The interaction by heat transfer between combustion gases-solid partic
les as one multiphase system and steam-water mixture as the other, thr
ough a rectangular metal wall, has been analyzed. A second order parti
al differential equation has been solved by a finite difference ADI sc
heme with variable iteration parameter. A series of computer programs
for the temperature fields prediction within the metal has been develo
ped in Decart 2-D system of coordinates. It was discussed for which of
the engineering problems and physical systems this kind of considerat
ion and these programs could be used as well as which of the calculati
ons and parametric studies could be done. One of the developed compute
r programs has been presented and applied to the separated tube fin of
water wall in a boiler furnace. The series of calculations has been d
one. It has been found that the temperatures of the fin considerably v
ary not only inside the metal but also along the fin surfaces. The con
cept of taking one uniform temperature of water wall as a boundary con
dition in the heat transfer analysis of the combustion gases-solid par
ticles system in the furnaces (so far widely used in many studies) sho
uld be reviewed. As the fin was taken apart from the tube and separate
ly analyzed, the obtained predictions will be compared with the result
s produced by the analysis of fin-tube integrated geometry. This is an
other study and the subject of the papers to be published.