Non-Darcian-Bènard Double Diffusive Magneto-Marangoni Convection in a Two Layer System with Constant Heat Source/Sink

The problem of non-Darcian-Bènard double diffusive magneto-Marangoni convection is considered in a horizontal infinite two layer system. The system consists of a two-component fluid layer placed above a porous layer, saturated with the same fluid with a constant heat sources/sink in both the layers, in the presence of a vertical magnetic field. The lower porous layer is bounded by rigid boundary, while the upper boundary of the fluid region is free with the presence of Marangoni effects. The system of ordinary differential equations obtained after normal mode analysis is solved in a closed form for the eigenvalue and the Thermal Marangoni Number (TMN) for two cases of Thermal Boundary Combinations (TBC); these are type (i) Adiabatic-Adiabatic and type (ii) Adiabatic-Isothermal. The corresponding two TMNs are obtained and the impacts of the porous parameter, solute Marangoni number, modified internal Rayleigh numbers, viscosity ratio, and the diffusivity ratios on the non-Darcian-Bènard double diffusive magneto - Marangoni convection are studied in detail.

Transient Marangoni convection induced by an isothermal sidewall of a rectangular liquid pool

Transient Marangoni convection induced by an isothermal sidewall of a rectangular pool under a zero-gravity condition is studied using scaling analysis. Scaling analysis shows that there exist a number of flow regimes in each evolution scenario, depending on the Marangoni number, the Prandtl number and the aspect ratio. In a typical evolution scenario, a horizontal surface flow and a vertical flow adjacent to the sidewall may appear. Additionally, a number of scaling laws of the velocity and thickness of transient Marangoni convection are obtained. Further, numerical simulation is performed for validation of the selected scaling laws. There exits good agreement between the numerical results and the scaling predictions.

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.

Combined effects of nonuniform temperature gradients and heat source on double diffusive Benard-Marangoni convection in a porous-fluid system in the presence of vertical magnetic field

The physical configuration of the problem is a porous-fluid layer which is horizontally unbounded, in the presence of uniform heat source/sink in the layers enclosed by adiabatic and isothermal boundaries. The problem of double diffusive Bènard-Marangoni convection in the presence of vertical magnetic field is investigated on this porous-fluid system for non-Darcian case and is subjected to uniform and nonuniform temperature gradients. The eigenvalue, thermal Marangoni number is obtained in the closed form for lower rigid and upper free with surface tension velocity boundary conditions. The influence of various parameters on the Marangoni number against thermal ratio is discussed. It is observed that the heat absorption in the fluid layer and the applied magnetic field play an important role in controlling Benard-Marangoni convection. The parameters which direct this convection are determined and the effect of porous parameter is relatively interesting.

Darcy-Benard double diffusive Marangoni convection in a composite layer system with constant heat source along with non uniform temperature gradients

The problem of Benard double diffusive Marangoni convection is investigated in a horizontally infinite composite layer system enclosed by adiabatic boundaries for Darcy model. This composite layer is subjected to three temperature gradients with constant heat sources in both the layers. The lower boundary of the porous region is rigid and upper boundary of the fluid region is free with Marangoni effects. The Eigenvalue problem of a system of ordinary differential equations is solved in closed form for the Thermal Marangoni number, which happens to be the Eigen value. The three different temperature profiles considered are linear, parabolic and inverted parabolic profiles with the corresponding thermal Marangoni numbers are obtained. The impact of the porous parameter, modified internal Rayleigh number, solute Marangoni number, solute diffusivity ratio and the diffusivity ratio on Darcy-Benard double diffusive Marangoni convection are investigated in detail.

Analysis of Buongiorno’s nanofluid model in marangoni convective flow with gyrotactic microorganism and activation energy

This communication is to analyze the Marangoni convection MHD flow of nanofluid. Marangoni convection is very useful physical phenomena in presence of microgravity conditions which is generated by gradient of surface tension at interface. We have also studied the swimming of migratory gyrotactic microorganisms in nanofluid. Flow is due to rotation of disk. Heat and mass transfer equations are examined in detail in the presence of heat source sink and Joule heating. Nonlinear mixed convection effect is inserted in momentum equation. Appropriate transformations are applied to find system of equation. HAM technique is used for convergence of equations. Radial and axial velocities, concentration, temperature, motile microorganism profile, Nusselt number and Sherwood number are sketched against important parameters. Marangoni ratio parameter and Marangoni number are increasing functions of axial and radial velocities. Temperature rises for Marangoni number and heat source sink parameter. Activation energy and chemical reaction rate parameter have opposite impact on concentration profile. Motile density profile decays via Peclet number and Schmidt number. Magnitude of Nusselt number enhances via Marangoni ratio parameter.

The Relative Contribution of Solutal Marangoni Convection to Thermal Marangoni Flow Instabilities in a Liquid Bridge of Smaller Aspect Ratios under Zero Gravity

The effect of solutal Marangoni convection on flow instabilities in the presence of thermal Marangoni convection in a Si-Ge liquid bridge with different aspect ratios As has been investigated by three-dimensional (3D) numerical simulations under zero gravity. We consider a half-zone model of a liquid bridge between a cold (top plane) and a hot (bottom plane) disks. The highest Si concentration is on the top of the liquid bridge. The aspect ratio (As) drastically affects the critical Marangoni numbers: the critical solutal Marangoni number (under small thermal Marangoni numbers (MaTAs≲1800)) has the same dependence on As as the critical thermal Marangoni number (under small solutal Marangoni numbers (400≲MaCAs≲800)), i.e., it decreases with increasing As. The azimuthal wavenumber of the traveling wave mode increases as decreasing As, i.e., larger azimuthal wavenumbers (m=6,7,11,12, and 13) appear for As=0.25, and only m=2 appears when As is one and larger. The oscillatory modes of the hydro waves have been extracted as the spatiotemporal structures by using dynamic mode decomposition (DMD). The present study suggests a proper parameter region of quiescent steady flow suitable for crystal growth for smaller aspect ratios of the liquid bridge.

The onset of Marangoni bio-thermal convection in a layer of fluid containing gyrotactic microorganisms

<abstract><p>The problem of the onset of Marangoni bio-thermal convection is investigated for a horizontal layer of fluid containing motile gyrotactic microorganisms. The fluid layer is assumed to rest on a rigid surface with fixed temperature and the top boundary of the layer is assumed to be a free non deformable surface. The resulting equations of the problem constitute an eigenvalue problem which is solved using the Chebyshev tau numerical method. The critical values of the thermal Marangoni number are calculated for several values of the bioconvection Péclet number, bioconvection Marangoni number, bioconvection Lewis number and gyrotaxis number. The results of this study showed that the existence of gyrotactic microorganisms increases the critical thermal Marangoni numbers. Moreover, the critical eigenvalues obtained were real-valued indicating that the mode of instability is via a stationary mode, however oscillatory mode is possible for some ranges of the parameters values.</p></abstract>

Characterization of Marangoni Forced Convection in Casson Nanoliquid Flow with Joule Heating and Irreversibility

The Marangoni forced convective inclined magnetohydrodynamic flow is examined. Marangoni forced convection depends on the differences in surface pressure computed by magnetic field, temperature, and concentration gradient. Casson nanoliquid flow by an infinite disk is considered. Viscous dissipation, heat flux, and Joule heating are addressed in energy expressions. Thermophoresis and Brownian motion are also examined. Entropy generation is computed. The physical characteristics of entropy optimization with Arrhenius activation energy are discussed. Nonlinear PDE’s are reduced to highly nonlinear ordinary systems with appropriate transformations. A nonlinear system is numerically computed by the NDSolve technique. The salient characteristics of velocity, temperature, concentration, entropy generation, and Bejan number are explained. The computational results of the heat-transfer rate and concentration gradient are examined through tables. Velocity and temperature have reverse effects for the higher approximation of the Marangoni number. Velocity is a decreasing function of the Casson fluid parameter. Temperature is enhanced for higher radiation during reverse hold for concentration against the Marangoni number. The Bejan number and entropy generation have similar effects for Casson fluid and radiation parameters. For a higher estimation of the Brinkman number, the entropy optimization is augmented.