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The influence of gravity on the Marangoni flow instability in half zone liquid bridges in the case of liquid metals is investigated by direct 3D and time‐dependent simulation of the problem. The computations are carried out for different heating conditions and environments (zero g conditions and on ground liquid zone heated from above or from below). The case of cylindrical shape (simplified model) and of melt/air interface deformed by the effect of gravity (real conditions) are considered. The comparison among these situations gives insight into the separate (gravity) effects of buoyancy forces and of the free surface deviation with respect to straight configuration. Body‐fitted curvilinear co‐ordinates are adopted to handle the non‐cylindrical problem. The liquid bridge exhibits different behaviours according to the allowed bridge shape. If the shape is forced to be cylindrical, the flow field is stabilized in the case of heating from above and destabilized if gravity is reversed. If the deformation is taken into account, gravity always stabilizes the Marangoni flow regardless of its direction (parallel or antiparallel to the axis) and the 3D flow structure is different according to the heating condition (from above or from below). In the latter case, the critical Marangoni number is larger and the critical wave number is smaller, compared with the opposite condition. In addition, for Pr=0.02 (Gallium), a surprising heretofore unseen behaviour arises. No steady bifurcation occurs and the flow becomes unstable directly to oscillatory disturbances. This phenomenon has never been reported before in the case of low Prandtl number liquids.

The influence of buoyancy forces on oscillatory Marangoni flow in liquid bridges of different aspect ratio is investigated by three‐dimensional, time‐dependent numerical solutions and by laboratory experiments using a microscale apparatus and a thermographic visualisation system. Liquid bridges heated from above and from below are investigated. The numerical and experimental results show that for each aspect ratio and for both the heating conditions the onset of the Marangoni oscillatory flow is characterized by the appearance of a standing wave regime; after a certain time, a second transition to a travelling wave regime occurs. The three‐dimensional flow organization at the onset of instability is different according to whether the bridge is heated from above or from below. When the liquid bridge is heated from below, the critical Marangoni number is larger, the critical wave number (m) is smaller and the standing wave regime is more stable, compared with the case of the bridge heated from above. For the critical azimuthal wave number, two correlation laws are found as a function of the geometrical aspect ratio A.

By solving a long-wave evolution model numerically for power-law fluids, the authors aim to investigate the hydrodynamic and thermal characteristics of thermocapillary flow in an evaporating thin liquid film of pseudoplastic fluid.

The flow reversal attributed to the thermocapillary action is manifestly discernible through the streamline plots.

The thermocapillary strength is closely related to the viscosity of the fluid, besides its surface tension. The thermocapillary flow prevails in both Newtonian and pseudoplastic fluids at a large Marangoni number and the thermocapillary effect is more significant in the former. The overestimate in the Newtonian fluid is larger than that in the pseudoplastic fluid, owing to the shear-thinning characteristics of the latter.

This study provides insights into the essential attributes of the underlying flow characteristics in affecting the thermal behavior of thermocapillary convection in an evaporating thin liquid film of the shear-thinning fluids.

The main purpose of this paper is to conduct on three-dimensional buoyancy and thermocapillary convection in an enclosure. Entropy generation is obtained from the calculated values of velocities and temperatures.

As numerical method, the vorticity-vector potential formalism allows, in a three-dimensional configuration, the elimination of the pressure, which is a delicate term to treat. The control volume finite difference method is used to discretize equations. The central-difference scheme for treating convective terms and the fully implicit procedure to discretize the temporal derivatives are retained. The grid is uniform in all directions with additional nodes on boundaries. The successive relaxation iterating scheme is used to solve the resulting non-linear algebraic equations.

Results are presented via entropy generation due to heat transfer, entropy generation due to fluid friction and total entropy generation. It is found that Marangoni number becomes more effective parameter on total entropy generation for lower values of Rayleigh numbers.

In any thermal system under buoyancy induced and thermocapillary flow.

It is believed that this is the first paper on three-dimensional solution of entropy generation in a cubical cavity under thermocapillary buoyancy flow.

A computational model is developed to describe convection in volatile liquids evaporating in capillary tubes. Experimental work has demonstrated the existence of such convective structures. The correlation between this convection and the phase change process has been experimentally established. Temperature distribution on the liquid‐vapour interface is considered in order to characterise the minimum of radial temperature gradient required to initiate and orientate Marangoni convection. Direct numerical simulation using finite volume approximation is used to investigate the heat and mass transfer in the liquid phase. The case of a capillary tube filled with a volatile liquid is investigated for various Marangoni numbers, to characterise heat and mass transfers under conditions close to realistic operating parameters. The simulation shows that a minimum irregularity in evaporative flux along the liquid‐vapour interface is necessary to trigger thermocapillary convection. The enhancement of heat and mass transfer by Marangoni convection is also investigated.

Analytical and numerical studies are conducted for two‐dimensional steady‐state coupled Marangoni and buoyancy convection of a non‐Newtonian power law fluid confined in a rectangular horizontal shallow cavity subjected to a horizontal temperature gradient between the two short vertical rigid sides, while the upper free surface and the lower rigid one are insulated. The results obtained by combining the two basic mechanisms (thermocapillarity and buoyancy) depend on whether their effects are aiding or opposite. The effect of the non‐Newtonian behavior on the fluid flow, the temperature field, and the heat transfer is studied. The parallel flow is obtained in some particular situations for which a good agreement is observed between the analytical results based on the parallel flow assumption and those corresponding to the numerical simulations.

The purpose of this study is to study the impacts of exponential space-dependent heat source (ESHS) and thermal radiation in Marangoni convective flow of Cross fluid. The passively controlled model is developed to exhibit the nanoparticles’ concentration on the surface.

The resulting problem under consideration is tackled by using the shooting approach.

Temperature field augments with enhancement of the thermophoretic, exponential-based space heat source (ESHS) and radiation parameters, whereas it decays with the increase of the Marangoni ratio parameter.

To the best of the authors’ knowledge, no such analysis has yet been reported.

The purpose of this paper is to conduct a numerical study of the effect of magnetic field on thermocapillary convection of a two layered system of Newtonian fluids, confined in a rectangular cavity. The flow within the cavity is subject to the horizontal temperature gradient. Attention is focused on how the heat transfer and flow properties are affected subject to the applied magnetic field, particularly in the lower layer. For this purpose, the fluid combinations of di‐Boron Trioxide (B₂O₃) over Gallium Arsenide GaAs (III‐V), and Silicon oil 10 cSt over Fluorinert FC 70 are considered in the present study.

The non‐linear two‐dimensional vorticity transport equations along with the energy equations are solved for the two liquid layers using the Alternate Direct Implicit method, whereas the elliptic partial differential equations of the stream function are solved using the Successive Over Relaxation method.

It was found that despite the significant reduction of flow in the two layers, the number of cells in the lower layer increases with the increase in Hartmann number Ha. However, the flow intensity decreases with the increase in Hartmann number. This decrease is more pronounced in the lower layer, as compared to the upper layer. The numerical scheme employed for the solution is found to be in good agreement with the previous work.

The analysis is made for two layer liquid system with undeformable interface and free surface. The detailed study of the effect of magnetic field on oscillatory Marangoni convection in two layer system with deformable interface is left for future work.

The approach is useful in optimizing the flow properties of the fluids in a two layer system, particularly the lower layer, to yield the results of potential practical interest.

The results of the study may be of some interest to researchers in the field of semiconductor technology, as the melt control is intensively investigated for the development in the manufacture of defect‐free semiconductors and crystals.

Analytical and numerical studies are conducted for two‐dimensional steady‐state Marangoni convection of a non‐Newtonian power law fluid confined in a rectangular horizontal shallow cavity subjected to a horizontal temperature gradient between the two short vertical rigid sides, while the upper free surface and the lower rigid one are insulated. The effect of the non‐Newtonian behavior on the hydrodynamic stability, the fluid flow, the temperature field, and the heat transfer is studied. The parallel flow is obtained in some particular situations for which a good agreement is observed between the analytical results based on the parallel flow assumption and those corresponding to the numerical simulations.

A linear stability analysis has been employed to investigate the thermocapillary instability occurring in a nonisothermal liquid bridge. The steady, axisymmetric basic state was solved numerically using a finite difference method. A mixed finite difference‐spectral method, combining the advantages of both methods, was then used to reduce the linear disturbance equations to an eigenvalue problem. The critical Marangoni numbers for axisymmetric disturbances are predicted for small Prandtl numbers and various aspect ratios. The effect of surface heat transfer is also investigated. The present results are compared with energy‐theory results and with the results of other experiments.