A-2 Top of Right Circular Cylinder to Center of its Base


This geometry is in Fig. A-2. Since θj = θk = θ, the integral in Eq. (A-1) becomes, for the top of the cylinder Aj radiating to the element dAk at the center of its base,

 

                                                 (A-4)

 

Since  Then, using cos θ = h/S,

 

                                         (A-5)

A006x002
FIGURE A-2 Geometry for exchange from top of gas-filled cylinder to center of its base.

 

Now let kλS = tλ to obtain

 

                              (A-6)

 

This integral can be expressed in terms of the exponential integral function defined in Appendix D, by writing

 

                          (A-7)

 

Letting  and , respectively, in the two integrals gives

 

 

The integral in (A-6) is then written in terms of the exponential integral function as

 

        (A-8)

 

so it can be readily evaluated for various values of the parameters R/h and kλh.