Journal ArticleDOI
Nonsteady Stagnation-Point Flows Over Permeable Surfaces: Explicit Solutions of the Nevier-Stokes Equations
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In this paper, explicit solutions of the Navier-Stokes equations with surface suction or injection were obtained using a new approach for finding explicit similarity solutions of partial differential equations.Abstract:
Some new explicit solutions of the unsteady two-dimensional Navier-Stokes equations describing nonsteady stagnation-point flows with surface suction or injection are presented. The solutions have been obtained using a new approach for finding explicit similarity solutions of partial differential equations. As distinct from the common Birkhoff's similarity transformation, which permits only one form of an unsteady potential flow field and only one form of time dependence for suction (or blowing) velocity, the transforms obtained permit consideration of a variety of special solutions differing in the forms of time dependenceread more
Citations
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Effects of thermal radiation and variable fluid viscosity on stagnation point flow past a porous stretching sheet
TL;DR: In this paper, the symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations, with the help of them the partial differential equations corresponding to momentum and energy equations are transformed into highly nonlinear ordinary differential equations.
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The boundary layers of an unsteady incompressible stagnation-point flow with mass transfer
TL;DR: In this article, the boundary layers of an unsteady incompressible stagnation-point flow with mass transfer were further investigated using numerical methods and the similarity equation group was solved using similarity transformation technique.
Hydromagnetic stagnation point flow with heat transfer over a permeable surface
TL;DR: In this article, the effect of suction on the Hiemenz flow problem has been introduced and the study of heat transfer in stagnation point flow has been considered in the hydrodynamic case.
Journal ArticleDOI
New similarity reductions of the steady-state boundary layer equations
TL;DR: In this article, the steady-state boundary layer equations were solved using similarity reductions and exact solutions of the steady state boundary layer equation. But the similarity solutions were derived using an extension of the non-classical method.
References
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Journal ArticleDOI
Exact Solutions of the Unsteady Navier-Stokes Equations
TL;DR: The unsteady Navier-Stokes equations as discussed by the authors are a set of nonlinear partial differential equations with very few exact solutions, and there are three main categories: parallel, concentric and related solutions, Beltrami and related solution, and similarity solutions.
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Unsteady Laminar Boundary Layers in an Incompressible Stagnation Flow
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Unsteady laminar boundary layers in a compressible stagnation flow
C. S. Vimala,G. Nath +1 more
TL;DR: In this article, the authors considered the unsteady laminar compressible boundary-layer flow in the immediate vicinity of a two-dimensional stagnation point due to an incident stream whose velocity varies arbitrarily with time, and the governing partial differential equations involving both time and the independent similarity variable were transformed into new co-ordinates with finite ranges by means of a transformation which maps an infinite interval into a finite one.
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The construction of special explicit solutions of the boundary-layer equations. steady flows
TL;DR: The generalization of the method for determining special explicit solutions of partial differential equations developed by the author (Q. Jl Mech. as mentioned in this paper ) is used to derive new explicit solutions for two-dimensional boundary-layer equations.