Paper Information

Journal:   INTERNATIONAL JOURNAL OF ENGINEERING   FEBRUARY 2004 , Volume 17 , Number 1 (TRANSACTIONS A: BASICS); Page(s) 99 To 108.
 
Paper: 

AXISYMMETRIC STAGNATION-POINT FLOW OF A VISCOUS FLUID ON A MOVING CYLINDER WITH TIME-DEPENDENT AXIAL VELOCITY

 
 
Author(s):  SALEH R., RAHIMI A.B.
 
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Abstract: 
The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an ‎infinite moving cylinder with time=dependent axial velocity is investigated. The ‎impinging free stream is steady with a strain rate k. An exact solution of the Navier-‎Stokes equations is derived in this problem. A reduction of these equations is obtained ‎by use of appropriate transformations. The general self-similar solution is obtained ‎when the axial velocity of the cylinder varies as specified time-dependent functions. ‎In particular, the cylinder may move with different velocity patterns. For ‎completeness, sample semi-similar solutions of the unsteady Navier-Stokes equations ‎have been obtained numerically using a finite-difference scheme. These solutions are ‎presented for special cases when the time-dependent axial velocity of the cylinder is a ‎step-function, a ramp, and a non-linear function. All the solutions above are ‎presented for Reynolds numbers, Re=ka^2/2n#, ranging from 0.1 to 100 where a is ‎cylinder radius and n# is kinematic viscosity of the fluid. Shear stresses corresponding ‎to all the cases increase with the Reynolds number. The maximum value of the shear ‎stress increases with increasing oscillation frequency and amplitude. An interesting ‎result is obtained in which a cylinder moving with certain axial velocity function and ‎at particular value of Reynolds number is axially stress-free‏.‏
 
Keyword(s): AXISYMMETRIC FLOW, STAGNATION FLOW, TIME-DEPENDENT AXIAL MOVEMENT, EXACT SOLUTION
 
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