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The mathematical property of one-dimensional steady solution for reverse smolder waves in the context of a model that permits both fuel-rich and fuel-lean has been studied using the method of analysis. Based on the equations and the boundary conditions some asymptotic properties of the solution at infinity are proved. It is shown that the value of oxygen or the mass of fuel (corresponding to the fuel-rich case and the fuel-lean case, respectively) tends to zero, and the temperature approaches to a fixed value. This is confirmed by other authors using large activation energy asymptotic methods. [ABSTRACT FROM AUTHOR]

In this paper, we extend the lattice Boltzmann method (LBM) in combination with the immersed boundary method (IBM) to simulate the steady-state fluid–solid conjugate heat transfer problems in complex geometries. The no-slip boundary condition is handled by the immersed boundary method. The “pseudo-solid-specific-heat” technique is used to ensure the continuity of heat flux at the fluid–solid interface. The present LB thermal field solver retains the simple structure of standards thermal LB model. The performance of the present method is validated by several heat conduction/convection problems. The numerical results agree well with exact solutions or published results. [ABSTRACT FROM AUTHOR]

This paper aims to present numerical solutions for the problem of steady natural convection heat transfer by double diffusion from a heated cylinder buried in a saturated porous media exposed to constant uniform temperature and concentration in the cylinder and in the media surface. A square finite domain 3?×?3 and acceptance criterion converged solution with an absolute error under 1?×?10-3 were considered to obtain results presented. The Patankar's power law for approaching of variables calculated T, C, and ϕ also was adopted. In order of method validation, an investigation of mesh points number as function of Ra, Le, and N was done. A finite volume scheme has been used to predict the flow, temperature, and concentration distributions at any space from a heat cylinder buried into a fluid-saturated porous medium for a bipolar coordinates system. Examples presented show that the differences in the flow distribution caused not only when Rayleigh number range is considered but also when Lewis number range is considered. Further, increase in the Rayleigh number has a significant influence in the flow distribution when the concentration distribution is considered. Steady natural convection heat transfer by double diffusion from a heated cylinder buried in a saturated porous medium is studied numerically using the finite volume method. To model fluid flow inside the porous medium, the Darcy equation is used. Numerical results are obtained in the form of streamlines, isotherms, and isoconcentrations. The Rayleigh number values range from 0 to 1000, the Lewis number values range from 0 to 100, and the buoyancy ratio number is equal to zero. Calculated values of average heat transfer rates agree reasonably well with values reported in the literature. [ABSTRACT FROM AUTHOR]

In engineering practice and thermodynamics texts, it is assumed that, for the expansion of a gas from a high-pressure tank to a low-pressure tank (through a valve) under adiabatic conditions, the process in the high-pressure tank is isentropic. No theoretical explanation or experimental proof is, however, cited in support of this assumption. A thorough theoretical investigation of this question is presented in this paper. The present numerical computation with an unsteady simulation using the first law of thermodynamics and with no explicit assumption regarding the thermodynamic process that takes place in the high-pressure tank establishes that the expansion in the high-pressure tank is indeed isentropic. Although an analytical proof has not been formulated, it is believed that the present computations constitute the first theoretical justification for the much-used isentropic assumption found in thermodynamics textbooks. A direct determination of a steady solution using an average exit enthalpy for the high-pressure tank also gives a correct result if the pressure ratio in the high-pressure tank is limited to 2. Even though the gas expansion in the high-pressure tank turns out to be isentropic, it is shown that the overall process of gas expansion and compression to the low-pressure tank is an irreversible process. [ABSTRACT FROM AUTHOR]

In this brief note, we show that the unsteady flow of a generalized second grade fluid due to a constant couple, as well as the similar flow of Newtonian and ordinary second grade fluids, ultimately becomes steady. For this, a new form of the exact solution for velocity is established. This solution is presented as a sum of the steady and transient components. The required time to reach the steady-state is obtained by graphical illustrations.

In this paper, we investigate a single server batch arrival non-Markovian retrial queueing model with random break down and Bernoulli vacation. Customers arrive in batches accordingly Poisson process with arrival rate λ but are served one by one with first come first served basis. All customers demand the first essential service, whereas only some of them demand the second optional service. The server is assumed to be unreliable so that it may encounter break down at any time. As the server has to be repaired, the repair process start immediately. The customer, who finds the server busy upon arrival, can either join the orbit with probability p or he/she can leave the system with probability 1-p. Upon completion of a service the server may go for a vacation with probability ϑ or stay back in the system to serve a next customer with probability 1 - ϑ, if any. After finishing a vacation, the server could not provide service as the it should go for a setup time. Assuming that, the retrial time, the service time, the repair time, the vacation completion time and the set up time of the server are all arbitrarily distributed. We obtain the transient solution and steady solution of the model by using supplementary variable technique. Also we derive the system performance measures, reliability indices for the prescribed model. [ABSTRACT FROM AUTHOR]

SUMMARY This paper reports numerical convergence study for simulations of steady shock-induced combustion problems with high-resolution shock-capturing schemes. Five typical schemes are used: the Roe flux-based monotone upstream-centered scheme for conservation laws (MUSCL) and weighted essentially non-oscillatory (WENO) schemes, the Lax-Friedrichs splitting-based non-oscillatory no-free parameter dissipative (NND) and WENO schemes, and the Harten-Yee upwind total variation diminishing (TVD) scheme. These schemes are implemented with the finite volume discretization on structured quadrilateral meshes in dimension-by-dimension way and the lower-upper symmetric Gauss-Seidel (LU-SGS) relaxation method for solving the axisymmetric multispecies reactive Navier-Stokes equations. Comparison of iterative convergence between different schemes has been made using supersonic combustion flows around a spherical projectile with Mach numbers M = 3.55 and 6.46 and a ram accelerator with M = 6.7. These test cases were regarded as steady combustion problems in literature. Calculations on gradually refined meshes show that the second-order NND, MUSCL, and TVD schemes can converge well to steady states from coarse through fine meshes for M = 3.55 case in which shock and combustion fronts are separate, whereas the (nominally) fifth-order WENO schemes can only converge to some residual level. More interestingly, the numerical results show that all the schemes do not converge to steady-state solutions for M = 6.46 in the spherical projectile and M = 6.7 in the ram accelerator cases on fine meshes although they all converge on coarser meshes or on fine meshes without chemical reactions. The result is based on the particular preconditioner of LU-SGS scheme. Possible reasons for the nonconvergence in reactive flow simulation are discussed.Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The goal of this contribution is to formulate the simplest possible model for the bubble column hydrodynamics and analyse it for steady states, stability, and unsteady behaviour. The governing equations are based on the mass balance of the gas phase. Two closures for the gas velocity are used and reflect two typical operational regimes, homogeneous (HoR) and heterogeneous (HeR). The model has five parameters: column height H, terminal bubble speed u0, hindrance exponent n, enhance exponent m, gas flow rate q. Three branches of steady solutions were found for HoR, one stable, one unstable, one neutrally stable. The first two are physically relevant, are of the nodetype, and merge in the turning point bifurcation at large enough gas input. Two branches of steady solutions were found for HeR, one stable and one neutrally stable. The first one is physically relevant, is of the node-type, and persists for all plausible parameter values. In both regimes, the neutrally stable solution was classified as unphysical. The transition regime (TrR) was obtained by matching the stable solutions of HoR and HeR, with help of a sigmoidal bridging function. The system stability was related to the model topology. The linear approximation of the bubble column dynamics was studied and the relaxation time estimated. The full nonlinear dynamics was demonstrated too. Both the steady and unsteady behaviour of the bubble column was compared with available experimental data. [ABSTRACT FROM AUTHOR]

We review some results on the stability of the incompressible fluids in an exterior domain. We categorize the survey according to the values of the steady solutions and to the values of the far field velocity, and to the spatial dimension. [ABSTRACT FROM AUTHOR]

This paper proposes a new approach to model unsteady laminar flows of dispenser systems in the semiconductor packaging industry. The approach is based on the exact steady solution. After an overview of dispensing technology and historical modeling of the unsteady flows, a new modeling approach of the unsteady laminar flow in a circular pipe and annular duct is developed. From the proposed model, the modeling results of unsteady flow in an arbitrary circular pipe and annular duct are obtained and compared with the spectral solution. In addition, a comparative work between the proposed analytical dynamic model and the finite-element model is undertaken in order to demonstrate the effectiveness of the proposed modeling methodology. [ABSTRACT FROM PUBLISHER]

We show that the Euler system of gas dynamics in R d , d = 2 , 3 , with positive far field density and arbitrary far field entropy, admits infinitely many steady solutions with compactly supported velocity. The same proof yields a similar result for the incompressible Euler system with variable density. In particular, these are examples of global in time smooth (non-trivial) solutions for the corresponding time-dependent systems. [ABSTRACT FROM AUTHOR]

In this paper, using wave decomposition and establishing uniform a priori C 1 estimates, we proved global stability of steady supersonic Fanno flows under small perturbations of initial-boundary values in a one-dimensional rectilinear finite duct with constant cross-sections. The flow is governed by the one-space dimensional compressible Euler equations with a nonlinear damping term representing frictions in the duct. Both isentropic and non-isentropic polytropic gases are considered. [ABSTRACT FROM AUTHOR]