Radiant heat transfer from a plate to the inside of a pipe.

[Bize]

I need to calculate the radiant heat transfer from a small "dX by dX" plate with a temperature "T1" radiating into the mouth of a "L1" length of pipe of inside diameter "D". The end opposite the plate is blanked off with a flat surface. The top "L2" length of the pipe metal is heated to "T2" but the rest of the pipe (and the blank end plate) is heated to "T3". (All temperatures are absolute.) The whole pipe and the plates have the same emissivity "e".

I need this calculation in two different configurations:
a) One side of the plate parallel to the length of the pipe with its edge being a distance "R" for the (longitudinal) centerline of the pipe and a length "L3" away from the mouth of the pipe.
b) One side of the plate perpendicular to the length of the pipe, a distance "R" from the centerline of the pipe and a length "L3" away from the mouth of the pipe.

The calculation can be numerical or (preferably) in equation form.

I know that this is not the easiest to understand, but can anyone help?

 

[SErgini0]

The book by Incropera and Dewitt, Fundementals of Heat and Mass Transfer can help you a lot.
Good luck.

 

[hacksaw]

It is a common problem in protection tube measurement and in radiation heat transfer classes. Consult a modern textbook or any good chemical or mechanical engineering handbook (Marks,Perry, etc.).