TY  - JOUR
JF  - Applied Mathematics Letters
VL  - 22
Y1  - 2009///
UR  - https://www.scopus.com/inward/record.uri?eid=2-s2.0-70349090945&doi=10.1016%2fj.aml.2009.05.010&partnerID=40&md5=1b29c4e10606bedc00c9c5c883db5d92
A1  - Nugroho, G.
A1  - Ali, A.M.S.
A1  - Abdul Karim, Z.A.
N1  - cited By 6
SP  - 1639
AV  - none
SN  - 08939659
N2  - The three-dimensional incompressible Navier-Stokes equations with the continuity equation are solved analytically in this work. The spatial and temporal coordinates are transformed into a single coordinate ξ. The solution is proposed to be in the form V = â?? Φ + â?? Ã? Φ where Φ is a potential function that is defined as Φ = P (x, ξ) R (ξ). The potential function is firstly substituted into the continuity equation to produce the solution for R and the resultant expression is used sequentially in the Navier-Stokes equations to reduce the problem to the class of nonlinear ordinary differential equations in P terms. Here, more general solutions are also obtained based on the particular solutions of P. Explicit analytical solutions are found to be mathematically similar for the cases of zero and constant pressure gradient. Two examples are given to illustrate the applicability of the method. It is also concluded that the selection of variables for the potential function can be interchanged from the beginning, resulting in similar explicit solutions. © 2009 Elsevier Ltd. All rights reserved.
IS  - 11
KW  - Analytical solution; Analytical solutions; Constant pressure gradient; Continuity equation; Continuity equations; Explicit solutions; General solutions; Incompressible Navier Stokes equations; Nonlinear ordinary differential equation; Particular solution; Potential function; Selection of variables; Special class
KW  -  Computational fluid dynamics; Fluid dynamics; Nonlinear equations; Ordinary differential equations; Organic polymers; Partial differential equations; Pressure gradient; Three dimensional; Viscous flow
KW  -  Navier Stokes equations
TI  - On a special class of analytical solutions to the three-dimensional incompressible Navier-Stokes equations
ID  - scholars679
EP  - 1644
ER  -