scholarly journals Comments on "Significance of improved Fourier-Fick laws in non-linear convective micropolar material stratified flow with variable properties"

2020 ◽  
pp. 353-353
Author(s):  
M.M. Awad
Keyword(s):  
Stratified Flow ◽  
Variable Properties ◽  
Non Linear ◽  
Micropolar Material

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scholarly journals Significance of improved Fourier-Fick laws in non-linear convective micropolar material stratified flow with variable properties

2019 ◽  
Vol 23 (6 Part B) ◽  
pp. 3809-3815 ◽  
Author(s):  
Muhammad Waqas ◽  
Muhammad Khan ◽  
Shahid Farooq ◽  
Tasawar Hayat ◽  
Ahmed Al-Saedi
Keyword(s):  
Material Flow ◽  
Skin Friction Coefficient ◽  
Series Solutions ◽  
Variable Properties ◽  
Temperature Dependent ◽  
Double Stratification ◽  
Temperature Dependent Conductivity ◽  
Research Article ◽  
Non Linear ◽  
Micropolar Material

Present research article describes the effectiveness of improved Fourier-Fick fluxes and temperature-dependent conductivity on the 2-D, incompressible steady micropolar material flow over a stretchable surface. Non-linear mixed convection, double stratification and heat generation aspects are considered. The considered flow non-linear PDE are converted to ODE via appropriate transformations. Through implementation of homotopy method the obtain system is solved for series solutions. The effects of pertinent parameters are discussed through graphical sketch. Skin friction coefficient (drag force) is calculated. Main findings are pointed out.

Application of non-Fourier heat flux theory in thermally stratified flow of second grade liquid with variable properties

2017 ◽  
Vol 55 (2) ◽  
pp. 230-241 ◽  
Author(s):  
T. Hayat ◽  
M. Zubair ◽  
M. Waqas ◽  
A. Alsaedi ◽  
M. Ayub
Keyword(s):  
Heat Flux ◽  
Stratified Flow ◽  
Second Grade ◽  
Variable Properties

Two Equation Two-Fluid Model Analysis for Stratified Flow Under Kinematic and Dynamic Instabilities

2013 ◽  
Author(s):  
Martin A. Lopez de Bertodano ◽  
William D. Fullmer
Keyword(s):  
Flow Regime ◽  
Linear Stability ◽  
Fluid Model ◽  
Stratified Flow ◽  
Equation Model ◽  
Gas Velocity ◽  
Hydrostatic Force ◽  
Non Linear ◽  
Two Fluid Model ◽  
Two Fluid

The unstable one-dimensional incompressible two-fluid model including a hydrostatic force is reduced to a two equation model in terms of the liquid volume fraction and the liquid velocity. For small density ratios the model may be simplified to a formulation that is equivalent tothe Shallow Water Theory (SWT) equations [Whitham, 1975] with a source term corresponding to the two-fluid model constitutive relations for wall and interfacial shear and to a void gradient term that contains the Kelvin-Helmholtz mechanism. Linear stability of the SWT equations shows that the model is made well-posed stable by the hydrostatic force. However, unlike the SWT equations, the two equation two-fluid model is only conditionally stable. As the gas velocity increases the model becomes unstable once the kinematic instability occurs, i.e., the Viscous Kelvin-Helmholtz (VKH) instability. When the gas velocity is increased further the model becomes dynamically unstable, i.e., it reaches the Inviscid Kelvin-Helmholtz (IKH) instability limit. Beyond the IKH limit the model becomes ill-posed and requires higher order modelling, e.g. surface tension. Simple analytic expressions for the two instabilities are obtained because of the simplified mathematics of the two equation model. Furthermore, the wave “sheltering” effect, which allows more accurate predictions of the flow regime transition, may be easily incorporated into the analysis. The theory is validated with the new HAWAC flow regime map [Vallee et al., 2010]. The two equation two-fluid model is consistent with all previous results of two-fluid model linear stability for stratified flow and, since it is a special case of SWT, it is amenable to non-linear stability analysis and a very broad body of mathematics literature on non-linear kinematic waves, e.g., Whitham (1974) is now directly applicable when the model is not IKH unstable.

B. The Non-Linear Calculations for Pulsating Stars

1967 ◽  
Vol 28 ◽  
pp. 105-176
Author(s):  
Robert F. Christy
Keyword(s):  
Major Part ◽  
Afternoon Session ◽  
Discussion Session ◽  
Pulsating Stars ◽  
Fourth Symposium ◽  
Non Linear ◽  
Considerable Discussion ◽  
Informal Approach ◽  
Preceding Session

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)

A decomposition method in non-linear programmm

Optimization ◽  
1975 ◽  
Vol 6 (4) ◽  
pp. 549-559
Author(s):  
L. Gerencsér
Keyword(s):  
Decomposition Method ◽  
Non Linear
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