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Hybrid Methods in Engineering

ISSN Print: 1099-2391
ISSN Online: 2641-7359

Archives: Volume 1, 1999 to Volume 4, 2002

Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v1.i2.20
16 pages

ON THE INTEGRAL TRANSFORM SOLUTION OF LAMINAR BOUNDARY LAYERS WITH DISTRIBUTED SUCTION

Jian Su
Interdisciplinary Nucleus of Fluid Dynamics, NIDF, Mechanical Eng. Dept., POLI & COPPE, Universidade Federal do Rio de Janeiro, Brazil; Nuclear Eng. Dept., POLI & COPPE, Universidade Federal do Rio de Janeiro, Brazil

ABSTRACT

The velocity field associated with perturbations to the Blasius solution through a distributed wall suction is considered. The generalized integral transform technique is employed in a hybrid numerical-analytical solution of the two-dimensional boundary-layer equations, written in terms of the perturbation velocities. The linearized boundary-layer equations are integral-transformed by eliminating the transversal coordinate and reducing the partial differential equations (PDEs) to an infinite system of coupled linear ordinary differential equations for the transformed potentials. A leading-order approximate solution, in analytic form, is obtained by neglecting all nondiagonal elements of the coefficient matrices. The approximate-analytic solution shows an algebraic decay of the disturbance, which is confirmed by a complete hybrid numerical-analytical solution of the full truncated system. This is handled through well-known initial-value problem solvers with automatic precision control. The original nonlinear boundary-layer equations are then recovered by adding the neglected quadratic terms to the linearized system and solved by the same integral transform technique. Better convergence behavior of the integral transform solutions is shown by comparison with the finite-difference solutions.


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