scholarly journals The response to a hot spot in a combustion problem

1981 ◽  
Vol 23 (1) ◽  
pp. 95-102 ◽  
Author(s):  
K. K. Tam ◽  
M. T. Kiang
Keyword(s):  
Steady State ◽  
Simple Model ◽  
Initial Value Problem ◽  
Initial Temperature ◽  
Hot Spot ◽  
Steady State Solution ◽  
Initial Value ◽  
Multiple Steady State ◽  
Steady State Solutions ◽  
Combustion Problem

AbstractA simple model for a problem in combustion theory has multiple steady state solutions when a parameter is in a certain range. This note deals with the initial value problem when the initial temperature takes the form of a hot spot. Estimates on the extent and temperature of the spot for the steady state solution to be super-critical are obtained.

Nonlinear Stability Considerations in Thermoelastic Contact

1999 ◽  
Vol 66 (1) ◽  
pp. 109-116 ◽  
Author(s):  
J. A. Pelesko
Keyword(s):  
Steady State ◽  
Perturbation Technique ◽  
Multiple Scale ◽  
Steady State Solution ◽  
Rigid Wall ◽  
Stable Steady State ◽  
Dynamic Information ◽  
Multiple Steady State ◽  
Singular Perturbation Technique ◽  
Steady State Solutions

The behavior of a one-dimensional thermoelastic rod is modeled and analyzed. The rod is held fixed and at constant temperature at one end, while at the other end it is free to separate from or make contact with a rigid wall. At this free end a pressure and gap-dependent thermal boundary condition is imposed which couples the thermal and elastic problems. Such systems have previously been shown to undergo a bifurcation from a unique linearly stable steady-state solution to multiple steady-state solutions with alternating stability. Here, the system is studied using a two-timing or multiple-scale singular perturbation technique. In this manner, the analysis is extended into the nonlinear regime and dynamic information about the history dependence and temporal evolution of the solution is obtained.

A New Solution of a Nonlinear Model of Upwelling

2005 ◽  
Vol 35 (4) ◽  
pp. 532-544 ◽  
Author(s):  
P. F. Choboter ◽  
R. M. Samelson ◽  
J. S. Allen
Keyword(s):  
Steady State ◽  
Pressure Gradient ◽  
Nonlinear Model ◽  
Initial Value Problem ◽  
Coastal Upwelling ◽  
Steady State Solution ◽  
Surface Flow ◽  
State Solution ◽  
Initial Value ◽  
Surface Jet

Abstract A two-dimensional, frictionless, nonlinear model of coastal upwelling is reexamined. The model has been solved previously at steady state and as an initial-value problem. The previous solution to the initial-value problem is inconsistent with the steady-state solution. A new solution to the spinup problem is presented that approaches the existing steady-state solution. In the new solution, a surface equatorward jet develops more rapidly than a poleward undercurrent, but the surface jet is of limited strength so that the undercurrent velocity eventually surpasses that of the surface flow. Consideration of dimensional scales implies that the magnitude of the wind stress determines how quickly steady state is approached but does not affect the steady-state fields. Exact solutions found with an arbitrary alongshore pressure gradient imply that there is no poleward flow without a poleward pressure gradient.

Waves on a shear flow

1974 ◽  
Vol 11 (2) ◽  
pp. 263-277 ◽  
Author(s):  
K.K. Puri
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Shear Flow ◽  
Initial Value Problem ◽  
Finite Depth ◽  
Steady State Solution ◽  
State Solution ◽  
Wave System ◽  
Initial Value ◽  
Oscillatory Pressure

The propogation of disturbance when a shear flow with a free surface, in a channel of infinite horizontal extent and finite depth, is disturbed by the application of time-oscillatory pressure, is studied. The initial value problem is solved by using transform techniques and the steady state solution is obtained therefrom in the limit t → ∞. The effect of the initial shear on the development of the wave system is investigated.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

scholarly journals Stability of the positive steady-state solutions of systems of nonlinear Volterra difference equations of population models with diffusion and infinite delay

2000 ◽  
Vol 23 (4) ◽  
pp. 261-270 ◽  
Author(s):  
B. Shi
Keyword(s):  
Steady State ◽  
Difference Equations ◽  
Infinite Delay ◽  
Steady State Solution ◽  
Population Models ◽  
Monotone Iterative ◽  
Positive Steady State ◽  
Infinite Delays ◽  
Steady State Solutions ◽  
Volterra Difference Equations

An open problem given by Kocic and Ladas in 1993 is generalized and considered. A sufficient condition is obtained for each solution to tend to the positive steady-state solution of the systems of nonlinear Volterra difference equations of population models with diffusion and infinite delays by using the method of lower and upper solutions and monotone iterative techniques.

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