A s t u d y is m a d e oI t h e flow of a viscous, compressible, h e a t conducting, a n d perfect gas in slender a x i s y m m e t r i c channels u n d e r t h e a d i a b a t i c wall condition. Solutions to t h e equations of m o t i o n for such a gas are o b t a i n e d using t h e m e t h o d of similar solutions. This a p p r o a c h reduces the equations of m o t i o n to a pair of coupled nonlinear o r d i n a r y differential equations which h a v e relatively simple closed form solutions. I t is found t h a t solutions of this t y p e are only possible in channels w i t h d i v e r g e n t walls a n d a favorable pressure gradient.
I n t h e p r e s e n t investigation it is found t h a t the velocity profiles are insensitive to m o d e r a t e variations in t h e P r a n d t l n u m b e r a n d ),, t h e ratio of specific heats. T h e t e m p e r a t u r e profiles, t o t a l t e m p e r a t u r e profiles, a n d Mach n u m b e r profiles are h o w e v e r v e r y sensitive to changes in P r a n d t l n u m b e r a n d ratio of specific heats. For a P r a n d t l n u m b e r less t h a n u n i t y t h e r e is a n a c c u m u l a t i o n of t o t a l energy near t h e c h a n n e l centerline a n d a deficit of t o t a l energy near t h e c h a n n e l walls. T h e recovery factor is found to be equal to t h e P r a n d t l n u m b e r .