double diffusive
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Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 98
Author(s):  
Xuejiao Chen ◽  
Yuanfei Li ◽  
Dandan Li

In this paper, we consider the Brinkman equations pipe flow, which includes the salinity and the temperature. Assuming that the fluid satisfies nonlinear boundary conditions at the finite end of the cylinder, using the symmetry of differential inequalities and the energy analysis methods, we establish the exponential decay estimates for homogeneous Brinkman equations. That is to prove that the solutions of the equation decay exponentially with the distance from the finite end of the cylinder. To make the estimate of decay explicit, the bound for the total energy is also derived.


2021 ◽  
Vol 933 ◽  
Author(s):  
Yantao Yang ◽  
Roberto Verzicco ◽  
Detlef Lohse ◽  
C.P. Caulfield

A sequence of two- and three-dimensional simulations are conducted for the double-diffusive convection (DDC) flows in the diffusive regime subjected to an imposed shear. For a wide range of control parameters, and for sufficiently strong perturbation of the conductive initial state, staircase-like structures spontaneously develop, with relatively well-mixed layers separated by sharp interfaces of enhanced scalar gradient. Such staircases appear to be robust even in the presence of strong shear over very long times, with early-time coarsening of the observed layers. For the same set of control parameters, different asymptotic layered states, with markedly different vertical scalar fluxes, can arise for different initial perturbation structures. The imposed shear significantly spatio-temporally modifies the vertical transport of the various scalars. The flux ratio $\gamma ^*$ (i.e. the ratio between the density fluxes due to the total salt flux and the total heat flux) is found, at steady state, to be essentially equal to the square root of the ratio of the salt diffusivity to the thermal diffusivity, consistent with the physical model proposed by Linden & Shirtcliffe (J. Fluid Mech., vol. 87, 1978, pp. 417–432) and the variational arguments presented by Stern (J. Fluid Mech., vol. 114, 1982, pp. 105–121) for unsheared double-diffusive convection.


Author(s):  
Jennifer A. MacKinnon ◽  
Matthew H. Alford ◽  
Leo Middleton ◽  
John Taylor ◽  
John B. Mickett ◽  
...  

Abstract Pacific Summer Water eddies and intrusions transport heat and salt from boundary regions into the western Arctic basin. Here we examine concurrent effects of lateral stirring and vertical mixing using microstructure data collected within a Pacific Summer Water intrusion with a length scale of ∼20 km. This intrusion was characterized by complex thermohaline structure in which warm Pacific Summer Water interleaved in alternating layers of O(1 m) thickness with cooler water, due to lateral stirring and intrusive processes. Along interfaces between warm/salty and cold/fresh water masses, the density ratio was favorable to double-diffusive processes. The rate of dissipation of turbulent kinetic energy (ε) was elevated along the interleaving surfaces, with values up to 3×10−8 W kg−1 compared to background ε of less than 10−9 W kg−1. Based on the distribution of ε as a function of density ratio Rρ , we conclude that double-diffusive convection is largely responsible for the elevated ε observed over the survey. The lateral processes that created the layered thermohaline structure resulted in vertical thermohaline gradients susceptible to double-diffusive convection, resulting in upward vertical heat fluxes. Bulk vertical heat fluxes above the intrusion are estimated in the range of 0.2-1 W m−2, with the localized flux above the uppermost warm layer elevated to 2- 10 W m−2. Lateral fluxes are much larger, estimated between 1000-5000 W m−2, and set an overall decay rate for the intrusion of 1-5 years.


Author(s):  
Safia Akram ◽  
Maria Athar ◽  
Khalid Saeed ◽  
Alia Razia ◽  
Taseer Muhammad ◽  
...  

The implications of double-diffusive convection and an inclined magnetic field on the peristaltic transport of a pseudoplastic nanofluid in an inclined asymmetric channel with slip boundaries were investigated in this research. The present problem is mathematically modeled using lubrication techniques, which results in highly nonlinear equations for the proposed problem that is solved using a numerical technique. The graphical findings show how temperature, pressure rise, concentration, pressure gradient, nanoparticle fraction, and stream functions affect key physical parameters of interest. It is revealed that the velocity value rises as the velocity slip parameter, temperature, and solutal Grashof number rise. Furthermore, increasing thermal slip, Dufour, Soret, Brownian motion, and thermophoresis factors increase the temperature profile. If [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] the viscous model of classical Newtonian fluid is a special case of the preceding model.


2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Prabhugouda Mallanagouda Patil ◽  
Madhavarao Kulkarni

AbstractThe present study focuses on double diffusive nonlinear (quadratic) mixed convective flow of nanoliquid about vertical wedge with nonlinear temperature-density-concentration variations. This study is found to be innovative and comprises the impacts of quadratic mixed convection, magnetohydrodynamics, diffusion of nanoparticles and liquid hydrogen flow around a wedge. Highly coupled nonlinear partial differential equations (NPDEs) and boundary constraints have been used to model the flow problem, which are then transformed into a dimensionless set of equations utilizing non-similar transformations. Further, a set of NPDEs would be linearized with the help of Quasilinearization technique, and then, the linear partial differential equations are transformed into a block tri-diagonal system through using implicit finite difference scheme, which is solved using Verga’s algorithm. The study findings were explored through graphs for the fluid velocity, temperature, concentration, nanoparticle volume fraction distributions and its corresponding gradients. One of the important results of this study is that the higher wedge angle values upsurge the friction between the particles of the fluid and the wedge surface. Rising Schmidt number declines the concentration distribution and enhances the magnitude of Sherwood number. Nanofluid’s temperature increases with varying applied magnetic field. The present study has notable applications in the designing and manufacturing of wedge-shaped materials in space aircrafts, construction of dams, thermal systems, oil and gas industries, etc.


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