New results of Falkner–Skan equation arising in boundary layer theory

Abstract

This paper presents a new nonexistence result and upper and lower bounds of the shear stress f ″ ( 0 ) to the well-known Falkner–Skan equation arising from the boundary layer problems f ‴ ( η ) + f ( η ) f ″ ( η ) + λ [ 1 - ( f ′ ) 2 ( η ) ] = 0 , η ∈ ( 0 , ∞ ) subject to the boundary condition f ( 0 ) = f ′ ( 0 ) = 0 , f ′ ( ∞ ) = 1 , and the side condition 0 < f ′ ( η ) < 1 for η ∈ ( 0 , ∞ ) .