scholarly journals An analytical study of the effects of vaporization of twodimensional laminar droplets on a triple flame

2011 ◽  
Vol 76 (11) ◽  
pp. 1567-1581 ◽  
Author(s):  
Mehdi Bidabadi ◽  
Ghazal Barari ◽  
Milad Azimi
Keyword(s):  
Temperature Field ◽  
Vertical Velocity ◽  
Flame Temperature ◽  
Lewis Number ◽  
Field Equations ◽  
Irreversible Reaction ◽  
Fuel Droplets ◽  
First Case ◽  
Energy Equations ◽  
Fuel Stream

The structure of triple flame propagation in combustion systems, containing uniformly distributed volatile fuel droplet was analyzed. The analysis was established for a one-step irreversible reaction with an asymptotic limit, where the value of the Zeldovich Number is large. Here, using unit Lewis number, the analytical results for the triple flame temperature were obtained considering two sections. In the first section, a non-vaporizing fuel stream was studied and in the second section, a volatile droplet fuel stream was taken into account. It is presumed that the fuel droplets vaporize to yield a gaseous fuel of known chemical structure, which is subsequently oxidized in the gaseous phase. Here two different cases are studied. In the first case, only the velocity parallel to the reactant flow was considered; while for the latter one, the vertical velocity was considered in addition. The energy equations were solved and the temperature field equations are presented. The results are first presented for a non-vaporizing fuel and compared to the experiment results. In addition, some other results of the temperature field for a vaporizing fuel stream are demonstrated within the comparison between the abovementioned cases which revealed the effect of the considering the vertical velocity component on the flame temperature field.

scholarly journals Heat Induction by Viscous Dissipation Subjected to Symmetric and Asymmetric Boundary Conditions on a Small Oscillating Flow in a Microchannel

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 499 ◽  
Author(s):  
Chih Tso ◽  
Chee Hor ◽  
Gooi Chen ◽  
Chee Kok
Keyword(s):  
Temperature Field ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Lower Plate ◽  
Brinkman Number ◽  
Energy Equations ◽  
Oscillation Rate

The heat induced by viscous dissipation in a microchannel fluid, due to a small oscillating motion of the lower plate, is investigated for the first time. The methodology is by applying the momentum and energy equations and solving them for three cases of standard thermal boundary conditions. The first two cases involve symmetric boundary conditions of constant surface temperature on both plates and both plates insulated, respectively. The third case has the asymmetric conditions that the lower plate is insulated while the upper plate is maintained at constant temperature. Results reveal that, although the fluid velocity is only depending on the oscillation rate of the plate, the temperature field for all three cases show that the induced heating is dependent on the oscillation rate of the plate, but strongly dependent on the parameters Brinkman number and Prandtl number. All three cases prove that the increasing oscillation rate or Brinkman number and decreasing Prandtl number, when it is less than unity, will significantly increase the temperature field. The present model is applied to the synovial fluid motion in artificial hip implant and results in heat induced by viscous dissipation for the second case shows remarkably close agreement with the experimental literature.

scholarly journals Dynamics of scalar potentials in theory of gravity

2019 ◽  
Vol 97 (8) ◽  
pp. 880-894
Author(s):  
M. Zubair ◽  
Farzana Kousar ◽  
Saira Waheed
Keyword(s):  
Scalar Field ◽  
Field Potential ◽  
Graphical Analysis ◽  
Chaplygin Gas ◽  
Field Potentials ◽  
De Sitter ◽  
Field Equations ◽  
Barotropic Fluid ◽  
First Case ◽  
De Sitter Universe

In this paper, we explore the nature of scalar field potential in [Formula: see text] gravity using a well-motivated reconstruction scheme for flat Friedmann–Robertson–Walker (FRW) geometry. The beauty of this scheme lies in the assumption that the Hubble parameter can be expressed in terms of scalar field and vice versa. Firstly, we develop field equations in this gravity and present some general explicit forms of scalar field potential via this technique. In the first case, we take the de Sitter universe model and construct some field potentials by taking different cases for the coupling function. In the second case, we derive some field potentials using the power law model in the presence of different matter sources like barotropic fluid, cosmological constant, and Chaplygin gas for some coupling functions. From graphical analysis, it is concluded that using some specific values of the involved parameters, the reconstructed scalar field potentials are cosmologically viable in both cases.

scholarly journals Cosmological dynamics of f(R) models in dynamical system analysis

2020 ◽  
Vol 35 (22) ◽  
pp. 2050124
Author(s):  
Parth Shah ◽  
Gauranga C. Samanta
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Critical Points ◽  
System Analysis ◽  
Late Time ◽  
Field Equations ◽  
Acceleration Phase ◽  
First Case ◽  
Acceleration Of The Universe ◽  
The Universe

In this work we try to understand the late-time acceleration of the universe by assuming some modification in the geometry of the space and using dynamical system analysis. This technique allows to understand the behavior of the universe without analytically solving the field equations. We study the acceleration phase of the universe and stability properties of the critical points which could be compared with observational results. We consider an asymptotic behavior of two particular models [Formula: see text] and [Formula: see text] with [Formula: see text], [Formula: see text], [Formula: see text] for the study. As a first case we fix the value of [Formula: see text] and analyze for all [Formula: see text]. Later as second case, we fix the value of [Formula: see text] and calculation are done for all [Formula: see text]. At the end all the calculations for the generalized case have been shown and results have been discussed in detail.

The temperature distribution along a radiating gas stream in which heat is being liberated by a chemical reaction

1951 ◽  
Vol 208 (1093) ◽  
pp. 247-262
Keyword(s):  
Heat Transfer ◽  
Heat Capacity ◽  
Heat Sink ◽  
Flame Temperature ◽  
Convection Heat Transfer ◽  
Combustion Products ◽  
Distance Curve ◽  
Fuel Jet ◽  
Initial Fuel ◽  
Fuel Stream

As a first approximation, to calculate the variation of flame temperature ( Y ) with distance ( X ) along a slowly burning flame, the flame is taken to consist of a central stream or jet of fuel which enters at the temperature ( T ) of the heat sink and entrains combustion air at a rate constant with respect to X . This entrained air is assumed to react rapidly with the fuel stream and the products of the reactions remain in the fuel stream, so that the temperature ( Y ) of the latter rises at a rate dY/dX which falls off as the heat capacity of this stream increases. When there is no heat loss from the fuel jet the temperature-distance curve is shown to be a rectangular hyperbola. The curvature at any point of the hyperbola increases as ( q ), the ratio of the heat capacity of the initial fuel stream to that of the final combustion products, decreases. In other cases heat transfer is supposed to take place by convection (α [ Y ─ T ]) orradiation (α [ Y 4 ─ T 4 ]) between the fuel jet and the heat sink with a heat-transfer coefficient which is assumed to be constant for a cylindrical flame and proportional to distance from the inlet for a conical flame. It is shown that in the case of the cylindrical flame the flame temperature must increase monotonically until combustion is complete, whereas the temperature in the conical flame can begin to fall off at an earlier stage. In the case of convection-heat transfer the shape of the temperature-distance curve is dependent only on ( q ) and on the ratio L/L 0 (where L ═ length for all combustion air to be entrained and L 0 ═ length in which all the combustion energy would be transferred to the surroundings if the flame remained at the adiabatic combustion temperature T a ). With radiative heat transfer the shape of the curves depends on ( q ) and L/L 0 but also on the ratio T/T a .

A Semi-Analytical Model for Evaporating Fuel Droplets

2005 ◽  
Vol 127 (2) ◽  
pp. 199-203 ◽  
Author(s):  
Achintya Mukhopadhyay ◽  
Dipankar Sanyal
Keyword(s):  
Gas Phase ◽  
Computational Cost ◽  
Lewis Number ◽  
Droplet Evaporation ◽  
Solution Procedure ◽  
Droplet Surface ◽  
Spray Combustion ◽  
Fuel Droplet ◽  
Cfd Model ◽  
Fuel Droplets

An algorithm for solution of a model for heating and evaporation of a fuel droplet has been developed. The objective of the work is to develop a computationally economic solution module for simulating droplet evaporation that can be incorporated in spray combustion CFD model that handles a large number of droplets. The liquid-phase transient diffusive equation has been solved semi-analytically, which involves a spatially closed-form and temporally discretized solution procedure. The model takes into account droplet surface regression, nonunity gas-phase Lewis number and variation of latent heat with temperature. The accuracy of the model is identical to a Finite Volume solution obtained on a very fine nonuniform grid, but the computational cost is significantly less, making this approach suitable for use in a spray combustion code. The evaporation of isolated heptane droplet in a quiescent ambient has been investigated for ambient pressures of 1 to 5 bar.

scholarly journals Evaporation and Precipitation Surface Effects in Local Mass Continuity Laws of Moist Air

2006 ◽  
Vol 63 (10) ◽  
pp. 2642-2652 ◽  
Author(s):  
Ulrike Wacker ◽  
Thomas Frisius ◽  
Fritz Herbert
Keyword(s):  
Tropical Cyclone ◽  
Mass Balance ◽  
Vertical Velocity ◽  
Total Mass ◽  
Climate Models ◽  
Weather Prediction ◽  
Simulation Models ◽  
Moist Air ◽  
Local Mass ◽  
First Case

Abstract The local mass balance equations of cloudy air are formulated for a model system composed of dry air, water vapor, and four categories of water condensate particles, as typically adopted for numerical weather prediction and climate models. The choice of the barycentric velocity as reference motion provides the most convenient form of the total mass continuity equation. Mass transfer across the earth’s surface due to precipitation and evaporation causes a nonvanishing barycentric vertical velocity ws and is proportional to the local difference between evaporation rate and rain plus snow rate. Hence ws vanishes only in the special situation that evaporation and precipitation balance exactly. Alternative concepts related to different reference motions are reviewed. However, the choice of the barycentric velocity turns out to be advantageous for several reasons. The implication of the nonvanishing total mass transport across the earth’s surface is estimated from model simulations for two extreme weather situations: a polar cold air outbreak and a tropical cyclone. While the effect is small in the first case, it is important in the latter. The large precipitation rates in the tropical cyclone case cause a loss of atmospheric mass, which corresponds to a vertical velocity at the surface larger than −20 mm s−1, and an instantaneous drop in pressure, which if sustained for 6 h, would correspond to about 49 hPa; this demonstrates the necessity of using the correct formulation of the mass balance in simulation models for moist air.

scholarly journals Inflation in anisotropic brane universe using tachyon field

2019 ◽  
Vol 28 (13) ◽  
pp. 1941010 ◽  
Author(s):  
Rikpratik Sengupta ◽  
Prasenjit Paul ◽  
Bikash Chandra Paul ◽  
Saibal Ray
Keyword(s):  
Gravitational Field ◽  
Cosmological Solution ◽  
Tachyon Field ◽  
Field Equations ◽  
Tachyonic Field ◽  
Bianchi I ◽  
Gravitational Field Equations ◽  
First Case ◽  
Cosmological Scenario ◽  
The Universe

Cosmological solution to the gravitational field equations in the generalized Randall–Sundrum model for an anisotropic brane with Bianchi-I geometry and perfect fluid as matter sources has been considered. The matter on the brane is described by a tachyonic field. The solution admits inflationary era and at a later epoch the anisotropy of the universe washes out. We obtain two classes of cosmological scenario: in the first case, universe evolves from singularity and in the second case, universe expands without singularity.

Sign in / Sign up

Export Citation Format

Share Document