This paper studies the dynamics of derivatives of various orders of the Falkner–Skan (FS) equation in the presence of a longitudinal pressure gradient. The FS equation is a nonlinear singularly perturbed third-order equation, and the behaviour of its solution and derivatives for various values of the form parameter ????, which is related to the pressure gradient, remains largely unexplored. The first derivative determines the velocity profile of the main flow in the boundary layer and is important for hydrodynamic stability analysis. The FS equation is reduced to a Cauchy problem for three nonlinear first-order ordinary differential equations, solved by the fourth-order Runge–Kutta method in vector form. Results are obtained for positive, zero, and negative pressure gradients. At ???? = 0 the profile coincides with the Blasius profile; for ???? < 0 the boundary layer thickens and may separate; for ???? > 0 its thickness decreases.
| Mualliflar | Тиловов, М.А., Tilovov, M.A. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashr sanasi | 2026-07-02 |
| Son | 3 |
| Betlar | 139-152 |
| Til | Rus |
| DOI | 10.71310/pcam.3_73.2026.10 |
DOI: 10.71310/pcam.3_73.2026.10 · Maqolaning asl sahifasi
Falkner–Skan equations, pressure gradient, velocity profile, уравнения Фолкнера–Скэна, градиент давления, профиль скорости
This study presents an efficient method for approximating the solutions of a certain class of first-order differential equations with variable coefficients. The approach constructs an auxiliary differential equation…
The paper addresses the formulation of plane elasticity problems in terms of stresses and their numerical solution by the Galerkin finite element method. Based on the equilibrium equations, geometric relations, and…
This study presents a mathematical and numerical model for filtration flow, solute transport, adsorption, and membrane fouling in a cylindrical porous filter. The model combines axisymmetric Brinkman–Darcy flow…
This work presents a comprehensive numerical and analytical study of hydrodynamic and thermal processes in closed pipelines of variable diameter, taking into account terrain relief and external thermal influences. The…
Within a non-conservative formulation of the quasi-one-dimensional linearized mass and momentum conservation equations, transient processes are studied in an elementary undulating pipeline section caused by step-like…
This paper presents a three-dimensional numerical study of a novel vertical-axis wind turbine (VAWT) with a unique aerodynamic profile and a passive blade-pitch mechanism. Rectangular blades are mounted on horizontal…
This paper develops a quasi-one-dimensional mathematical model of steady-state heat transfer from a thin rectangular fin installed on a cylindrical pipeline parallel to its generatrix. Unlike classical formulations…
This paper investigates how the propagation velocity of small pressure disturbances in a gas–liquid medium varies with the mass concentration of air. Two cases are considered: a rigid pipeline and a pipeline accounting…
This paper presents an improved quasi-one-dimensional model of unsteady compressible fluid flow in main pipelines for studying water hammer damping. Its novelty lies in a rigorous nonlinear boundary condition based on…
A three-dimensional mathematical model is proposed for the inflow of a turbid (sediment-laden) river flow into a density-stratified reservoir, accounting for phase separation and the breakdown of the layered structure…