a closed cylindric

A 6-cm dismeter sphere is suspended inside a closed cylindrical container 0.18m long and 12 cm in diameter. Determine the view factor from the cylindrical container to the sphere.

Solution

Data Given

Diameter of the sphere = 6cm = 0.06m

Radius = 0.06/2 = 0.03m

Total surface area of the sphere = 4 x pi x r^2 = 4 x 3.14 x 0.03^2

= 0.011 m^2

Assuming the diameter of the cylinder to be the inner diameter(d) = 12 cm = 0.12m

Length of the cylinder(L) = 0.18m

Inner surface area of the cylinder = Pie x d x L

= 3.14 x 0.12 x 0.18

= 0.068 m^2

By considering sphere as component 1 and enclosed cylinder as component 2

View factor relation is givenby

A1F 1-2 = A2F 2-1

A1 = Surface area of the 1st component (Sphere)

A2 = Surface area of the 2nd component ( inner area of the cylinder)

F1-2 is the view factor from sphere to cylinder

F2-1 is the view factor from cylinder to sphere

Since component 1 ie; sphere is completely enclosed inside the cylinder F1-2 =1

Substituting F 1-2 =1 in the main equation

0.011 x 1 = 0.068 x F 2-1

F 2-1 = 0.011/0.068

= 0.162 ( Answer)