Topic
Similarity solution
About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, a nonlinear model of heat propagation is presented, from which a new heat conduction equation is derived, and an exact similarity solution in closed form of this equation is obtained, which reveals the travelling wave characteristics for the transient temperature distribution.
Abstract: A nonlinear model of heat propagation is presented, from which a new heat conduction equation is derived. An exact similarity solution in closed form of this equation is obtained, which reveals the travelling wave characteristics for the transient temperature distribution. It is shown that the temperature disturbances propagate with finite velocity, which is a monotonically decreasing function of time.
22 citations
TL;DR: In this article, the effects of thermal dispersion and viscous dissipation in both aiding and opposing flows are analyzed in a mixed convection flow and heat transfer about an isothermal vertical wall embedded in a fluid saturated porous medium with uniform free stream velocity.
Abstract: Mixed convection flow and heat transfer about an isothermal vertical wall embedded in a fluid saturated porous medium with uniform free stream velocity is considered and the effects of thermal dispersion and viscous dissipation in both aiding and opposing flows are analysed. Similarity solution is not possible due to the inclusion of the viscous dissipation term, series solution is obtained, first and second order effects of dissipation revealed that viscous dissipation lowers the heat transfer rate. Observations also revealed that the thermal dispersion effect enhances the heat transfer rate and the effect of viscous dissipation is observed to increase with increasing values of the dispersion parameter.
22 citations
TL;DR: In this paper, a theoretical and numerical analysis of multiple similarity solutions of the two-dimensional MHD boundary-layer flow over a permeable surface, with a power law stretching velocity, in the presence of a magnetic field B applied normally to the surface is presented.
22 citations
TL;DR: In this paper, a numerical model was developed to study the confinement of low-pressure plasmas in simple axially symmetric configurations, which contained the effects of resistivity, plasma inertia, and pressure gradients along the field.
22 citations
TL;DR: In this article, the authors explore the relevance of the idealized Jeffery-Hamel similarity solution to the practical problem of flow in a diverging channel of finite (but large) streamwise proportions.
Abstract: We explore the relevance of the idealized Jeffery�Hamel similarity solution to the
practical problem of flow in a diverging channel of finite (but large) streamwise
extent. Numerical results are presented for the two-dimensional flow in a wedge of
separation angle 2I±, bounded by circular arcs at the inlet/outlet and for a net radial
outflow of fluid. In particular, we show that in a finite domain there is a sequence
of nested neutral curves in the (Re, I±) plane, each corresponding to a midplane
symmetry-breaking (pitchfork) bifurcation, where Re is a Reynolds number based on
the radial mass flux. For small wedge angles we demonstrate that the first pitchfork
bifurcation in the finite domain occurs at a critical Reynolds number that is in
agreement with the only pitchfork bifurcation in the infinite-domain similarity solution,
but that the criticality of the bifurcation differs (in general). We explain this apparent
contradiction by demonstrating that, for I±
1, superposition of two (infinite-domain)
eigenmodes can be used to construct a leading-order finite-domain eigenmode. These
constructed modes accurately predict the multiple symmetry-breaking bifurcations of
the finite-domain flow without recourse to computation of the full field equations. Our
computational results also indicate that temporally stable, isolated, steady solutions
may exist. These states are finite-domain analogues of the steady waves recently
presented by Kerswell, Tutty, & Drazin (J. Fluid Mech., vol. 501, 2004, pp. 231�250)
for an infinite domain. Moreover, we demonstrate that there is non-uniqueness of
stable solutions in certain parameter regimes. Our numerical results tie together, in a
consistent framework, the disparate results in the existing literature.
22 citations