Thermohaline staircase formation in the diffusive convection regime: a theory based upon stratified turbulence asymptotics

We describe a mechanism that leads to the spontaneous formation of a thermohaline staircase in the high-latitude oceans. Our analysis of this mechanism is based upon a model in which uniform gradients of temperature and salinity are assumed and is applied to a simplified mean-field model of stratified turbulence. Detailed analysis employs a parametrization of turbulent diapycnal diffusivities (Bouffard & Boegman, Dyn. Atmos. Oceans, vol. 61, 2013, pp. 14–34). This parametrization is apparently unique in that it distinguishes between the diapycnal diffusivities for heat and salt on the basis of their Prandtl (Schmidt) numbers. Our model predicts that the temperature and salinity profiles will be susceptible to linear instability if the buoyancy Reynolds number lies in the range 0.18–91, and a nonlinear mean-field model simulation demonstrates that it evolves into a well-defined thermohaline staircase that matches the characteristics of those found in the high-latitude oceans. The criterion for initial instability is furthermore shown to be consistent with the observed regional variability of staircase occurrence in the Arctic Ocean as determined by the most recent observational datasets.

Study on MHD Flow over a Stretching Surface with Convective Boundary Condition by Numerical Method

The thermal and mass diffusive MHD flow through a stretching sheet has been inspected in the presence of a chemically reactive solute under convective boundary conditions in the present paper. The non-linear PDEs of the system concerning the flow, temperature, and species are recasted into a set of non-linear ODEs using ST. The consequential system of the differential equations is numerically resolved by using an implicit FDS in combination with the QL technique. The velocity ratio factor plays an important role in reducing the thickness of the velocity boundary layer, whereas the presence of magnetic parameters decreases the thickness of the velocity boundary layer profile. The study reveals that the fluid moves away from the surface during injection, resulting in a fall of the velocity gradient, whereas the opposite effect is observed in suction. The thermal and concentration boundary layer thicknesses are influenced by non-dimensional numbers, namely Prandtl and Schmidt numbers. The reaction rate parameter acts as a decelerating agent, and it thins the solute boundary layer formed in the neighborhood of the sheet. An increase in the convective parameter leads to an increase in the plate surface temperature. The present results of the paper are compared with the existing one, and good agreement is found between them.

Critical Solutal Marangoni Number Correlation for Short-Scale Convective Instabilities in Drying Poly(vinyl acetate)-Methanol Thin Films

A new empiric correlation for the critical solutal Marangoni number as function of the Péclet and Schmidt numbers is proposed. It is based on previously published experimental flow field data in drying poly(vinyl acetate)-methanol films with an initial thickness in the range of – and an initial solvent load of to , as well as newly derived concentration profile measurements and 1D drying simulations. The analysis accounts for realistic transient material properties and describes the occurrence of short-scale convective Marangoni (in)stabilities during the entire drying process with an accuracy of 9%. In addition, the proposed correlation qualitatively follows trends known from theory. As convective Marangoni instabilities in drying polymer films may induce surface deformations, which persist in the dry film, the correlation may facilitate future process design for either thin films with uniform thickness or deliberate self-assembly.

Magneto-Bioconvection Flow of Williamson Nanofluid over an Inclined Plate with Gyrotactic Microorganisms and Entropy Generation

The fluid flow through inclined plates has several applications in magneto-aerodynamics, materials processing and magnetohydrodynamic propulsion thermo-fluid dynamics. Inspired by these applications, the rate of entropy production in a bio-convective flow of a magnetohydrodynamic Williamson nanoliquid over an inclined convectively heated stretchy plate with the influence of thermal radiation, porous materials and chemical reaction has been deliberated in this paper. The presence of microorganisms aids in stabilizing the suspended nanoparticles through a bioconvection process. Also, the thermal radiation assumed an optically thick limit approximation. With the help of similarity transformations, the coupled partial differential equations are converted to nonlinear ordinary differential equations and the resulting model is numerically tackled using the shooting method. The influences of the determining thermo-physical parameters on the flow field are incorporated and extensively discussed. The major relevant outcomes of the present analysis are that the upsurge in values of Schmidt number decays the mass transfer characteristics, but the converse trend is depicted for boost up values of the thermophoresis parameter. Enhancement in bioconvection Peclet and Schmidt numbers deteriorates the microorganism density characteristics. Further, the upsurge in the Williamson parameter declines the Bejan number and irreversibility ratio.

Optimal spacings for channels with Hagen-Poiseuille fluid-flow and mass transfer - the role of the Bejan number

This work is a continuation of the recent studies [1, 2], revealing that the unique form of the Bejan number is robust (unchangeable) and appears independently in all Hagen-Poiseuille fluid-flows with heat or mass transfer by convection. The other dimensionless groups, derived from the First law of thermodynamics (related to the convection heat or mass transfer), and named Bejan numbers are combinations of the unique Bejan number with Prandtl or Schmidt numbers, respectively, and ratios of geometrical parameters of the system. In this paper we continue developing this idea through presenting new examples of problems in the field of convection mass transfer in pure laminar duct flows.

A Note on Heat Transport with Aspect of Magnetic Dipole and Higher Order Chemical Process for Steady Micropolar Fluid

Heat transfer through non-uniform heat source/sink is the most significant aspect in view of many physical problems. Heat sink/source with heat transfer help to change the energy distribution in fluids, which consequently disturbs the particle deposition rate like as nuclear reactors, semiconductors and electronic devices. Further, also, the vital role of heat transfer is to enhance the thermal conductivity of micro sized solid particles in fluid. This study scrutinizes the heat transport of steady micropolar fluid via non-uniform heat sink/ source and mass transfer is scrutinized through higher order chemical reaction over a stretching surface with variable heat flux. Moreover, the velocity of micropolar fluid is studied by considering aspects of magnetic dipole and Newtonian heating; velocity slip conditions are also examined. The numerical results have been performed by using the well-known numerical shooting technique and comparison is performed with the Matlab built-in solver bvp4c. Geometrically explanation reveals the properties of numerous parameters that are the system parts. The observed outcomes show that the local skin-friction coefficient and Sherwood number values goes up with the increase of chemical reaction rate parameters and Schmidt numbers. Chemical reaction based parameters boosts up the rate of heat as well as mass transfer. The stress of wall couple increased by increasing the Schmidt and chemical parameters. Moreover, the plots of dimensionless parameters have been drawn, as well as some parameter results are tabulated.